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ELECTRONS IN ATOMS
Wave description of light
Electromagnetic spectrum - made of electromagnetic radiation (forms of energy that exhibit wavelike behavior as they travel through space)
Electromagnetic waves - combination of electrical and magnetic fields which travel at the speed of light
c = 300 x 108 msec
Wavelength λ (lambda) ndash usually measured in
nm or Aringngstroms (Aring)
Relative sizes of wavelengths
FrequencyFrequency ν (Greek letter nu) (or f) ndash
units are usually cyclessec sec ndash1 or Hertz (Hz)
c = λ ν = 30 x 108 msec
wwwatmoswashingtonedu~hakim301handoutshtml
The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal The number of electrons and theirenergies dependson the brightnessof the incidentlight
httpwwwastrovirginiaeduclassoconnellastr30imphotoelectric-effect-2jpg
Max Planck (1900)
He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant
6626 x 10-34 Jmiddots
E = h ν
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Wave description of light
Electromagnetic spectrum - made of electromagnetic radiation (forms of energy that exhibit wavelike behavior as they travel through space)
Electromagnetic waves - combination of electrical and magnetic fields which travel at the speed of light
c = 300 x 108 msec
Wavelength λ (lambda) ndash usually measured in
nm or Aringngstroms (Aring)
Relative sizes of wavelengths
FrequencyFrequency ν (Greek letter nu) (or f) ndash
units are usually cyclessec sec ndash1 or Hertz (Hz)
c = λ ν = 30 x 108 msec
wwwatmoswashingtonedu~hakim301handoutshtml
The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal The number of electrons and theirenergies dependson the brightnessof the incidentlight
httpwwwastrovirginiaeduclassoconnellastr30imphotoelectric-effect-2jpg
Max Planck (1900)
He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant
6626 x 10-34 Jmiddots
E = h ν
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Wavelength λ (lambda) ndash usually measured in
nm or Aringngstroms (Aring)
Relative sizes of wavelengths
FrequencyFrequency ν (Greek letter nu) (or f) ndash
units are usually cyclessec sec ndash1 or Hertz (Hz)
c = λ ν = 30 x 108 msec
wwwatmoswashingtonedu~hakim301handoutshtml
The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal The number of electrons and theirenergies dependson the brightnessof the incidentlight
httpwwwastrovirginiaeduclassoconnellastr30imphotoelectric-effect-2jpg
Max Planck (1900)
He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant
6626 x 10-34 Jmiddots
E = h ν
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Relative sizes of wavelengths
FrequencyFrequency ν (Greek letter nu) (or f) ndash
units are usually cyclessec sec ndash1 or Hertz (Hz)
c = λ ν = 30 x 108 msec
wwwatmoswashingtonedu~hakim301handoutshtml
The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal The number of electrons and theirenergies dependson the brightnessof the incidentlight
httpwwwastrovirginiaeduclassoconnellastr30imphotoelectric-effect-2jpg
Max Planck (1900)
He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant
6626 x 10-34 Jmiddots
E = h ν
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
FrequencyFrequency ν (Greek letter nu) (or f) ndash
units are usually cyclessec sec ndash1 or Hertz (Hz)
c = λ ν = 30 x 108 msec
wwwatmoswashingtonedu~hakim301handoutshtml
The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal The number of electrons and theirenergies dependson the brightnessof the incidentlight
httpwwwastrovirginiaeduclassoconnellastr30imphotoelectric-effect-2jpg
Max Planck (1900)
He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant
6626 x 10-34 Jmiddots
E = h ν
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
c = λ ν = 30 x 108 msec
wwwatmoswashingtonedu~hakim301handoutshtml
The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal The number of electrons and theirenergies dependson the brightnessof the incidentlight
httpwwwastrovirginiaeduclassoconnellastr30imphotoelectric-effect-2jpg
Max Planck (1900)
He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant
6626 x 10-34 Jmiddots
E = h ν
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal The number of electrons and theirenergies dependson the brightnessof the incidentlight
httpwwwastrovirginiaeduclassoconnellastr30imphotoelectric-effect-2jpg
Max Planck (1900)
He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant
6626 x 10-34 Jmiddots
E = h ν
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Max Planck (1900)
He suggested that the object emits energy in small specific amounts called quanta A quantum is the minimum quantity of energy that can be lost or gained by an atom He proposed E = h ν where E = energy in Joules ν = frequency and h = Planckrsquos constant
6626 x 10-34 Jmiddots
E = h ν
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
What is a Joule
James Prescott Joule
A Joule is the derived unit of energy in the SI system It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter
I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x
meter=
kgmiddot ms2 m = kgm2s2
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Einstein and wave-particle duality (1905)
abyssuoregonedu~jsimageswave_particlegif
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Light ndash particle and waveEach particle of lightcarries a quantum ofenergy which Einsteincalled photons A photon isa particle of
electromagneticradiation having zero
massand carrying a quantum ofenergy
For an electron to be ejected from the surface of a metal the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Spectroscopy
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
The Hydrogen-atom Bright Line-Emission Spectrum
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state it emits aphoton of radiation
ΔEphoton = E2-E1
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Bohr (Niels) Model of the Atom - 1913 The allowed
orbits have specific energies given by a simple formula En = (-RH) n = 1234
RH is the Rydberg constant
218 x 10-18 J
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Evidence for Electrons in Fixed-Energy Levels
The collection of narrow bands of light energy is referred to as an emission line spectrum and the individual bands of light are called spectral lines
The concept of electron energy levels is supported by spectral lines
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Combining equationsGiven E = h ν and ΔE = E2-E1
combining them results in
ν = ΔE = ( RH) (1 - 1 )
h h n2i n2
f
Further simplification
ΔE = ( RH) (1 - 1 )
n2i n2
f
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Bohr Model of the atom Electrons in hydrogen atoms exist in
only specified energy states Electrons in hydrogen atoms can absorb
only certain specific amounts of energy and no others
When the excited electrons in a hydrogen atom lose energy they lose only specific amounts of energy as photons
Different photons produce different color lines as seen in a bright line-emission spectrum
The main problem was that this explanation could not explain the behavior of any other element besides hydrogen
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
What led to quantum theory
The visible bands in aspectra are called theBalmer series The UVand IR lines are calledLyman and Paschenseries respectivelyScientists expected tosee a continuousspectrumThis observation of thehydrogen atom led toquantum theory
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
If electrons behave as both particles
and waves where are they located in
an atom
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Heisenberg Uncertainty Principle (1927)
It is impossible to determine simultaneously both
the position and velocity of an electron or any
other particle (Δp) (Δ x) = h (Planckrsquos constant)
Δp = uncertainty in momentumΔx = uncertainty in position
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
The Quantum Model of the Atom
1924 Louis de Broglie
Electrons should beconsidered as wavesconfined to the spacearound the nucleus
httpyoutubecomwatchv=x_tNzeouHC4Bohr applethttpwwwcoloradoeduphysics2000quantumzonebohrhtml
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Derivation of the de Broglie wavelength equation
Einstein PlanckE = mc2 E = h νTherefore mc2 = h ν [Substitute v (any velocity) for c]
mv2 = h ν[rearrange and substitute v for c in c = λν then solve for ν = v ]
λ
mv2 = hv λ
Substitute rearrange solve for λ = hv and simplify even further mv2
λ = h This is the de Broglie wavelength
mv equation
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Germer and DavissonDe Brogliersquos equation was applicable to
anyobject not just atoms The wave
propertiesof electrons were demonstrated in 1927
by Germer and Davisson (US) usingdiffraction by crystals
This technique is used today in electron microscopy
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Erwin Schroumldinger and thewave mechanical model
(Ψ + Ψ + Ψ ) + 8π2m (E-V) Ψ = 0 x2 y2 z2 h2
Ψ(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx y and z are the coordinates in space where the equation is solved
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved These regions of space arecalled orbitals
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals There are4 quantum numbers the first three of whichresult from the solutions to Schroumldingerrsquos waveequation
Principal quantum number (n) ndash the main energylevel occupied by the electron
n= 1234 The total number of orbitals within a given shell isequal to n2 The total number of electrons within agiven shell is equal to 2n2
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Orbital (or azimuthal) quantum number (l) or angular momentum
quantum numberValues include l = 0 up to and including n-1The letter designations originally stood for
sharpprincipal diffuse and fundamental These
words were used to describe different series of spectral
linesemitted by the elements
Orbital quantum number
Letter designation
Number of orbitals
Number of electrons per sublevel
0 s 1 2
1 p 3 6
2 d 5 10
3 f 7 14
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Magnetic and spin quantum numbers
Magnetic quantum number (ml) ndash indicates the
orientation of an orbital around the nucleusValues range from ndashl to +l (defines how
many ofeach type of orbital exists) Spin quantum number (ms) ndash indicates
the twopossible spin states of electrons in orbitals Values are either + frac12 or ndash frac12
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Principal quantum number
Orbital quantum number
Magnetic quantum number
Spin quantum numbersEither clockwise (+ frac12) or counterclockwise (- frac12)
n = 1 l = 0 (s) ml = 0 + frac12 ndash frac12
n = 2 l = 0 (s) l = 1 (p)
ml = 0ml = -1 0 +1
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 3 l = 0 (s) l = 1 (p)l = 2 (d)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
n = 4 l = 0 (s) l = 1 (p)l = 2 (d)l = 3 (f)
ml = 0ml = -1 0 +1ml = -2 -1 0 +1 +2ml = -3 -2 -1 0 +1 +2 +3
+ frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12+ frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12 + frac12 ndash frac12
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
s orbital
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
p orbitals
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
d orbital
s
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
f orbitals
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Electron configuration notation Long hand configuration (always
start with 1s) Short hand or noble gas
configuration (use the noble gas immediately preceding the element in question put its symbol in brackets [ ] and then write out the outer shell configuration
Orbital diagramnotation configuration
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Electron configurations- rules
Aufbau principle
An electron occupies thelowest energyorbital that canreceive it
Diagonal Rule
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Ord
er
of
orb
ital fi
llin
g
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Energy in orbital filling
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Hundrsquos Rule orbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron
andall electrons in singly occupied orbitalsmust have the samespin
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Pauli Exclusion principle
no two electrons in the same atomhave the same set of four
quantumnumbers The first three may bethe same but the spin must beopposite
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Order of orbital filling
httpintrochemokstateeduWorkshopFolderElectronconfnewhtml
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Example 1Boron ndash atomic number 5 Longhand 1s22s22p1
Shorthand [He]2s22p1
Orbital diagram
1s 2s 2p
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Example 2Polonium ndash atomic number 84Longhand
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4
Shorthand [Xe] 6s24f145d106p4
Orbital diagram
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Exceptions to the Aufbau principle
For Chromium (Cr) we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d4 but it is actually --gt1s2 2s2 2p6 3s2 3p6 4s13d5
For Copper (Cu)we would predict 1s2 2s2 2p6 3s2 3p6 4s2
3d9 but it is actually --gt 1s2 2s2 2p6 3s2 3p6 4s1
3d10
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Degenerate orbitalsa group of orbitals with the same
energyExamples Chromium (24) CrShorthand [Ar]4s13d5 NOT [Ar]4s23d4
Mo and W are similar
Copper (29) CuShorthand [Ar]4s13d10 NOT [Ar]4s23d9
Ag and Au are similar
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Additional Definitions
Paramagnetic An atom has unpaired
electrons in its electron configuration
(Look at its orbital diagram)
Diamagnetic All electrons in an atom
are paired (Look at its orbital diagram)
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6
Ion Configurations
Electrons will be added to or taken away from
orbitals in the following order s p d f (ie the ldquoouterrdquo or ldquovalencerdquo shell first)
ExamplesCl- 1s22s22p63s23p5 for Chlorine becomes
1s22s22p63s23p6
Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6