ElectronicStructureof Atoms
Unit 7Electronic Structure
of Atoms
CHM 1045: General Chemistry and Qualitative Analysis
Dr. Jorge L. AlonsoMiami-Dade College –
Kendall CampusMiami, FL
Textbook Reference:
•Module #9
ElectronicStructureof Atoms
Atoms and Electromagnetic RadiationAtoms absorb and emit energy, often in the form of electromagnetic radiation
(visible light, microwaves, radio & TV waves, u.v., infrared,etc)
{Fireworks}
ElectronicStructureof Atoms
The Nature of Light Energy(1) White Light is not white,
VIB G.Y O RSpectroscope
ed
range
ellow
reen
lue
iolet
ndigo
(3) Light does not travel in truly straight lines, it travels in waves
(2) Light is electrical and magnetic (electromagnetic)
it is colored: the Spectrum:
{3D-Wave}
ElectronicStructureof Atoms
Light Energy as Waves: two important characteristics
1. wavelength (): the distance (m) between corresponding points on adjacent waves
For waves traveling at the same velocity, the longer the wavelength,
the smaller the frequency
Knowing and , you calculate the speed of light !
= high
= low
1
(c)constant
c (1/sec) (m)
2. frequency () or (f ): the number of waves passing a given point per unit of time (1/s = s1-)
short
long
Speed (c) = wave length (λ) x frequency ()m/sec = m x 1/sec
SPEED = DISTANCE x PER UNIT TIME
ElectronicStructureof Atoms
Electromagnetic RadiationA form of energy characterized by waves (or pulses) of
varying frequencies ( and wavelengths ().
{Wavelength of v. l.}
c
c
{3D-Wave}
{*Light Waves}
ElectronicStructureof Atoms
Electromagnetic Radiation• Speed of Light: All
electromagnetic radiation travels at the same velocity (c), 3.00 108 m/s.
Einstein’s Theory of Special Relativity: Energy and mass are different forms of the same thing
mc2
Frequency (f )
1 α
c
Problem: What is the wavelength of a photon of light that has a frequency of 3.8 x 109 s-1 ?
c
c
1-9
-18
s 10 x 3.8
s m 10 x 00.3 = 7.89x10-2 m
ElectronicStructureof Atoms
The Nature of Energy:Discrete vs. ContinuousDigital:
0110100101001Analog
Waves:Quanta (Photon):
Eggs:
Water:
particles
ElectronicStructureof Atoms
{Photoelectric Effect}
Energy as a Particle (Photon, Quanta)
When light energy shines on a metal, an electron current is generated.
Light is behaving as a particle (photon)
that knocks-off valence electrons from the metal.
waves
particles
Light Energy
ElectronicStructureof Atoms
Energy from electrons comes in discrete quantities (bundles) that are whole number multiples of h
• The wave nature of light does not explain how an object can glow when its temperature increases.
{Metals & EM Radiation}
Planck concluded that energy (E) is proportional to frequency
where h is Planck’s constant, 6.63 10−34 J-s.
• Max Planck explained it by assuming that energy comes in packets called quanta (energy bundle, photon). Max Planck (1848-1947)
hEFor any particular frequency () there is a particular bundle of Energy (E) that exists as a discrete quantity (quanta) that is a multiple of Planck’s constant (h).
Energy as a Particle (Photon, Quanta)
1
2
ElectronicStructureof Atoms
The Nature of Energy Since c = then
c
h
Problem: What is the wavelength (in Å) of a ray whose energy is 6.16 x 10-14 erg? {Note: Modules use erg =10-7 Joule}
c
h E
Therefore, if one knows the wavelength of light, one can calculate the energy in
one photon, or packet, of that light.
ElectronicStructureof Atoms
The Nature of EnergyE = h
c
h
Problem: What is the wavelength (in Å) of a ray whose energy is 6.16 x 10-21 Joules? {Note: Modules use erg =10-7 Joule}
E
ch
Joules
m21-
834-
10 x 16.6
sec/10 x 0.3 Joules.sec10 x 63.6
m-510 x 3.23
m-510 x 3.23 Å? Å10 x 23.310
Å1 510-
m
ElectronicStructureof Atoms
ElectronicStructureof Atoms
c =
c
h h E
c
(1) Waves
(2) Particle (Photon, Quanta)
Energy as……
ΔE =h
mc2
(3) Matter
E
ElectronicStructureof Atoms
The Wave-Particle Duality of Matter
• Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties.
=h
mv
(where h is Planck’s constant, 6.63 10−34 J-s, and v is velocity of light)
{ElectonWaves}• Electromagnetic radiation can behave as a particle or as wave phenomena
• He demonstrated that the relationship between mass (m) and wavelength () was:
velocity (v) ∝
1 m
= eq given
ElectronicStructureof Atoms
The Wave Nature of MatterProblem: An electron has a mass of 9.06 x 10-25 kg and
is traveling at the speed of light. Calculate its wavelength?
=h
mvm x102.44
m/s)10 x (3.00 x ) kg 10 x 9.06(
)/10 x 63.6( 18-825-
-34
sJ
J = Joule = kg.m2
Problem: What is the wavelength of a 70.0 kg skier traveling down a mountain at 15.0 m/s?
=h
mvm x10 6.31
m/s) (15.0 x ) 0.70(
)/10 x 63.6( 37--34
kg
sJ
ElectronicStructureof Atoms
The Nature of EnergyWhite Light’s Continuous Spectrum:
VIB G.Y O R
ElectronicStructureof Atoms
{Flame Tests.Li,Na,K} {Na,B} {AtomicSpectra}
Substances both absorb and emit only certain Discrete Spectra
The Nature of Energy
ElectronicStructureof Atoms
• Niels Bohr adopted Planck’s assumption and explained atomic phenomena in this way:
1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies, frequencies and wavelengths, because E=h=h c/λ).
3. Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by
E = h
2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.
The Bohr “Planetary” Model of the Atom (1913)
1st EL f = 4
2nd EL f = 5
ElectronicStructureof Atoms
The Bohr Model of the Atom
The larger the fall the greater the energy{ExcitedElectrons*}
Which series releases most energy?
ElectronicStructureof Atoms
The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the
RH ( )1nf
2
1ni
2-
where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron. Z is the atomic number
1
Rydberg formula for hydrogen (1885)
Rydberg formula for hydrogen-like elements (He+, Li 2+, Be3+ etc., )
1
Atomic Spectra & Bohr Atom
ElectronicStructureof Atoms
if
-18-18
E E 10 x 2.180
- 10 x 2.180
E
2
i
2
f n
J
n
J
E = RH ( )1nf
2
1ni
2-
where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.
10 x 2.180
E-18
n 2n
Joule
= eq given
Since energy and wavelength are mathematically related, the Rydberg Equation can also be expressed in terms of energy:
The energy possessed by an electron at a particular energy level (En) can be expressed as:
Atomic Spectra & Bohr Atom
= ( )RH
nf2
RH
ni2
-
1
ElectronicStructureof Atoms
Atomic Spectra and the Bohr AtomProblem: How much energy (J) is liberated when an
electron changes from n = 4 to n = 2? What is the wavelength (m) of the light emitted?
E
ch
J10x 4088.0
s/m10x 0.3 J.s10x 63.6
18-
834-
c
c
h E
E E E if
2
-18
2
-18 10 x 2.180 -
10 x 2.180
if n
J
n
J
c
h
2
i
-18
2
f
-18
4
J10x 2.180 -
2
J10x 2.180
Jx -18-18-18 10 4088.0 J) 10 x (0.1362- J) 10 x (0.545 E
To convert energy to wavelength, we must employ the equations:
m10x 4.865 -7
ElectronicStructureof Atoms
Atomic Spectra and the Bohr Atom
m10x 4.865 -7
Notice that the wavelength calculated from the Rydberg equation matches the wavelength of the green colored line in the H spectrum.
J10 x 4088.0 E -18
ElectronicStructureof Atoms
2006 (B)
Ele 1
Ele 2
ElectronicStructureof Atoms
Heisenberg’s Uncertainty Principle• Heisenberg showed that the more
precisely the momentum of a particle is known, the less precisely is its position known:
• In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!
(x) (mv) h4
ElectronicStructureof Atoms
Quantum Model of the Atom• Max Planck (energy quanta, Planck’s constant)• Albert Einstein (energy and frequency) • Niels Bohr (electrons and Spectra) • Louis de Broglie (particle-wave duality of matter)• Werner Heisenberg (electron uncertainty)• Erwin Schrödinger (probability wave function, the four
quantum numbers)• Jörge L. Alônsø (diagrammatic quantum mechanical
atomic model)
Solvay Conference in Brussels 1911
Prof. Alonso
ElectronicStructureof Atoms
Energy Levels =
1, 2, 3, etc
Sublevel Orbital
types = s, p, d, f
Orbital cloud orientation (x, y, z, etc)
Electron pair spin in Orbital cloud (2e- ea)
1s
2s 2px
2py
2pz
3py
3px
3pz
3s
3dxy3dxz
3dyz
3dx2
y2
3dx2
1
2
3 4
ElectronicStructureof Atoms
Energy Levels =
1, 2, 3, etc
Sublevel Orbital
types = s, p, d, f
Orbital cloud orientation (x, y, z, etc)
Electron pair spin in Orbital cloud (2e- ea)
1s
2s 2px
2py
2pz
3py
3px
3pz
3s
3dxy3dxz
3dyz
3dx2
y2
3dx2
1
2
3 4
ElectronicStructureof Atoms
Quantum Numbers
• Describe the location of electrons within atoms.
• There are four quantum numbers: Principal = describes the energy level (1,2,3,etc)Azimuthal = energy sublevel, orbital type (s2, p6,
d10, f14)Magnetic = orbital orientation or cloud (2
electrons on each cloud) Example: three p clouds: px, py, pz
Spin = which way the electron is spinning (↑↓)
ElectronicStructureof Atoms
Electron Configuration, Orbital Notation and Quantum Numbers
1s2 2s2 2p6 3s23p63d10 4s24p64d104f14
Principal (n)= energy level Azimuzal () = sublevel orbital type
Magnetic (ml) = orbital cloud orientation (2e-
per orbital)
Spin (ms) = electron + or -
ElectronicStructureof Atoms
Electron ConfigurationTwo issues:
(1)Arrangement of electrons within an atom
1s2 2s2 2p6 3s23p63d10 4s24p64d104f14
(2) Order in which electrons fill the orbitals
1s22s22p63s23p64s23d104p65s24d105p66s24f14
Aufbau Process: Using Periodic Table Sub-blocks:
ElectronicStructureof Atoms
Schrödinger (1926)Bohr (1913)
Historic Development of Atomic Theory
ElectronicStructureof Atoms
The Schrödinger Equation
• is the imaginary unit, (complex number whose square is a negative real
number)
• is time, • is the partial derivative with respect to t, • is the reduced Planck's constant (Planck's constant divided by 2π),
• ψ(t) is the wave function,
• is the Hamiltonian (a self-adjoint operator acting on the state space).
ψ(t)
i
t
ElectronicStructureof Atoms
Quantum Mechanics• Developed by Erwin Schrödinger, it
is a mathematical model incorporating both the wave & particle nature of electrons.
• The wave function is designated with a lower case Greek psi ().
• The square of the wave function, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.
{QuantumAtom}
ElectronicStructureof Atoms
• Solving the wave equation gives a set of wave functions , or orbitals, and their corresponding energies.
• Each orbital describes a spatial distribution of electron density.
• An orbital is described by a set of three quantum numbers.
The Schrödinger Equation
ψ(t )
ElectronicStructureof Atoms
Principal Quantum Number, n
• The principal quantum number, n, describes the energy level on which the orbital resides.
• The values of n are integers ≥ 0.
1 2 3
ElectronicStructureof Atoms
Azimuthal Quantum Number,
• This quantum number defines the shape of the orbital.• Allowed values of are integers ranging from 0 to n − 1.• We also use letter designations:
Value of 0 1 2 3
Type of orbital s p d f
= 0 = 1 = 2 = 3
ElectronicStructureof Atoms
Magnetic Quantum Number, ml
• Describes the three-dimensional orientation of the orbital.
• Values are integers ranging from -l to l:
−l ≤ ml ≤ l.
• Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.
0 -1+1
0
ElectronicStructureof Atoms
Values of Quantum Numbers
• Principal Quantum #: values of n are integers ≥ 0. • Azimuthal Quantum #: values of are integers ranging from 0 to n − 1.• Magnetic Quantum #: values are integers ranging from - to :
− ≤ ml ≤ .
ElectronicStructureof Atoms
s Orbitals ( = 0)
Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.
{RadialElectronDistribution}
ElectronicStructureof Atoms
s Orbitals ( = 0)
• Spherical in shape.
• Radius of sphere increases with increasing value of n.
{1s} {2s} {3s}
ElectronicStructureof Atoms
p Orbitals ( = 1)
• Have two lobes with a node between them.
{pz}{px} {py}{www.link}
0 -1+1
ElectronicStructureof Atoms
“P” orbital electrons arerepelled by the “S” orbitalelectrons and so spend moretime further from the nucleus.
“P” orbital electrons alsorepel from each others’ sublevels, so they run alongthe axes.
2s
2p
1s
Orbital Overlap: 1s2 2s2 2p6
ElectronicStructureof Atoms
d Orbitals ( = 2)
•Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.
{www.link}{*Orbitals.s.p.d}01
-1 2 -2
ElectronicStructureof Atoms
f Orbitals ( = 3)
• There are seven f orbitals per n level.The f orbitals have
complicated names.They have an = 3m = -3,-2,-1,0,+1,+2,
+3 7 values of m
The f orbitals have important effects in the lanthanide and actinide elements.
{www.link.f}
0
1 -1
-22
-33
ElectronicStructureof Atoms
Energies of Orbitals
• For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
• That is, they are degenerate (collapsed).
ElectronicStructureof Atoms
Energies of Orbitals
• As the number of electrons increases, though, so does the repulsion between them.
• Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.
{E.L. vs FillingOrder}
ElectronicStructureof Atoms
Electron Configuration & Periodic Table
ElectronicStructureof Atoms
Spin Quantum Number, ms
• 1920s: it was discovered that two electrons in the same orbital do not have exactly the same energy.
The “spin” of an electron
describes its magnetic
field, which affects its energy.
{e-spin}
ElectronicStructureof Atoms
Electron Configurations
• Distribution of all electrons in an atom.
• Consist of Number denoting the
energy level. Letter denoting the type
of orbital. Superscript denoting the
number of electrons in those orbitals.
ElectronicStructureof Atoms
Orbital Diagrams
• Each box represents one orbital.
• Half-arrows represent the electrons.
• The direction of the arrow represents the spin of the electron.
ElectronicStructureof Atoms
Basic Principles of Electron Configuration Notations
• Pauli Exclusion Principle
• Hund’s Rule of Maximum Multiplicity• Alonso’s Rules of the Stability of Degenerate Orbitals
ElectronicStructureof Atoms
Pauli Exclusion Principle
• No two electrons in the same atom can have exactly the same energy (identical sets of quantum numbers)
Only two electrons can occupy an orbital and they must have opposite spins.
ElectronicStructureof Atoms
Hund’s Rule of Maximum Multiplicity
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”
{Electron Configuration} {Electron Configuration2}
One electron fills each orbital before a second of opposite spin accompanies it.
ElectronicStructureof Atoms
Alonso’s Rules of the Stability of Degenerate Orbitals
Completely Filled Completely Filled
Completely Filled Half Filled
Half Filled Half Filled
Completely Filled Not even Half Filled
s d
Phenomenon also occurs between degenerate s and f orbitals
Most Stable Electron
Configuration
ElectronicStructureof Atoms
Periodic Table and Electron
Configuration
{e- filling order}
ElectronicStructureof Atoms
1s
2s2p
3s3p
3d4s
Electronic configuration : 1s2
Nitrogen
2s22p3
FeMnVTiScK
Na
ZnCuNiCr Co
Mg
Ca
Be
H
As
O
S
Se
F
Cl
BrGa
C
Si
Ge
N
P
He
Ne
Ar
Kr
1 2 GROUP 3 4 5 6 7 0
Li
Al
B
1
2
3
4
Hund’s Rule
ElectronicStructureof Atoms
Neon
1s
2s2p
3s3p
3d4s
1s2Electronic configuration: 2s22p6
FeMnVTiScK
Na
ZnCuNiCr Co
Mg
Ca
Be
H
As
O
S
Se
F
Cl
BrGa
C
Si
Ge
N
P
He
Ne
Ar
Kr
1 2 GROUP 3 4 5 6 7 0
Li
Al
B
1
2
3
4
Hund’s Rule
ElectronicStructureof Atoms
1s
2s2p
3s3p
3d4s
1s2Electronic configuration: 2s22p6 3s2 3p6 4s2 3d3
Vanadium
FeMnVTiScK
Na
ZnCuNiCr Co
Mg
Ca
Be
H
As
O
S
Se
F
Cl
BrGa
C
Si
Ge
N
P
He
Ne
Ar
Kr
1 2 GROUP 3 4 5 6 7 0
Li
Al
B
1
2
3
4
[Ne]
[Ar]
ElectronicStructureof Atoms
Chromium
1s
2s2p
3s3p
3d4s
1s2Electronic configuration: 2s22p6 3s2 3p6 4s1 3d5
Notice that one of the 4s electronshas been transferred to 3d so that 3d is now a half filled shell with extrastability. 4s and 3d contain onlyunpaired electrons.
FeMnVTiScK
Na
ZnCuNiCr Co
Mg
Ca
Be
H
As
O
S
Se
F
Cl
BrGa
C
Si
Ge
N
P
He
Ne
Ar
Kr
1 2 GROUP 3 4 5 6 7 0
Li
Al
B
1
2
3
4
[Ne]
[Ar]
ElectronicStructureof Atoms
1s
2s2p
3s3p
3d4s
1s2Electronic configuration: 2s22p6 3s2 3p6 4s2 3d8
Nickel
FeMnVTiScK
Na
ZnCuNiCr Co
Mg
Ca
Be
H
As
O
S
Se
F
Cl
BrGa
C
Si
Ge
N
P
He
Ne
Ar
Kr
1 2 GROUP 3 4 5 6 7 0
Li
Al
B
[Ne]
1
2
3
4
[Ar]
ElectronicStructureof Atoms
1s
2s2p
3s3p
3d4s
1s2Electronic configuration: 2s22p6 3s2 3p6 4s13d10
Copper
Notice that again one of the 4s electronshas been promoted to 3d so that 3d is now a completely filled shell with extrastability.
FeMnVTiScK
Na
ZnCuNiCr Co
Mg
Ca
Be
H
As
O
S
Se
F
Cl
BrGa
C
Si
Ge
N
P
He
Ne
Ar
Kr
1 2 GROUP 3 4 5 6 7 0
Li
Al
B
1
2
3
4
ElectronicStructureof Atoms
Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.
Some Anomalies
ElectronicStructureof Atoms
Some AnomaliesElectron configuration for copper is[Ar] 4s1 3d5
rather than the expected[Ar] 4s2 3d4.
•This occurs because the s and d orbitals are very close in energy.
ElectronicStructureof Atoms
Some Anomalies• These anomalies also occur in f-block atoms, as well.
ElectronicStructureof Atoms
Electron Configuration
1s2 2s2 2p6 3s2 3p6 4s2 3d6
1s2 2s2 2p6 3s2 3p6 3d6 4s2
[Ar] 4s2 3d6
[Ar] 4s0 3d6
Fe
Identify elements which posses the following electron configurations:
Fe
Fe
Fe2+
[Ne] 3s2 3p6 Write Elect-Config for S2-
{Aufbau order of filling}
{Energy level order}
{Previous Nobel Gas Abbreviation}
{Cations formed by removal of outermost electrons}
ElectronicStructureof Atoms
ElectronicStructureof Atoms
Periodic Table and Electron
Configuration
{e- filling order}
ElectronicStructureof Atoms
Transition Metals
1234567
Have additional electrons, but they are in an energy level that is lower than the valence electrons.
Uses dots to represent Valence Electrons = those in outermost
Energy Level
ElectronicStructureof Atoms
ElectronicStructureof Atoms
Electrons behave as waves (like standing waves above) and particles.
Electron position cannot be pinned down.
Electons don’t follow orbits, but rather orbitals describe their paths.
ElectronicStructureof Atoms
The Energy of Electromagnetic Waves
Einstein concluded that energy (E) is proportional to frequency
where h is Planck’s constant, 6.63 10−34 J-s.
Energy from electrons comes in whole number multiples of h = eq given
hE
ElectronicStructureof Atoms
The Bohr Model of the Atom (1913)
ElectronicStructureof Atoms
The Nature of Energy
• One does not observe a continuous spectrum, as one gets from a white light source.
• Only a line spectrum of discrete wavelengths is observed.
ElectronicStructureof Atoms
ElectronicStructureof Atoms
Atoms and Electromagnetic Radiation
Atoms absorb and emit energy, often in the form of electromagnetic radiation (light, microwaves, radio & TV waves, u.v., infrared,etc)
•To understand the electronic structure of atoms, one must understand the nature of waves.