Topic 1_Atomic_structure

8/7/2019 Topic 1_Atomic_structure

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Atomic StructureAtomic Structure

Miss Rubia Binti IdrisMiss Rubia Binti IdrisSST, UMS



RadioactivityRadioactivity

Discovered by accidentDiscovered by accident

BecquerelBecquerel

Three types Three types

alphaalpha-- helium nucleus (+2 charge, largehelium nucleus (+2 charge, large

mass)mass)betabeta-- high speed electronhigh speed electron

gammagamma-- high energy lighthigh energy light



Rutherford·s ExperimentRutherford·s Experiment

Used helium to produce alpha particles.Used helium to produce alpha particles.

Aimed alpha particles at gold foil by drilling a Aimed alpha particles at gold foil by drilling a

hole in a lead block.hole in a lead block. Since the mass is evenly distributed in goldSince the mass is evenly distributed in gold

atoms, alpha particles should go straightatoms, alpha particles should go straight

through.through.

Used gold foil because it could be madeUsed gold foil because it could be madeatoms thin.atoms thin.



Lead

block Uranium

Gold Foil

Florescent

Screen

Experiment setExperiment set--upup



What he expected What he expected



Because

P articles would pass through P articles would pass through



Because, he thought the mass was

evenly distributed in the atom.

m ass was evenly distributed m ass was evenly distributed



What he got What he got



+

Atom is mostly empty Atom is mostly empty

Small dense,Small dense, positivepositivepiece at center.piece at center.

Alpha particles Alpha particlesare deflected by it if they are deflected by it if they get close enough.get close enough.

H ow he explained it H ow he explained it



What Rutherford Observed What Rutherford Observed

+



Models of the AtomModels of the Atom

DaltonDalton

Smallest indivisible particleSmallest indivisible particle

Thomson Thomson

Included the electron into the atomIncluded the electron into the atom

RutherfordRutherford

Nuclear atom with a layer of electrons.Nuclear atom with a layer of electrons.



Modern View Modern View

The atom is mostly The atom is mostly empty space.empty space.

Two regions Two regions

NucleusNucleus-- protons andprotons andneutrons.neutrons.

Electron cloudElectron cloud-- regionregion where you might find an where you might find anelectron.electron.





Max Plank added a twistMax Plank added a twist

with his Quantum Theory with his Quantum Theory

In 1900, Plank proposed that:

atom energy is absorbed or liberated in packets

or chunks of energy. Plank called these

packages of energy "quanta".

In order for an atom to absorb a packet of energy, itmust absorb the whole packet or none at all.



Enter EinsteinEnter Einstein

.Plank's critics were legion. It wasn't until1902 that a young man who worked at atelegraph office near Berlin designed anexperiment that would be known as the"Photoelectric Effect".

This young man was Albert Einstein.



Enter EinsteinEnter Einstein

In his experiment Einstein showed that as thefrequency of radiation was directly proportional tothe energy that was absorbed by the electrons.

The math statement of this relationship is stated as:

E = hR

W here E is the energy, absorbed by the electrons, h

is Plank·s Constant and R is frequency of radiation.



Niels Bohr puts it allNiels Bohr puts it all

togethertogether

Bohr added Plank·s quanta idea to

the Rutherford·s atomic model.

. . . FINALLY



Bohr·s TheoryBohr·s Theory

HeHe proposedproposed thatthat thethe electronselectrons existedexisted atatsetset levelslevels of of energy,energy, atat fixedfixed distancesdistances

fromfrom thethe nucleusnucleus..

If If thethe atomatom absorbedabsorbed energy,energy, thethe

electronelectron jumpedjumped toto aa levellevel furtherfurther fromfromthethe nucleusnucleus



Bohr·s TheoryBohr·s Theory

If If itit radiatedradiated energy,energy, itit fellfell toto aa levellevelclosercloser toto thethe nucleusnucleus..

HisHis modelmodel was was aa hugehuge leapleap forwardforward ininmaking making theory theory fitfit thethe experimentalexperimentalevidenceevidence thatthat otherother physicistsphysicists hadhadfoundfound overover thethe yearsyears..



The Bohr Model of the Atom The Bohr Model of the Atom

NucleusNucleus

ProtonsProtons NeutronsNeutrons

ShellsShells ElectronsElectrons

In the center, contains protons & neutronsIn the center, contains protons & neutrons

positive, one atomic mass unit (amu)positive, one atomic mass unit (amu) neutral, one amuneutral, one amu

energy levels around nucleusenergy levels around nucleus

negative, no effective massnegative, no effective mass




Protons positive

Neutronsneutral

e-e-

e-

e-

e-

e-

e-

e-

e-e-




The atomic number ( The atomic number ( Z Z ) is the number of ) is the number of

protons in an atomprotons in an atom

Each element has a unique atomic numberEach element has a unique atomic number

oror

Each element has a different number of protonsEach element has a different number of protons



W hen the light is passed through a prism only afew wavelengths are present in resulting spectra

These appear as lines separated by dark areas,

and thus are called line spectra

W hen the spectrum emitted by hydrogen gas was

passed through a prism and separated into itsconstituent wavelengths four lines appeared at

characteristic wavelengths







Bohr began with the assumption that electrons

were orbiting the nucleus, much like the earth

orbits the sun.

From classical physics, a charge traveling in acircular path should lose energy by emitting

electromagnetic radiation



If the "orbiting" electron loses energy, it shouldend

up spiraling into the nucleus (which it does not).

Therefore, classical physical laws either don't apply

or are inadequate to explain the inner workings of the atom





Bohr borrowed the idea of quantize energy from

Planck

He proposed that only orbits of certain radii,

corresponding to defined energies, are "permitted"

An electron orbiting in one of these "allowed" orbits:

Has a defined energy state

W ill not radiate energy

W ill not spiral into the nucleus



If the orbits of the electron are restricted,

the energies that the electron can possess are

likewise restricted and are defined by theequation:



R

e !

2

4

2 4

0

2 2

T Q

TI h

Bohr Model of the H atom

Q = reduced mass (nucleus and electron)Z = nuclear charge (1 for H)e = charge of electronI0 = permittivity of a vacuumh =

Plank¶s constant

E Z

n R

n R

n !

¨

ª©©

¸

º¹¹ !

¨

ª©©

¸

º¹¹

2

2 2

1

R = 13.6 eV radius(n ) = n 2a0a0 = Bohr radius = 0.529 Å



Bohr ModelH atom



n = principal p Energy, Size p SHELL

n = 1, 2, 3 «g

n = 1 : ground state

n =2 : first excited state

n = 3 : second excited state

E n

n !

¨

ª©©

¸

º¹¹13 6

12.

E 1 = -13.6 eV

E 2 = -3. 0 eV

E 3 = -1.51 eV

E 4 = -0.85 eV

E 5 = -0.54 eVE g = 0 eV





Johann Rydberg, 19 Johann Rydberg, 19thth century spectroscopiccentury spectroscopic

All wavelengths ( All wavelengths (, lambda) can be described, lambda) can be described

± R is Rydberg constant, 1.097 x 107 m-1

± n are integers; n1 = 1,2«. and n2 = n1 + 1, n1 + 2«.

± Series with n1 = 1 lies in ultraviolet region

L y m an series

± Series with n1 = 2 lies in visible region Bal m er series

± Infrared series includes:

Paschen series (n1 = 3)

Brackett series (n1 = 4)



The spectrum of atomic hydrogen and its analysis into series





Examples in Bohr theoryExamples in Bohr theory

Calculate the wavelengths of the first line andCalculate the wavelengths of the first line andthe series limit for Lyman series for hydrogenthe series limit for Lyman series for hydrogen

F

irst line

Series limit



A. Waves A. Waves

W avelength W avelength ( ( PP ) ) -- length of one complete wavelength of one complete wave

Frequency Frequency ( ( RR ) ) ² ² Number of waves that pass aNumber of waves that pass apoint during a certain time periodpoint during a certain time period

hertz ( Hz) = 1/shertz ( Hz) = 1/s

Amplitude Amplitude (A)(A) -- distance from the origin to thedistance from the origin to thetrough or cresttrough or crest



A. Waves A. Waves

P

A

greater

amplitude(intensity)

greater frequency

(color)

crest

origin

troughP



B. EM SpectrumB. EM Spectrum

L

O

W

E

N

ER

G

Y

H

I

G

H

E

N

ER

G

Y

R O Y G. B I V

red orange yellow green blue indigo violet




L

O

W

E

N

ER

G

Y

H

I

G

H

E

N

ER

G

Y




Frequency and wavelength are inversely Frequency and wavelength are inversely

proportionalproportional

c = PRc: speed of light (3.00 v 108 m/s)P: wavelength (m, nm, etc.)R: frequency ( Hz)




GIVEN:

R = ?

P = 434 nm

= 4.34 v 10-7 m

c = 3.00 v 108 m/s

WORK:R = c / P

R = 3.00 v 108 m/s4.34 v 10-7 m

R = 6.91 v 1014 Hz

EX EX: Find the frequency of a photon with a: Find the frequency of a photon with a wavelength of 434 n wavelength of 434 nm.m.



C. Quantum TheoryC. Quantum Theory

Planck Planck (1900)(1900)

ObservedObserved -- emission of light from hotemission of light from hot

objectsobjectsConcludedConcluded -- energy isenergy is

emitted in small, specificemitted in small, specific

amounts (quanta)amounts (quanta)




QuantumQuantum -- minimum amount of energy changeminimum amount of energy change

Energy can be released (or absorbed) by atomsEnergy can be released (or absorbed) by atoms

only in "packets" of some minimum size.only in "packets" of some minimum size.

This minimum energy packet is called a This minimum energy packet is called a q uantu m q uantu m




The energy ( The energy ( E E ) of a quantum is related to its ) of a quantum is related to itsfrequency ( frequency ( RR ) by some constant ( ) by some constant ( h h ): ):

E = E = hhRR

h is known as "is known as "P lanck's constant P lanck's constant ", and has a value", and has a valueof 6.63 x 10of 6.63 x 10--3434 Joule seconds ( Js) Joule seconds ( Js)

Electrom agnetic energy is always e m itted or absorbed in Electrom agnetic energy is always e m itted or absorbed in whole nu m ber m ultiples of (h* whole nu m ber m ultiples of (h* RR ) )




EinsteinEinstein (1905)(1905)

ObservedObserved -- photoelectric effectphotoelectric effect




LightLight shining shining onon aa metallicmetallic surfacesurface cancan causecausethethe surfacesurface toto e m it e m it electronselectrons

ForFor eacheach metalmetal therethere isis a a m ini m u m m ini m u m fre q uency fre q uency of of

light light below below which which nono electrons electrons are are e m itted e m itted ,, regardlessregardlessof of thethe intensity intensity of of thethe lightlight




The The higherhigher thethe light'slight's frequency frequency aboveabove thisthis

minimumminimum value, value, thethe greatergreater thethe kinetickinetic energy energy

of of thethe releasedreleased electronelectron (s)(s)

By By Planck'sPlanck's resultsresults EinsteinEinstein ( (19051905) ) was was ableable toto

establishedestablished thethe photoelectricphotoelectric effecteffect




EinsteinEinstein assumedassumed thatthat thethe lightlight was was aa streamstream

of of tiny tiny energy energy packetspackets calledcalled P hotons P hotons

EachEach photonphoton hashas anan energy energy proportionalproportional toto itsits

frequency frequency ( ( E= E=hhRR ) )




W hen W hen aa photonphoton strikesstrikes thethe metalmetal itsits energy energy isistransferredtransferred toto anan electronelectron

A A certaincertain amountamount of of energy energy isis neededneeded toto

overcomeovercome thethe attractiveattractive forceforce betweenbetween thetheelectronelectron andand thethe protonsprotons inin thethe atomatom




Thus, Thus, if if thethe quantaquanta of of lightlight energy energy absorbedabsorbedby by thethe electronelectron areare insufficientinsufficient forfor thethe

electronelectron toto overcomeovercome thethe attractiveattractive forcesforces ininthethe atom,atom, thethe electronelectron will will notnot bebe ejectedejected --

regardlessregardless of of thethe intensity intensity of of thethe lightlight..




If If thethe quantaquanta of of lightlight energy energy absorbedabsorbed arearegreatergreater thanthan thethe energy energy neededneeded forfor thethe electronelectron

toto overcomeovercome thethe attractiveattractive forcesforces of of thethe atom,atom,thenthen thethe excessexcess energy energy becomesbecomes kinetickinetic energy energy of of thethe releasedreleased electronelectron..




An An importantimportant featurefeature of of thisthis experimentexperiment isis thatthat

thethe electronelectron isis emittedemitted fromfrom thethe metalmetal with with aa

specificspecific kinetickinetic energy energy (i(i..ee.. aa specificspecific speed)speed)..







EinsteinEinstein (1905)(1905)

ConcludedConcluded -- light has properties of both waveslight has properties of both waves

and particlesand particles

´́ wave wave--particle duality particle dualityµµ

PhotonPhoton -- particle of light that carries aparticle of light that carries a

quantum of energy quantum of energy




E:E: energy ( J, joules)energy ( J, joules)

h:h: Planck·s constant (6.6262Planck·s constant (6.6262 vv 1010--3434 J·s) J·s)RR:: frequency ( Hz)frequency ( Hz)

E = hR

The energy of a photon is proportional to its The energy of a photon is proportional to itsfrequency.frequency.




GIVEN:E = ?

R = 4.57 v 1014 Hz

h = 6.6262 v 10-34 J·s

WORK:E = hR

E = (6.6262 v 10-34 J·s)

(4.57 v 1014 Hz)

E = 3.03 v 10-19 J

EX EX: Find the energy of a red photon with a: Find the energy of a red photon with afrequency of 4.57frequency of 4.57 vv 10101414 Hz.Hz.



Energy quantum ( E ) = hRSo, we need to know the frequency R

RP= c

R = c/PR = (3.00 x 108 m/s)/(589 x 10-9 m)R = 5.09 x 1014 s-1

plugging into Planck's equation:

E = (6.63 x 10-34 Js)*( 5.09 x 1014 s-1 )E (1 quanta) = 3.37 x 10-19 J

Calculate the smallest amount of energy (i.e. onequantum) that an object can absorb from yellow light with

a wavelength of 589 nm.



III. Quantum Model of AtomIII. Quantum Model of Atom



A. Electrons as Waves A. Electrons as Waves

Louis de BroglieLouis de Broglie (1924)(1924)

Electromagnetic radiation considered consist of Electromagnetic radiation considered consist of particles called photons and at the same timeparticles called photons and at the same timeexhibit waveexhibit wave--like properties (interference andlike properties (interference anddiffraction)diffraction)

Applied wave Applied wave--particle theory to eparticle theory to e--

ee-- exhibit wave propertiesexhibit wave properties

The Dual Nature of the Electron



Depending on experimental circumstances, EM radiationappears to have either a wavelike or a particle like (photon )

character .

Íf radiant energy could, under appropriate circu m stances behave

as though it were a strea m of particles, then could m atter, under

appropriate circu m stances, exhibit wave-like properties.µ

Louis de Broglie (1892-1987) who was working on his

Ph.D. degree at the time, made a daring hypothesis:



He went further and reasoned that since wavesare described by their wavelength

and particles are described by their momentum, p



W e can relate these two variables by recalling that

hchE !!

pcmcE 2 !!

Quantum theory says,

Relativity says,

2mc

hc! mc

h!Equate these two equations or

mv

h!

mv

h !oror



The first real experimental proof of this relationshipcame from Davisson and Germer in 1925, who foundthat electrons will diffract and interfere like waves, just likeX-ray photons (light).

For example, an electron with a velocity of 5.97 X 106

m/s (mass of an electron =9.11 X 10-28 g) has a

wavelength of:mvh !



So, matter and light are composed of particles that

have wave-like properties.



A. Electrons as Waves A. Electrons as Waves

EV IDENCE: DIFFRA C TION PATTER NS

ELECTR ONS VISIBLE LIGH T



B. Quantum MechanicsB. Quantum Mechanics

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

Impossible to know both the velocity andImpossible to know both the velocity andposition of an electron at the same timeposition of an electron at the same time




ForFor aa relatively relatively largelarge solidsolid object,object, likelike aa bowling bowling ball,ball, we we cancan determinedetermine itsits positionposition andand velocity velocity atatany any givengiven momentmoment with with aa highhigh degreedegree of of

accuracy accuracy..

However,However, if if anan objectobject (like(like anan electron)electron) hashas

wave wave--likelike propertiesproperties thenthen how how cancan we we accurately accurately definedefine its'its' position?position?




W erner W erner Heisenberg Heisenberg ( (19011901--19761976) ) concludedconcluded thatthatduedue toto thethe dualdual naturenature of of mattermatter (both(both particleparticleandand wavelike wavelike properties)properties) itit isis impossibleimpossible toto

simultaneously simultaneously know know bothboth thethe positionposition andandmomentummomentum of of anan objectobject asas smallsmall asas anan electronelectron..

Thus, Thus, itit isis notnot appropriateappropriate toto imagineimagine thetheelectronselectrons asas moving moving inin well well--defineddefined circularcircularorbitsorbits aboutabout thethe nucleusnucleus..

B Q M h iB Q M h i




SchrödingerSchrödinger W

ave Equation W

ave Equation (1926)(1926)Schrödinger's wave e q uation incorporates both wave-

and particle-like behavior for the electron.

Opened a new way of thinking about sub-atomicparticles, leading the area of study known as wave

m echanics , or q uantu m m echanics .

Schrödinger's equation results in a series of so

called wave functions, represented by letter ] (psi )




SchrödingerSchrödinger Wave Equation Wave Equation

finite # of solutionsfinite # of solutions quantized energy levelsquantized energy levelsdefines probability of finding an edefines probability of finding an e--



From the classical law of energy, the total energy E is theFrom the classical law of energy, the total energy E is thesum of the kinetic energy K and potential energy V,sum of the kinetic energy K and potential energy V,

K + V = EK + V = E (1)(1) The kinetic energy K = The kinetic energy K = (2)(2)

Potential energy V =Potential energy V = (3)(3)

Total energy E = Total energy E = (4)(4)

Schrödinger Schrödinger Equation

2mv2

1

r

e 2

2mv

2

1

r

e2



The fundamental equation for wave propagation in any

medium along x ²direction at any time t is representedby a partial differential equation,

(5)

W here is the displacement of wave velocity c, in thedirection of x-axis.

J

2

2

22

2

1t

cx J J !



Taking Taking intointo considerationconsideration of of CartesianCartesian coco--ordinatesordinates

x,x, y y andand z,z, thethe generalgeneral equationequation becomes,becomes,

2

2

22

2

2

2

2

2 1

t

cz

y

x

J J J J ! (6)

J



W here W here isis aa functionfunction of of timetime andand thethe exponentialexponentialformform of of thethe motionmotion of of thethe wave wave of of frequency frequency isis

givengiven by by thethe equationequation

]

t ie RT] J 2!

J R

(7)

W here W here isis thethe amplitudeamplitude of of wave wave andand aa functionfunction of of x,x, y y

andand z,z, butbut notnot of of timetime unlikeunlike andand ii isis equalequal toto squaresquarerootroot of of --11.. J



OnOn differentiationdifferentiation twicetwice of of thethe equationequation ( (77) ) with with respectrespect toto¶¶tt·,·, we we get,get,

t iet

RT] RTJ 222

2

2

4! (8)

Similarly,Similarly, onon differentiating differentiating twicetwice of of thethe equationequation ( (77) ) with withrespectrespect toto x,x, y,y, zz coco--ordinateordinate andand adding,adding, we we have,have,

¹¹ º ¸©©

ª¨ !

2

2

2

2

2

22

2

2

2

2

2

2

z

y

xe

z

y

x t i ] ] ] J J J RT (9)



On substituting the identities from equation (6) and (8),

t it i ecz

y

x

e RTRT ] RT

] ] ] 222

22

2

2

2

2

22 4

1 !¹¹ º ¸

©©ª¨

2

22

2

2

2

2

2

2 4

cz

y

x

] RT ] ] ] ! (10)Or

2

2

22

2

2

2

2

22 1

t

cz

y

x

e t i J ] ] ] RT !¹¹

º

¸©©ª

¨



The SchrödingerSchrödinger wave equation, may be written as,

0

V-h

m82

2

2

2

2

2

2

2

! ]

T ] ] ]

z

y

x

(11)



W hen look at the results obtained from the

SchrödingerSchrödinger wave equation, we talk in terms of the radial and angular parts of the W ave

functions.

Having solved the wave equation, what are the

results?



The wave function is a solution of the

SchrödingerSchrödinger equation and describes thebehavior of an electron in region of space

called the atomic orbital.

W e can find energy values that are associated with particular wave functions.

The quantization of energy level arises, fromthe SchrödingerSchrödinger equation.

]



Energy of the particle in a one dimension box:



Energy of the particle in a one dimension box

Thus,

E1 = h2 / 8a2m when n = 1

E2 = 4h2 / 8a2m when n = 2

E3 = 9h2 / 8a2m when n = 3

E4 = 16h2 / 8a2m when n = 4

r = (nr = (nT T /a)/a)22 = 8= 8T T 22mE / hmE / h22

E = nE = n22hh22 / 8a/ 8a22m where n = 1, 2, 3 «.m where n = 1, 2, 3 «.



Energy of the particle in a one dimension box

E1, n=1

E2, n=2

E3, n=3

E4, n=4

Thus energy of the particle in a one dimension box is quantized, it is not continuous as particle

by classical theory. Hence energy,

E = n2

h2

/ 8a2

m

B Quantum MechanicsB Quantum Mechanics




Radial Distribution CurveRadial Distribution CurveOrbitalOrbital

OrbitalOrbital (électron cloudµ)(électron cloudµ)

Region in space where there is 90% probability of Region in space where there is 90% probability of finding an efinding an e--

Thus, Schrödinger's equation does not tell us exact location of electron, rather it describes probability of an electron.

Wave functions and Orbitals



Wave functions and Orbitals

polar coordinates

= = wave function=2 = probability density

4T r2=2 = radial probability function



Departure from the Bohr model of the atom

In the Bohr model, the electron is in a defined orbit , in theSchrödinger model we can speak only of probability distributions for a given energy level of the electron.

For example, an electron in the ground state in aHydrogen atom would have a probability distribution which looks something like this (a more intense color

indicates a greater value for ]2, a higher probability of finding the electron in this region, and consequently,greater electron density):

C Q N bC Q N b



C . Quantu m Nu m bers C . Quantu m Nu m bers

Four Quantum Numbers:Four Quantum Numbers:

Specify the áddressµ of each electron in an atomSpecify the áddressµ of each electron in an atom

C Q N bC Q N b



C. Quantum NumbersC. Quantum Numbers

1. Principal Quantum Number (1. Principal Quantum Number ( nn ))

Energy levelEnergy level

Size of the orbitalSize of the orbital

nn2 = no. of orbitals in= no. of orbitals inthe energy levelthe energy level

C Q N bC Q N b



corresponds tocorresponds to n n from Bohr modelfrom Bohr model

describesdescribes energy levelenergy level andand sizesize of orbitalof orbital

n n = 1, 2, 3, ...= 1, 2, 3, ...

asas n n increases,increases,

orbitals get largerorbitals get larger orbital energy increasesorbital energy increases


C Q N bC Q N b




s p

d f

2. Angular Momentum Quantum2. Angular Momentum Quantum ( ( l l ) )

Energy sublevelEnergy sublevel

Shape of the orbitalShape of the orbital

C Q N bC Q N b



l = Orbital angular m om entu m q uantu m l = Orbital angular m om entu m q uantu m

describesdescribes shapeshape of orbitalof orbital

l l can have integral values from 0 tocan have integral values from 0 to n n --11

l l values describe a specific shape of orbital: values describe a specific shape of orbital:

if if l =l = 00 11 22 33

ss pp dd f f


Th l ifi i f bi l i b h ll d h llTh l ifi i f bi l i b h ll d h ll



The classification of orbitals into subshells and shells The classification of orbitals into subshells and shells

C Q t N bC Q t N b




nn == no. of sublevels per levelno. of sublevels per level nn22 == no. of orbitals per levelno. of orbitals per level

Sublevel sets:Sublevel sets: 11s,s, 33p,p, 55d,d, 77f f

C Q t N bC Q t N b




3. Magnetic Quantum Number3. Magnetic Quantum Number ( m ( m l l ) )

O

rientation of orbitalO

rientation of orbital Specifies the exact orbitalSpecifies the exact orbital

within each sublevel within each sublevel



m m l l = m agnetic q uantu m = m agnetic q uantu m

describesdescribes orientationorientation of orbital in spaceof orbital in space

m m l l can have integral values fromcan have integral values from --ll to +to +l l




C Q N bC Q N b




p pxx p p y y

p pzz

C Q t N bC Q t N b




Orbitals combine to form a spherical shape.Orbitals combine to form a spherical shape.

2s

2pz2py

2px

Quantum Number RelationshipsQuantum Number Relationships



Quantu m Nu m ber Relationships Quantu m Nu m ber Relationships

Orbital Energy L evels for H ydrogen Orbital Energy L evels for H ydrogen



gy f y ggy f y g

Orbitals with same n are degenerate (at same energy)

C Q t N bC Q t N b



M ulti M ulti- - Electron Atom s Electron Atom s

Schrödinger equation can be solvedSchrödinger equation can be solved only only forforhydrogen atom (a one electron system)!hydrogen atom (a one electron system)!

For other multiFor other multi--electron atoms, assume orbitalselectron atoms, assume orbitals

areare hydrogenhydrogen--likelike..


Orbital Energy L evels in M ulti Orbital Energy L evels in M ulti- - Electron Atom s Electron Atom s



gygy

For multi-electron atoms, orbitals with same n are NOT degenerate

For same n, s < p < d < f

C Quantum NumbersC Quantum Numbers




4. Spin Quantum Number4. Spin Quantum Number ( ( m m ss ) )

Electron spinElectron spin (anti Clockwise, +½ or Clockwise(anti Clockwise, +½ or Clockwise --½)½)

An orbital can hold 2 electrons that spin in opposite An orbital can hold 2 electrons that spin in opposite

directions.directions.




m m ss= = electron spin q uantu m nu m ber electron spin q uantu m nu m ber

m m ss = +½ or= +½ or --½½

spinspin--up spinup spin--downdown

oo qq


C Q N bC Q N b



Rules for ElectronsRules for Electrons

Aufbau Principle

Pauli Exclusion Principle

Hund·s Rule




Aufbau P rinciple Aufbau P rinciple

Aufbau is German for ´building upµ Aufbau is German for ´building upµ

Electrons enter orbitals of Electrons enter orbitals of lowest energy first.lowest energy first.


General RulesGeneral Rules




Aufbau Principle Aufbau Principle

Electrons fill theElectrons fill thelowest energy lowest energy orbitals first.orbitals first.

´Lazy Tenant´Lazy TenantRuleµRuleµ



P auli Exclusion P rinciple P auli Exclusion P rinciple

An atomic orbital may at most An atomic orbital may at mostdescribe two electrons.describe two electrons.






1. Principal Q. N.1. Principal Q. N. pp

2. Angular Mom. Q. N.2. Angular Mom. Q. N. pp

3. Magnetic Q. N.3. Magnetic Q. N. pp

4. Spin Q. N.4. Spin Q.N. pp

energy levelenergy level

sublevel (s,p,d,f)sublevel (s,p,d,f)orbitalorbital

electronelectron

Pauli Exclusion PrinciplePauli Exclusion Principle

No two electrons in an atom can have the same 4No two electrons in an atom can have the same 4quantum numbers.quantum numbers.

Each eEach e-- has a unique áddressµ:has a unique áddressµ:

G l R lG l R l




Pauli Exclusion PrinciplePauli Exclusion Principle

Each orbital can holdEach orbital can hold T WO T WO electrons with oppositeelectrons with opposite

spins.spins.

C Q t N bC Q t N b



Hund·s RuleHund·s Rule

W

hen electrons occupy orbitals of W

hen electrons occupy orbitals of equal energy,equal energy,

one electron enters each orbitalone electron enters each orbital

until all the orbitals contain oneuntil all the orbitals contain oneelectron with parallel spins.electron with parallel spins.





RIGHTWRONG


Hund·s RuleHund·s Rule

W ithin a sublevel, place one e W ithin a sublevel, place one e-- per orbital beforeper orbital beforepairing them.pairing them.

NO Émpty Bus Seat RuleµNO Émpty Bus Seat Ruleµ

El C fi iEl C fi i



Electron ConfigurationElectron Configuration

Notation for Electron Distribution Notation for Electron Distribution



ff

Number of ElectronsNumber of Electrons1s2

Here we see the

electron

configuration for theelement HELIUM

Principle Quantum Number

Angular Momentum

Principle quantum number ¶n·Principle quantum number ¶n·



P rinciple q uantu m nu m ber n P rinciple q uantu m nu m ber n

The The largelarge numbernumber ""11"" refersrefers toto thetheprincipleprinciple quantumquantum numbernumber "n""n"

1s2

which stands for the energy level. It tells us thatthe electrons of helium occupy the first energy level of the atom.

Angular momentum quantum number IAngular momentum quantum number I



Angular m om entu m q uantu m nu m ber I Angular m om entu m q uantu m nu m ber I

The The letterletter "s""s" standsstands forfor thethe angularangular

momentummomentum quantumquantum numbernumber "l""l"..

It tells us that the two electrons of the heliumelectron occupy an "s" or spherical orbital.

1s2

T l N b f ElT l N b f El



T otal Nu m ber of Electrons T otal Nu m ber of Electrons

The The exponentexponent ""22"" refersrefers toto thethe totaltotal numbernumber of of

electronselectrons inin thatthat orbitalorbital oror subsub--shellshell..

In this case, we know that there are two electrons inthe spherical orbital at the first energy level.

1s2

Principle Quantum Number (n) and SublevelsPrinciple Quantum Number (n) and Sublevels



P rinciple Quantu m Nu m ber (n ) and Sublevels P rinciple Quantu m Nu m ber (n ) and Sublevels

The number of sublevels that an energy level The number of sublevels that an energy level

can contain is equal to the principle quantumcan contain is equal to the principle quantumnumber of that level.number of that level.

SublevelsSublevels



The second energy level would have two sublevels, The second energy level would have two sublevels,

The third energy level would have three sublevels. The third energy level would have three sublevels.

The first sublevel is called an s sublevel. The first sublevel is called an s sublevel.

The second sublevel is called a p sublevel. The second sublevel is called a p sublevel.

The third sublevel is called a d sublevel and The third sublevel is called a d sublevel and

the fourth sublevel is called an f sublevel.the fourth sublevel is called an f sublevel.

Although Although energy energy levelslevels thatthat areare higherhigher thanthan 44 would would containcontainadditionaladditional sublevels,sublevels, thesethese sublevelssublevels havehave notnot beenbeen namednamed becausebecause nono

knownknown atomatom inin itsits groundground statestate would would havehave electronselectrons thatthat occupy occupy themthem

T otal Nu m ber of Orbital and Electrons per Energy L evel T otal Nu m ber of Orbital and Electrons per Energy L evel



f p gyf p gy

An An easy easy way way toto calculatecalculate thethe numbernumber of of orbitalsorbitals foundfoundinin anan energy energy levellevel isis toto useuse thethe formulaformula nn22..

F

orF

or example,example, thethe thirdthird energy energy levellevel (n=(n=33) ) hashas aa totaltotalof of 3232,, oror ninenine orbitalsorbitals..

This This makesmakes sensesense becausebecause we we know know thatthat thethe thirdthird

energy energy levellevel would would havehave 33 sublevelssublevels;; anan ss sublevelsublevel with with oneone orbital,orbital, aa pp sublevelsublevel with with 33 orbitalsorbitals andand aa ddsublevelsublevel with with 55 orbitalsorbitals.. 11 ++ 33 ++ 55 == 99,, soso thetheformulaformula nn22 works! works!

Orbital Energy L evels in M ulti Orbital Energy L evels in M ulti- - Electron Atom s Electron Atom s



THE ULTIMATE TOOLTHE ULTIMATE TOOL



THE U LT I M ATE T OOL THE U LT I M ATE T OOL

THE TOOLTHE TOOL



THE T OOL THE T OOL

RememberRemember toto startstart atat thethe beginning beginning of of eacheach

arrow,arrow, andand thenthen follow follow itit allall of of thethe way way toto thetheend,end, filling filling inin thethe sublevelssublevels thatthat itit passespasses

throughthrough.. InIn otherother words, words, thethe orderorder forfor filling filling inin thethe sublevelssublevels becomesbecomes;;

11s,s, 22s,s, 22p,p, 33s,s, 33p,p, 44s,s, 33d,d, 44p,p, 55s,s, 44d,d, 55p,p, 66s,s, 44f,f,

55d,d, 66p,p, 77s,s, 55f,f, 66d,d,77pp..



NotationNotation



O

8e-

Orbital DiagramOrbital Diagram

Electron ConfigurationElectron Configuration

1s2 2s2 2p4

1s 2s 2p

NotationNotation



Shorthand ConfigurationShorthand Configuration

S 16e-

Valence ElectronsCore Electrons

S 16e- [Ne] 3s2 3p4

1s2 2s2 2p6 3s2 3p4

Longhand ConfigurationLonghand Configuration

Periodic PatternsPeriodic Patterns



© 1998 b y Har cour t Brace & C ompan y

s p

d ( n-1)

f ( n-2)

1

2

34

5

6

7

6

7

Periodic PatternsPeriodic Patterns



III.III. Atomic Electron ConfigurationsAtomic Electron Configurations



C.C. Box DiagramsBox Diagrams -- OrbitalsOrbitals are represented by boxes andare represented by boxes and

electrons are represented by arrows.electrons are represented by arrows.

ElementElement

LiLi

BeBe

BB

CC

NN

OO

FF

OrbitalsOrbitals

1s1s 2s2s 2p2p

NeNe

HundHund¶¶ss RuleRule ± ± TheThe

most stable arrangementmost stable arrangement

of electrons is that withof electrons is that with

the maximum number of the maximum number of

unpaired electrons, allunpaired electrons, allwith the same spinwith the same spin

direction.direction.

III.III. tomic Electron onfigurationstomic Electron onfigurations



ElementElement

aa

ScSc

TiTi

VV

rr

MnMn

ee

OrbitalsOrbitals

4s4s 3d3d

ZnZn

ooii

uu

III.III. A o o Co g a oA o o Co g a o

N b l t bit lN b l t i bit l



D.D. spdf spdf No a oNo a o 1s1s11

ElementElement

LiLi

BeBe

BB

CC

NN

FF

italsOrbitals

1s1s 2s2s 22

NeNe

electr on shell (electr on shell (nn))

Nu ber o electr ons n orbital Nu ber o electr ons in orbital

Orbital type (Orbital type (l l ))

spdf spdf notationnotation

1s1s2 2 2s2s11

1s1s2 2 2s2s22

1s1s2 2 2s2s2 2 2 p2 p11

1s1s2 2 2s2s2 2 2 p2 p22

1s1s2 2 2s2s2 2 2 p2 p33

1s1s2 2 2s2s2 2 2 p2 p44

1s1s2 2 2s2s2 2 2 p2 p66

1s1s2 2 2s2s2 2 2 p2 p66

III.III. tomic Electron onfigurationstomic Electron onfigurations



.. s pd s pd otationotation -- 1s1s11

ElementElement

aa

gg

ll

SiSi

PP

SS

ll

OrbitalsOrbitals

3s3s 3p3p

rr

electron shellelectron shell nn))

Number of electrons in orbital Number of electrons in orbital

rbital typerbital type l l ))

s pd s pd notationnotation

[[ Ne Ne] 1s] 1s2 2 2s2s11

[[ Ne Ne] 1s] 1s2 2 2s2s22

[[ Ne Ne] 1s] 1s2 2 2s2s2 2 2 p2 p11

[[ Ne Ne] 1s] 1s2 2 2s2s2 2 2 p2 p22

[[ Ne Ne] 1s] 1s2 2 2s2s2 2 2 p2 p33

[[ Ne Ne] 1s] 1s2 2 2s2s2 2 2 p2 p44

[[ Ne Ne] 1s] 1s2 2 2s2s2 2 2 p2 p66

[[ Ne Ne] 1s] 1s2 2 2s2s2 2 2 p2 p66

Electron Configuration ExamplesElectron Configuration Examples



g pg p

W rite ground state electron configurations W rite ground state electron configurations(using noble gas notation) for the following:(using noble gas notation) for the following:

a) potassium, K ( a) potassium, K ( Z = 19Z = 19 ) )

b) iodine, I ( b) iodine, I ( Z= 53Z= 53 ) )

c) bismuth, Bi ( c) bismuth, Bi ( Z=

83Z=

83 ) )

[Ar] 4s1

[K r] 5s2 4d10 5p5

[Xe

] 6s2

4f 14

5d10

6p3

Som e Electron C onfiguration Exceptions Som e Electron C onfiguration Exceptions



Chromium, Cr (Z=24)Chromium, Cr (Z=24)

expected: [Ar]4sexpected: [Ar]4s22 3d3d44

actual: [Ar] 4sactual: [Ar] 4s11

3d3d55

Copper, Cu (Z=29)Copper, Cu (Z=29)

expected: [Ar] 4sexpected: [Ar] 4s22 3d3d99

actual: [Ar] 4sactual: [Ar] 4s11 3d3d1010

Why ExceptionsWhy Exceptions??



Why Exceptions Why Exceptions ??

Recall: energy levels get closer in energy asRecall: energy levels get closer in energy as n n

increases.increases.

Also, special stability of filled or half Also, special stability of filled or half--filledfilledsubshells.subshells.

StabilityStability



Electron Configuration ExceptionsElectron Configuration Exceptions

CopperCopper

EXPECTEXPECT:: [Ar] 4s[Ar] 4s22 3d3d99

ACTU ALLY ACTU ALLY :: [Ar] 4s[Ar] 4s11 3d3d1010

Copper gainsCopper gains stability stability with a full with a fulldd--sublevel.sublevel.

StabilityStability

StabilityStability



Electron Configuration ExceptionsElectron Configuration Exceptions

ChromiumChromium

EXPECTEXPECT:: [Ar] 4s[Ar] 4s22 3d3d44

ACTU ALLY ACTU ALLY :: [Ar] 4s[Ar] 4s11 3d3d55

Chromium gainsChromium gains stability stability with a half with a half--full dfull d--sublevel.sublevel.

StabilityStability

Electrons in Subshells Electrons in Subshells - - a C loser L ooka C loser L ook



Electrons in SubshellsElectrons in Subshells a Closer ooka Closer ook

N (Z=7): 1sN (Z=7): 1s22 2s2s22 2p2p33

1s 2s 2p1s 2s 2p

P ara m agnetic vs Dia m agnetic P ara m agnetic vs Dia m agnetic



g gg g

ParamagneticParamagnetic -- at least one unpaired electron.at least one unpaired electron.

DiamagneticDiamagnetic -- all electrons are paired.all electrons are paired.

Paramagnetic species areParamagnetic species are attracted attracted to a magneticto a magnetic

field.field.

Diamagnetic species areDiamagnetic species are repelled repelled by a magneticby a magnetic

field.field.

Electron C onfigurations for Ions Electron C onfigurations for Ions



f g ff g f

MetalsMetals loselose ee-- and nonmetalsand nonmetals gaingain ee--..

W rite configuration for parent atom, then add W rite configuration for parent atom, then addor remove electrons in outermost shell.or remove electrons in outermost shell.

ex:F

eex:F

e3+3+

Fe (Z=26) [Ar]4sFe (Z=26) [Ar]4s22 3d3d66

FeFe3+3+ [Ar][Ar] 3d3d55

C ore Electrons vs Valence Electrons C ore Electrons vs Valence Electrons



core electronscore electrons -- electrons in inner shellselectrons in inner shells

valence electrons valence electrons -- electrons in outer shellelectrons in outer shell

Cl (Z=17): [Ne] 3s2 3p5

core electrons

valence electrons

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Topic 1_Atomic_structure