Modern Theory of the Atom:Modern Theory of the Atom:

Quantum Mechanical ModelQuantum Mechanical Model

Recap of Bohr ModelRecap of Bohr Model• Electrons are particles moving in circular orbitsElectrons are particles moving in circular orbits

– Specific speed, position, energySpecific speed, position, energy

• Quantization of energy levels is imposedQuantization of energy levels is imposed

• Ground state: electrons closest to nucleusGround state: electrons closest to nucleus

• Electrons can move between energy levels Electrons can move between energy levels

– higher energy levels farther from nucleushigher energy levels farther from nucleus– moving up to higher E level: electron moving up to higher E level: electron absorbsabsorbs energy energy– moving down to lower E level: electron moving down to lower E level: electron emits lightemits light energy energy

1924: De Broglie1924: De Broglie

• Proposed:Proposed:– if light can show both particle and wave behavior, if light can show both particle and wave behavior,

maybe matter can toomaybe matter can too

2 kinds of waves2 kinds of wavesTraveling waveTraveling wave

• Wave not confined to Wave not confined to given spacegiven space

• Travels from one Travels from one location to anotherlocation to another

• Interrupted by Interrupted by boundary or another boundary or another wavewave

Standing waveStanding wave• Confined to given space Confined to given space

(ends are pinned) (ends are pinned)

• Interference between Interference between incident & reflected incident & reflected waveswaves

• At certain frequencies:At certain frequencies:– certain points seem to be certain points seem to be

standing stillstanding still– Other points - displacement Other points - displacement

changes in regular waychanges in regular way

Traveling Wave #1

• Traveling Wave #2

Guitar string

• Standing wave #1

DeBroglie Electron-Wavewavelength describing wavelength describing electron depends on energy electron depends on energy of electronof electron

At certain energies, electron At certain energies, electron waves make standing waves waves make standing waves in atomin atom

wave does not represent wave does not represent electron pathelectron path

Modern TheoryModern Theory

• Electron treated as waveElectron treated as wave– CannotCannot specify both position & speed of electron specify both position & speed of electron– CanCan determine determine probabilityprobability of locating electron in of locating electron in

given region of spacegiven region of space

• Quantized energy levels arise naturally out of Quantized energy levels arise naturally out of wave treatmentwave treatment

Bohr Model vs. Modern TheoryBohr Model vs. Modern Theory

• Electron = particleElectron = particle

• OrbitOrbit

• Holds 2nHolds 2n22 electrons electrons

• Circular Circular

• Each orbit has Each orbit has specific energyspecific energy

• Can find Can find exactexact position/ speedposition/ speed

• Electron = WaveElectron = Wave

• OrbitalOrbital

• Holds 2 electronsHolds 2 electrons

• Not necessarily circularNot necessarily circular

• Each orbit has specific Each orbit has specific energyenergy

• ProbableProbable location location

Orbital – Modern TheoryOrbital – Modern Theory

• Orbital = term used to describe region Orbital = term used to describe region where electron might be where electron might be

• Each orbital has specific energy and Each orbital has specific energy and specific shapespecific shape

• Described by 4 parameters of wave Described by 4 parameters of wave function (like an address): function (like an address): – quantum numbers = n, l, m, s quantum numbers = n, l, m, s

What can orbitals do for us?What can orbitals do for us?

• Physical structure of orbitals explain:Physical structure of orbitals explain:– BondingBonding– MagnetismMagnetism– Size of atomsSize of atoms– Structure of crystalsStructure of crystals

Heisenberg uncertainty principleHeisenberg uncertainty principle

• Fundamentally impossible to know Fundamentally impossible to know velocity and position of particle at same velocity and position of particle at same timetime

• Impossible to make observation without Impossible to make observation without influencing systeminfluencing system

n: principal quantum numbern: principal quantum number

• Specifies atom’s principalSpecifies atom’s principal energy levelsenergy levels

• whole number values: 1, 2, 3, 4, …whole number values: 1, 2, 3, 4, …

• Maximum # electrons in any principal Maximum # electrons in any principal energy level = 2nenergy level = 2n22

l = Describes sublevelsl = Describes sublevels

• Principal energy levels have sublevels Principal energy levels have sublevels

• # sublevels depends on principal energy # sublevels depends on principal energy levellevel– 11stst principal energy level has principal energy level has 11 sublevel sublevel– 22ndnd “ “ “ “ “ “ “ “ 22 “ “– 33rdrd “ “ “ “ “ “ “ “ 33 “ “– 44ThTh “ “ “ “ “ “ “ “ 44 “ , etc. “ , etc.

Naming sublevelsNaming sublevels

• Sublevels are labeled by shapes:Sublevels are labeled by shapes:– s, p, d, fs, p, d, f

• s orbitals: sphericals orbitals: spherical

• p orbitals: dumbbell shapedp orbitals: dumbbell shaped

• d & f orbitals: more complex shapesd & f orbitals: more complex shapes

m = 3m = 3rdrd quantum number quantum number

• Sublevels made up Sublevels made up of orbitalsof orbitals

• Each sublevel has Each sublevel has specific # of orbitalsspecific # of orbitals

77ff

55dd

33pp

11ss

# of orbitals# of orbitalsSublevelSublevel

s orbitalss orbitals

p orbitalsp orbitals

d orbitalsd orbitals

44thth quantum number = s quantum number = s

• Electron spin: 2 possible valuesElectron spin: 2 possible values

• 4 quantum numbers = address for each 4 quantum numbers = address for each electronelectron

• No 2 electrons in atom can have same 4 No 2 electrons in atom can have same 4 quantum numbers quantum numbers – only 2 electrons per orbitalonly 2 electrons per orbital= Pauli exclusion principle= Pauli exclusion principle

141477ff

101055dd

6633pp

2211ss44

101055dd

6633pp

2211ss33

6633pp

2211ss22

2211ss11

Total # elecTotal # elec# orbitals# orbitalsSublevelsSublevelsPrin.E LevelPrin.E Level

11stst principal energy level, 1 sublevel – s principal energy level, 1 sublevel – s

22ndnd principal energy level, 2 sublevels – principal energy level, 2 sublevels – s & ps & p

33rdrd principal energy principal energy level, 3 sublevelslevel, 3 sublevels

Each box represents an orbital and holds 2 electronsEach box represents an orbital and holds 2 electrons

Order of fill: Aufbau principleOrder of fill: Aufbau principle• Each electron occupies lowest energy Each electron occupies lowest energy

orbital availableorbital available

• Learn sequence of orbitals from lowest to Learn sequence of orbitals from lowest to highest energyhighest energy

• Some overlap between sublevels of Some overlap between sublevels of different principal energy levelsdifferent principal energy levels

1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f

6s 6p 6d 6f

7s 7p

Sequence of orbitals:Sequence of orbitals:1s, 2s, 2p, 3s, 3p, 4s, 3d, 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, …4p, 5s, 4d, …

Follow arrowsFollow arrows

Exceptions do occur: Exceptions do occur: - half-filled orbitals - half-filled orbitals have extra stabilityhave extra stability

Electron Configurations

Compare Bohr & Schrodinger

Frequencies in Chemistry

Electron Configuration & PT

PrinciplePrincipleEnergyEnergyLevelsLevels

SublevelsSublevels OrbitalsOrbitalshold 2hold 2electrons maxelectrons max

n = 1,2,3,4n = 1,2,3,4

holds 2nholds 2n22

electrons maxelectrons max

11stst E level has 1 sublevel : s E level has 1 sublevel : s 22ndnd “ “ 2 sublevels : s and p “ “ 2 sublevels : s and p33rdrd “ “ 3 “ : s, p, and d “ “ 3 “ : s, p, and d44thth “ “ 4 “ : s, p, d, and f “ “ 4 “ : s, p, d, and f

s sublevel holds 1 orbitals sublevel holds 1 orbitalp sublevel holds 3 orbitalsp sublevel holds 3 orbitalsd sublevel holds 5 orbitald sublevel holds 5 orbitalf sublevel holds 7 orbitalsf sublevel holds 7 orbitals