Modern Theory of the Atom: Quantum Mechanical Model

Recap of Bohr Model Electrons are particles moving in circular orbitsElectrons are particles moving in circular orbits –Specific 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 levelsElectrons can move between energy levels –higher energy levels farther from nucleus –moving up to higher E level: electron absorbs energy –moving down to lower E level: electron emits light energy

1924: De Broglie Proposed:Proposed: –if light can show both particle and wave behavior, maybe matter can too

2 kinds of waves Traveling wave Wave not confined to given spaceWave not confined to given space Travels from one location to anotherTravels from one location to another Interrupted by boundary or another waveInterrupted by boundary or another wave Standing wave Confined to given space (ends are pinned)Confined to given space (ends are pinned) Interference between incident & reflected wavesInterference between incident & reflected waves At certain frequencies:At certain frequencies: –certain points seem to be standing still –Other points - displacement changes in regular way

Traveling Wave #1 Traveling Wave #2

Guitar string Standing wave #1

DeBroglie Electron-Wave wavelength describing electron depends on energy of electron At certain energies, electron waves make standing waves in atom wave does not represent electron path

Modern Theory Electron treated as waveElectron treated as wave –Cannot specify both position & speed of electron –Can determine probability of locating electron in given region of space Quantized energy levels arise naturally out of wave treatmentQuantized energy levels arise naturally out of wave treatment

Bohr Model vs. Modern Theory Electron = particleElectron = particle OrbitOrbit Holds 2n 2 electronsHolds 2n 2 electrons CircularCircular Each orbit has specific energyEach orbit has specific energy Can find exact position/ speedCan find exact position/ speed Electron = WaveElectron = Wave OrbitalOrbital Holds 2 electronsHolds 2 electrons Not necessarily circularNot necessarily circular Each orbit has specific energyEach orbit has specific energy Probable locationProbable location

Orbital – Modern Theory Orbital = term used to describe region where electron might beOrbital = term used to describe region where electron might be Each orbital has specific energy and specific shapeEach orbital has specific energy and specific shape Described by 4 parameters of wave function (like an address):Described by 4 parameters of wave function (like an address): –quantum numbers = n, l, m, s

What can orbitals do for us? Physical structure of orbitals explain:Physical structure of orbitals explain: –Bonding –Magnetism –Size of atoms –Structure of crystals

Heisenberg uncertainty principle Fundamentally impossible to know velocity and position of particle at same timeFundamentally impossible to know velocity and position of particle at same time Impossible to make observation without influencing systemImpossible to make observation without influencing system

n: principal quantum number Specifies atom’s principalenergy levelsSpecifies atom’s principal energy levels whole number values: 1, 2, 3, 4, …whole number values: 1, 2, 3, 4, … Maximum # electrons in any principal energy level = 2n 2Maximum # electrons in any principal energy level = 2n 2

l = Describes sublevels Principal energy levels have sublevelsPrincipal energy levels have sublevels # sublevels depends on principal energy level# sublevels depends on principal energy level – 1 st principal energy level has 1 sublevel – 2 nd “ “ “ “ 2 “ – 3 rd “ “ “ “ 3 “ – 4 Th “ “ “ “ 4 “, etc.

Naming sublevels Sublevels are labeled by shapes:Sublevels are labeled by shapes: – s, 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 = 3 rd quantum number Sublevels made up of orbitalsSublevels made up of orbitals Each sublevel has specific # of orbitalsEach sublevel has specific # of orbitals 7f 5d 3p 1s # of orbitals Sublevel

s orbitals

p orbitals

d orbitals

4 th quantum number = s Electron spin: 2 possible valuesElectron spin: 2 possible values 4 quantum numbers = address for each electron4 quantum numbers = address for each electron No 2 electrons in atom can have same 4 quantum numbersNo 2 electrons in atom can have same 4 quantum numbers – only 2 electrons per orbital = Pauli exclusion principle

147f 105d 63p 21s4 105d 63p 21s3 63p 21s2 21s1 Total # elec # orbitals Sublevels Prin.E Level

1 st principal energy level, 1 sublevel – s 2 nd principal energy level, 2 sublevels – s & p 3 rd principal energy level, 3 sublevels Each box represents an orbital and holds 2 electrons

Order of fill: Aufbau principle Each electron occupies lowest energy orbital availableEach electron occupies lowest energy orbital available Learn sequence of orbitals from lowest to highest energyLearn sequence of orbitals from lowest to highest energy Some overlap between sublevels of different principal energy levelsSome overlap between sublevels of different 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: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, … Follow arrows Exceptions do occur: - half-filled orbitals have extra stability

Electron Configurations

Compare Bohr & Schrodinger

Frequencies in Chemistry

Electron Configuration & PT

PrincipleEnergyLevels SublevelsOrbitals hold 2 electrons max   n = 1,2,3,4 holds 2n 2 electrons max  1 st E level has 1 sublevel : s 2 nd “ “ 2 sublevels : s and p 3 rd “ “ 3 “ : s, p, and d 4 th “ “ 4 “ : s, p, d, and f s sublevel holds 1 orbital p sublevel holds 3 orbitals d sublevel holds 5 orbital f sublevel holds 7 orbitals 