Modern Theory of the AtomModern Theory of the Atom

Quantum Mechanical ModelQuantum Mechanical ModelOrOr

Wave Mechanical ModelWave Mechanical ModelOrOr

Schrodinger’s ModelSchrodinger’s Model

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Recap of Bohr ModelRecap of Bohr Model• Electrons treated as particles moving in circular Electrons treated as particles moving in circular

orbits. Specify speed, position, energy.orbits. Specify speed, position, energy.• Quantization of energy levels is imposed.Quantization of energy levels is imposed.• Ground state: electrons close to nucleusGround state: electrons close to nucleus• Electron transitions between energy levels can Electron transitions between energy levels can

occur. Higher energy levels are farther from occur. Higher energy levels are farther from nucleus.nucleus.– Moving up, electron absorbs energyMoving up, electron absorbs energy– Moving down, electron emits light energyMoving down, electron emits light energy

• Wavelengths of light in H spectrum can be Wavelengths of light in H spectrum can be predicted. Depend on energy difference of 2 predicted. Depend on energy difference of 2 levels involved in transition.levels involved in transition.

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1924: De Broglie1924: De Broglie

• Proposed that if light can show both Proposed that if light can show both particle and wave behavior, maybe matter particle and wave behavior, maybe matter can too.can too.

Every wavelength of light has Every wavelength of light has its own unique frequency and its own unique frequency and its own unique energy.its own unique energy.

2 kinds of waves2 kinds of wavesTraveling waveTraveling wave

• Wave is not confined Wave is not confined to a given spaceto a given space

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

• Interrupted by a Interrupted by a boundary or another boundary or another wave wave

Standing waveStanding wave• Confined to a given Confined to a given

space. (Ends pinned.)space. (Ends pinned.)• Interference between Interference between

incident & reflected incident & reflected waves.waves.

• At certain frequencies, At certain frequencies, certain points seem to certain points seem to be be standing stillstanding still..

• Other points, Other points, displacement changes displacement changes in a regular way. in a regular way.

Traveling Wave #1

• Traveling Wave #2

Guitar string

• Standing wave #1

DeBroglie Electron-WaveThe wavelength describing The wavelength describing an electron depends on an electron depends on the energy of the electron.the energy of the electron.

At certain energies, At certain energies, electron waves make electron waves make standing waves in the standing waves in the atom. atom.

The wave does not The wave does not represent electron path.represent electron path.

Guitar vs. ElectronGuitar vs. Electron• In the guitar string, only multiples of half-In the guitar string, only multiples of half-

wavelengths are allowed.wavelengths are allowed.

• For an orbiting electron, only whole numbers of For an orbiting electron, only whole numbers of wavelengths allowed.wavelengths allowed.

= h/mv= h/mvWhere h=Planck’s constant, m=mass, v=velocityWhere h=Planck’s constant, m=mass, v=velocity

Modern TheoryModern Theory

• Electron is treated as a wave.Electron is treated as a wave.• CannotCannot specify both position & speed of specify both position & speed of

electron.electron.• CanCan determine determine probabilityprobability of locating the of locating the

electron in a given region of space.electron in a given region of space.• Quantized energy levels arise naturally out Quantized energy levels arise naturally out

of wave treatment.of wave treatment.

Heisenberg uncertainty principleHeisenberg uncertainty principle

• Fundamentally impossible to know the Fundamentally impossible to know the velocity and position of a particle at the velocity and position of a particle at the same time.same time.

• Impossible to make an observation without Impossible to make an observation without influencing the system.influencing the system.

Bohr Model vs. Modern TheoryBohr Model vs. Modern Theory

• Electron = particleElectron = particle• OrbitOrbit• Holds 2nHolds 2n22 electrons electrons• CircularCircular• Each orbit has a Each orbit has a

specific energyspecific energy• Can find position, Can find position,

speedspeed

• Electron = WaveElectron = Wave• OrbitalOrbital• Holds 2 electronsHolds 2 electrons• Not necessarily Not necessarily

circularcircular• Each orbital has a Each orbital has a

specific energyspecific energy• ProbableProbable location location

Orbital – Modern TheoryOrbital – Modern Theory

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

• Each orbital has a specific energy and a Each orbital has a specific energy and a specific shape. Each holds 2 electrons.specific shape. Each holds 2 electrons.

• Described by 4 parameters in the wave Described by 4 parameters in the wave function – quantum numbers = n, l, m, s – function – quantum numbers = n, l, m, s – like an addresslike an address

s orbitalss orbitals

p orbitalsp orbitals

d orbitalsd orbitals

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

• Physical structure of orbitals explainsPhysical structure of orbitals explains– BondingBonding– MagnetismMagnetism– Size of atomsSize of atoms– Structure of crystalsStructure of crystals

Quantum Numbers

• Each electron in an atom has a set of 4 quantum numbers – like an address.

• No two electrons can have all 4 quantum numbers the same.– n = principal energy level, n = 1,2,3,4,. . .– l = type of orbital, l= 0,1,2,3,n-1– ml = orientation of orbital, ml = -l, …, 0, … +l

– s or ms = electron spin = +1/2 or -1/2

Energy Level DiagramEnergy Level Diagram

n: principal quantum numbern: principal quantum number

• Specifies atom’s major (principal)Specifies atom’s major (principal) energy energy levelslevels

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

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

l = Describes sublevelsl = Describes sublevels

• Principal energy levels have energy Principal energy levels have energy sublevels or fine structure or splitting.sublevels or fine structure or splitting.

• The number of sublevels depends on the The number of sublevels depends on the principal energy level.principal energy level.– 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 s, p, d, or fSublevels are labeled s, p, d, or f by by shapeshape

• s orbitals – sphericals orbitals – spherical• p orbitals – dumbbell shapedp orbitals – dumbbell shaped• d & f orbitals have more complex d & f orbitals have more complex

shapesshapes

m = 3m = 3rdrd quantum number quantum number

• Sublevels are Sublevels are made up of orbitalsmade up of orbitals

• Each kind of Each kind of sublevel has a sublevel has a specific # of specific # of orbitalsorbitals

SublevelSublevel # of orbitals# of orbitals

ss 11

pp 33

dd 55

ff 77

44thth quantum number = s quantum number = s

• Electron spin - 2 possible valuesElectron spin - 2 possible values• 4 quantum numbers = address for 4 quantum numbers = address for

each electron.each electron.• No 2 electrons in an atom can have No 2 electrons in an atom can have

the same 4 quantum numbers. Thus, the same 4 quantum numbers. Thus, only 2 electrons per orbital.only 2 electrons per orbital.

• Pauli exclusion principle.Pauli exclusion principle.

Prin.En.LevPrin.En.Lev SublevelsSublevels # orbitals/sl# orbitals/sl Total # elecTotal # elec11 ss 11 2222 ss 11 22

pp 33 6633 ss 11 22

pp 33 66dd 55 1010

44 ss 11 22pp 33 66dd 55 1010ff 77 1414

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

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

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

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

Order of fill: Aufbau principleOrder of fill: Aufbau principle

• Each electron occupies the lowest Each electron occupies the lowest orbital availableorbital available

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

• Is some overlap between sublevels of Is some overlap between sublevels of different principal energy levelsdifferent principal energy levels

1s2s 2p3s 3p 3d4s 4p 4d 4f5s 5p 5d 5f6s 6p 6d 6f7s 7p

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

Follow the arrowsFollow the arrowsExceptions do Exceptions do occur: half-filled occur: half-filled orbitals have orbitals have extra stability.extra stability.

Hund’s RuleHund’s Rule

• Distribution of electrons in equal energy Distribution of electrons in equal energy orbitals: Spread them out as much as orbitals: Spread them out as much as possible!possible!

Electron Configurations

Compare Bohr & Schrodinger

Frequencies in Chemistry

Electron Configuration & P.T.

http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/text_images/CH08/FG08_06.JPG

PrinciplePrincipleEnergyEnergyLevelsLevels

SublevelsSublevels OrbitalsOrbitals Hold 2Hold 2ElectronsElectronsMaxMax

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

Holds 2nHolds 2n22

ElectronsElectronsmaxmax

11stst energy level has 1 sublevel : s energy 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