Modern Theory of the Atom Quantum Mechanical Model Or Wave Mechanical Model Or Schrodinger’s Model

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Recap of Bohr Model Electrons treated as particles moving in circular orbits. Specify speed, position, energy.Electrons treated as particles moving in circular 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 occur. Higher energy levels are farther from nucleus.Electron transitions between energy levels can occur. Higher energy levels are farther from nucleus. –Moving up, electron absorbs energy –Moving down, electron emits light energy Wavelengths of light in H spectrum can be predicted. Depend on energy difference of 2 levels involved in transition.Wavelengths of light in H spectrum can be predicted. Depend on energy difference of 2 levels involved in transition.

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

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

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

Traveling Wave #1 Traveling Wave #2

Guitar string Standing wave #1

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

Guitar vs. Electron In the guitar string, only multiples of half- wavelengths are allowed.In the guitar string, only multiples of half- wavelengths are allowed. For an orbiting electron, only whole numbers of wavelengths allowed.For an orbiting electron, only whole numbers of wavelengths allowed. = h/mv = h/mv Where h=Planck’s constant, m=mass, v=velocity

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

Heisenberg uncertainty principle Fundamentally impossible to know the velocity and position of a particle at the same time.Fundamentally impossible to know the velocity and position of a particle at the same time. Impossible to make an observation without influencing the system.Impossible to make an observation without influencing the system.

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

Orbital – Modern Theory Orbital = term used to describe region where an electron might be.Orbital = term used to describe region where an electron might be. Each orbital has a specific energy and a specific shape. Each holds 2 electrons. Each orbital has a specific energy and a specific shape. Each holds 2 electrons. Described by 4 parameters in the wave function – quantum numbers = n, l, m, s – like an addressDescribed by 4 parameters in the wave function – quantum numbers = n, l, m, s – like an address

s orbitals

p orbitals

d orbitals

What can orbitals do for us? Physical structure of orbitals explainsPhysical structure of orbitals explains –Bonding –Magnetism –Size of atoms –Structure 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 –m l = orientation of orbital, m l = -l, …, 0, … +l –s or m s = electron spin = +1/2 or -1/2

Energy Level Diagram Energy Level Diagram

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

l = Describes sublevels Principal energy levels have energy sublevels or fine structure or splitting.Principal energy levels have energy sublevels or fine structure or splitting. The number of sublevels depends on the principal energy level.The number of sublevels depends on the 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 s, p, d, or fby shapeSublevels are labeled s, p, d, or f by shape s orbitals – sphericals orbitals – spherical p orbitals – dumbbell shapedp orbitals – dumbbell shaped d & f orbitals have more complex shapesd & f orbitals have more complex shapes

m = 3 rd quantum number Sublevels are made up of orbitalsSublevels are made up of orbitals Each kind of sublevel has a specific # of orbitalsEach kind of sublevel has a specific # of orbitals Sublevel # of orbitals s1 p3 d5 f7

4 th quantum number = s Electron spin - 2 possible valuesElectron spin - 2 possible values 4 quantum numbers = address for each electron.4 quantum numbers = address for each electron. No 2 electrons in an atom can have the same 4 quantum numbers. Thus, only 2 electrons per orbital.No 2 electrons in an atom can have the same 4 quantum numbers. Thus, only 2 electrons per orbital. Pauli exclusion principle.Pauli exclusion principle.

Prin.En.LevSublevels # orbitals/sl Total # elec 1s12 2s12 p36 3s12 p36 d510 4s12 p36 d510 f714

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 the lowest orbital availableEach electron occupies the lowest orbital available Learn sequence of orbitals from lowest to highest energyLearn sequence of orbitals from lowest to highest energy Is some overlap between sublevels of different principal energy levelsIs some 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 the arrows Exceptions do occur: half-filled orbitals have extra stability.

Hund’s Rule Distribution of electrons in equal energy orbitals: Spread them out as much as possible!Distribution of electrons in equal energy orbitals: Spread them out as much as possible!

Electron Configurations

Compare Bohr & Schrodinger

Frequencies in Chemistry

Electron Configuration & P.T.

PrincipleEnergyLevels SublevelsOrbitals Hold 2 ElectronsMax   n = 1,2,3,4 Holds 2n 2 Electronsmax  1 st energy 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 