Modern Theory of the Atom: Quantum Mechanical Model

Recap of Bohr Model electrons: particles moving in circular orbits with specific speed, position, & energy quantization of energy levels is imposed electrons 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 Ground state: electrons located in lowest possible energy levels closest can be to nucleus

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

2 kinds of waves Traveling wave wave not confined to given space travels from one location to another interrupted by hitting boundary or another wave Standing wave confined to given space (ends are pinned) interference between incident & reflected waves at certain frequencies: certain points seem to be standing still other points - displacement changes in regular way

Traveling Wave

Standing wave

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 path of electron

Modern Theory electron treated as wave cannot specify both position & speed of electron can determine probability of electron’s location in given region of space Quantized energy levels arise naturally out of wave treatment

Bohr Model vs. Modern Theory electron = particle e- path is orbit holds 2n2 electrons circular path each orbit has specific energy can find exact position/ speed electron = wave e– path is orbital holds 2 electrons not necessarily circular each orbit has specific energy probable location

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

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

Orbital – Modern Theory orbital: term describes region where e- might be found each orbital: specific energy & specific shape described by 4 parameters of wave function (like an address) quantum numbers = n, l, m, s

n: principal quantum number specifies atom’s principal energy levels whole number values: 1, 2, 3, 4, … maximum # electrons in any principal energy level = 2n2

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

Naming sublevels Sublevels are labeled by shapes: s, p, d, f s orbitals: spherical p orbitals: dumbbell shaped d & f orbitals: more complex shapes

m = 3rd quantum number sublevels made up of orbitals each sublevel has specific # of orbitals sublevel # of orbitals s 1 p 3 d 5 f 7

s orbital shapes

p orbital shapes

d orbital shapes

f orbital shapes

4th quantum number = s e- spin: 2 possible values clockwise and counter clockwise

Address for each electron 4 quantum numbers no 2 e- can occupy the same space in atom can have same 4 quantum numbers therefore only 2 electrons per orbital (Pauli exclusion principle)

principle energy level sublevels # orbitals total # e- 1 s 2 p 3 6 d 5 10 4 f 7 14

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

Order of fill: Aufbau Principle each electron occupies lowest energy orbital available learn sequence of orbitals from lowest to highest energy some overlap between sublevels of different principal energy levels

Aufbau Principle Follow arrows 1s 2s 2p sequence of orbitals: 3s 3p 3d 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, … exceptions do occur: - half-filled orbitals have extra stability - magic # is 8 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p

Electron Configurations

Compare Bohr & Schrodinger

Frequencies in Chemistry

Electron Configuration & PT

Principle Energy Levels hold 2 electrons max  Sublevels  Orbitals   1st E level has 1 sublevel : s 2nd “ “ 2 sublevels : s and p 3rd “ “ 3 “ : s, p, and d 4th “ “ 4 “ : s, p, d, and f  n = 1,2,3,4 holds 2n2 electrons max s sublevel holds 1 orbital p sublevel holds 3 orbitals d sublevel holds 5 orbital f sublevel holds 7 orbitals