Modern Theory of the Atom: Quantum Mechanical Model

Recap of Bohr Model electrons: electrons: particles moving in circular orbits with specific speed, position, & energy energy levels possess specific quantum of energy electrons can move between energy levels higher energy levels farther from nucleus higher energy levels farther from nucleus e - moving up to higher E level: electron absorbs energy e - moving up to higher E level: electron absorbs energy e - moving down to lower E level: electron emits light energy e - moving down to lower E level: electron emits light energy ground state: electrons located in lowest possible energy levels, closest can be to nucleus

Bohr Model vs. Modern Theory electron = particleelectron = particle e - path is orbite - path is orbit –holds 2n 2 electrons circular pathcircular path each energy level has specific energyeach energy level has specific energy can find exact position/ speed of e -can find exact position/ speed of e - electron = waveelectron = wave e – path is orbitale – path is orbital –holds 2 electrons not necessarily circularnot necessarily circular each energy level has specific energyeach energy level has specific energy probable location of e -probable location of e -

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

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, … 2n 2 = maximum # e - in any principal2n 2 = maximum # e - in any principal energy level energy level

l = describes sublevels sublevels are labelled by shape:sublevels are labelled by shape: –s, p, d, f

s orbitals: spherical spherical

p orbitals: dumbbell shaped

d orbitals: complex shapes

f orbitals: complex shapes too

Sublevels 1 st principal energy level: s (1 sublevel) 2 nd level: s,p (2 sublevels) 3 rd level: s,p,d (3 sublevels) 4 th level: s,p,d,f (4 sublevels)

m = 3 rd quantum number (orbitals) s has 1 orbital p has 3 orbitals d has 5 orbitals f has 7 orbitals each sublevel contains 1 or more orbitals each orbital holds a max of 2 electrons 1st PEL =s (1 sublevel) = 1 orbital (__ electrons) 2 nd PEL =s,p (2 sublevels) = 4 orbitals (__ e - ) 3 rd PEL = s,p,d (3 sublevels) = 9 orbitals (___ e - ) 4 th PEL s,p,d,f (4 sublevels) = 16 orbitals (___ e - )

4 th quantum number = s e - spin: 2 possible valuese - spin: 2 possible values –clockwise and counter clockwise –Illustrated by arrows with opposite directions 

address for each electron 4 quantum numbers4 quantum numbers no 2 e - canno 2 e - can –occupy same space in atom –have same 4 quantum numbers max 2 electrons per orbital (Pauli exclusion principle)

Memorize s pd f e - 6e - 10e - 14e - s p d f *each orbital holds 2 e - sublevels # of orbitals max # of electrons

electron configurations add e - to atoms starting with lowest energy levels (most stable) –start with 1s, then work upward increasing in energy follow Aufbau Principle.

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 

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

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 4f 14 5s 2 5p 6 5d 10 5f 14 6s 2 6p 6 6d 10 7s 2 7p 6 7d 10 He C Mg Zn 1s 2 1s 2 2s 2 2p 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 2p 6 2s 2

He C Mg Zn 1s 2 1s 2 2s 2 2p 2 1s 2 2s 2 2p 6 3s 2 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 from modern configurations can figure out Bohr configurations: add e - in each energy level (shell) 1 = = 22 = – 4 1 = 22 = = 2 2 – 8 – 2 1 = 2 2 = = =2 2 – 8 – 18 – 2

Hund’s Rule most e - with same spin, so if more than one same orbital: e - fill orbitals one at time before pairing up ex: oxygen 1s 2 2s 2 2p 4

Which element? How many unpaired e-? How many principal energy level ’ s occupied? How many principal energy level ’ s are fully occupied? How many sublevels contain e - ? How many sublevels full? How many orbitals contain e - ? boron