Quantum Mechanics and Atomic Orbitals

Bohr and Einstein particle nature of light

DeBroglie wave nature of particles

Schrödinger theoretical descriptions of atomsHeisenberg Dirac

quantum or wave mechanics

wave function =

every allowed e- state has unique

to calculate energy use Ĥ

Ĥ = E

solved for hydrogen wave functions

energies 2 = probability distribution

Ĥ = E

E

probability of finding an e- in Hat a particular distance from the nucleus

orbital

orbital requires 3 quantum numbersn l ml

principal 1, 2, 3, …size and energy

angular momentum

0, 1, 2, …, (n - 1)shape

magnetic-l, …, lorientation

“address”

orbital requires 3 quantum numbersn l ml

principal quantum number sizeenergy

as n increases orbitals become larger

e- is further from the nucleusn = 1n = 2n = 3n = 4n = 5n = 6n = 7

orbital requires 3 quantum numbersn l ml

angular momentum shape n - 1n = 1 l = 0n = 2 l = 0, 1n = 3 l = 0, 1, 2n = 4 l = 0, 1, 2, 3

designated by letters

l = 0 s orbitall = 1 p orbital

l = 2 d orbitall = 3 f orbital

0

n = 1 l = 0n = 2 l = 0, 1n = 3 l = 0, 1, 2n = 4 l = 0, 1, 2, 3

designated by letters

l = 0 s orbitall = 1 p orbital

l = 2 d orbitall = 3 f orbital

n = 1n = 2n = 3n = 4n = 5n = 6n = 7

sp

d

f

orbital requires 3 quantum numbersn l ml

magnetic quantum number -l,…, l

n = 1 l = 0 m = 0

n = 2 l = 0 m = 0

l = 1 m = -1m = 0m = 1

n = 3 l = 0 m = 0

l = 2

l = 1 m = -1m = 0m = 1

m = -2m = -1m = 0m = 1m = 2

row s

s

p

sp

d

1

1

3

3

1

51 s orbital3 p orbitals

5 d orbitals

1 s orbital3 p orbitals

5 d orbitals

n = 1n = 2n = 3n = 4n = 5n = 6n = 7

p

d

f

s

each orbital holds 2e- 4th quantum number ms

f orbitals7

spin

1s orbital

spherical

2

2s and 3s 2

1p orbital

2p orbitals 3dumbbell shape

3p, 4p, 5p etc. similar shapes larger

d orbitals3 5cloverleaf

larger n same shapes larger

Pauli exclusion principle

Polyelectronic Atoms

no 2 electrons same 4 quantum numbers

lowest energy orbitals fill first

1s orbital is lowest energy

H 1e- 1s1

He 2e- 1s2

which orbital fills next?

2s2p3s3p4s where is 3d?

1s 2s 2px 2py 2pz 3s 3px 3py 3pz 4s 3d 3d 3d 3d 3d

HHeLiBeBC

no! Hund’s rule parallel spins

NOF

Ne

Na [Ne]

K [Ar]4s 3dxz 3dxy3dyz 3dx2-z2 3dz2 4px

Ca [Ar]Sc [Ar]

Ti [Ar]

V [Ar]

Cr [Ar] no

half full shell stable

Mn [Ar]

Cu [Ar] no

full shell stable