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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
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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
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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”
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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
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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
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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
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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
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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
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1s orbital
spherical
2
2s and 3s 2
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1p orbital
2p orbitals 3dumbbell shape
3p, 4p, 5p etc. similar shapes larger
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d orbitals3 5cloverleaf
larger n same shapes larger
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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?
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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]
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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