Shapes and Energies of Orbitals
type
n
l
ml
s
≥1
0
0
shapes
s
z
p
≥2
1
–1 0 +1
y
x
px
py
pz
z
y
d
dxz
≥3
2
–2 –1 0 +1 +2
x
dz2
dyz
y
dxy
dx2–y2
Screening and Penetration
2
Because E = –RH( Z eff
n2
), as Zeff ↓, E ↑ for the same value of n.
s
p
d
f
←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→
good penetration
poor penetration
high Zeff
low Zeff
low E
high E
One-electron system: E depends only on n! 3s, 3p, 3d are degenerate
Multi-electron system: because of screening/penetration differences
E depends on n and l! E(3s) < E(3p) < E(3d)
x
Aufbau (“Building Up”)
As Z increases in multielectron atoms, electrons are added one by one from the lowest
energy to progressively higher energy orbitals:
spdf notation
orbital diagram
1s
↑
Lowest energy orbital:
1s (only orbital with n = 1)
He: 1s2
1s
↑↓
Pauli Principle: each orbital
occupied by two electrons with
opposite spin.
Li: [He]2s1
1s
↑↓
2s
↑
1s is full, so 3rd electron goes to
next-lowest energy orbital. Of n = 2,
s is lowest energy.
1s
↑↓
2s
↑↓
4th electron also in the 2s orbital,
opposite spin.
1s
↑↓
2s
↑↓
H: 1s
1
Be: [He]2s
2
2
B: [He]2s 2p
1
2p
2s is full. 2p is next lowest energy
↑
2p
↑
2nd p electron occupies different p
orbital, with same spin as first.
Hund’s Rule: in degenerate
orbitals, electrons occupy different
orbitals and adopt parallel spins.
↑
2p
↑
↑
3rd p electron occupies 3rd p orbital
↑
2
2
1s
↑↓
2s
↑↓
2
3
1s
↑↓
2s
↑↓
2
4
1s
↑↓
2s
↑↓
2p
↑↓ ↑
↑
4th p electron must pair spins
2
5
1s
↑↓
2s
↑↓
2p
↑↓ ↑↓
↑
5th p electron pairs in 2nd p orbital
1s
↑↓
2s
↑↓
2p
↑↓ ↑↓ ↑↓
Ne has filled all orbitals of n = 2
1s
↑↓
2s
↑↓
2p
↑↓ ↑↓ ↑↓
3s
↑
C: [He]2s 2p
N: [He]2s 2p
O: [He]2s 2p
F: [He]2s 2p
2
Ne: [He]2s 2p
Na: [Ne]3s
1
6
Na begins the new n = 3 shell