Filling of Electronic States - usual filling sequence: - consider ...

Hydrogen (H, Z = 1) Spectrum:
- states labeled by n and l
- selection rule: Δl = ± 1
detailed structure of n = 2 and
n = 3 states:
- splitting of H α line into 7 sub
lines
- states with same n and different
j have different energies
- also states with same n and j but
different l have different energies
Lamb shift (discovered 1947)
between 2 2 S 1/2 and 2 2 P 1/2
phys4.10 Page 15
Sodium (Na, Z = 11) Spectrum:
- electron configuration 1s 2 2s 2 2p 6 3s 1
- single outer s electron in potential of nucleus
screened by closed inner shells
- spectrum similar to that of Hydrogen for large l
states (3d, 4f, 5f, 6f)
- lower angular momentum states have higher
probability densities close to the nucleus, resulting
in stronger binding and thus lower energies
single electron atom
radial electron
probability densities
P(r) dr in dependence
on angular quantum
number l
phys4.10 Page 16