Thermal X-ray radiation (PDF) - SRON

Z Element configuration term
1 H 1s 2 S 1/2
2 He 1s 2 1 S 0
3 Li 2s 2 S 1/2
4 Be 2s 2 1 S 0
5 B 2p 2 P 1/2
6 C 2p 2 3 P 0
All noble gases have a closed shell with L = 0, S = 0 and as a consequence their
ground state is always 1 S 0 . The ground term of a shell that is filled only half is
always an S term, for example for nitrogen 2p 3 4 S 3/2 .
3.2.5 Statistical weight
The statistical weight of an energy level with quantum number J is the number
of directions that the vector ⃗ J can take with respect to some preferred direction,
for example the magnetic field. This is also the allowed number of sublevels. The
projection of ⃗ J on the preferred direction is called MJ (or m j for a single electron
with angular momentum ⃗j). In the case of a magnetic field M J is the socalled
magnetic quantum number (Zeeman effect). M J can take any value between
−J, −J + 1,...,0,...,J − 1, J. This gives 2J + 1 possible orientations of ⃗ J with
respect to the preferred direction. Therefore the statistical weight g J = 2J + 1.
Example 3.6. The 3 D 2 level has g 2 = 5. Note that for 3 D we have L = 2,
S = 1. The total statistical weight of the 3 D term (levels with J = 3, 2, and 1) is
g = 7 + 5 + 3 = 15.
In a strong magnetic field the vectors ⃗ L and ⃗ S are decoupled ( ⃗ J does not exist
any more) and they are arranged independently with respect to ⃗ B. Instead of the
4 quantum numbers n, L, J and M J (Zeeman effect), one then takes n, L, M L and
M S , with M L and M S the projections of ⃗ L and ⃗ S on ⃗ B (Paschen Back effect). In that
case we find for the 3 D term M L = −2, −1, 0, 1, 2, M S = −1, 0, 1 → g = 5 × 3 = 15.
3.2.6 The periodic system
With the knowledge obtained before we now consider the periodic system. The
table shows how the electronic subshells are being filled. Note also that there are
sometimes small irregularities, such as for Mn.
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