# Term Symbols

1. May 13, 2010

### oliver.smith8

I'm just going through a past paper for an exam im revising for and I cant work out how to solve this question!

it's
" Total spin S, total orbital angular momentum L and total angular moment J are specified according to spectroscopic notation by the term symbol $$^{S+1}L_{J}$$

i) For Helium show the the levels 1s2p and 1s3d include the terms $$^{1}P_{1}$$ and $$^{1}D_{2}$$
ii) Determine allowed optical transitions between the $$^{1}P_{1}$$ and $$^{1}D_{2}$$ levels in the presences of an external magnetic field. How many transitions occur? How many spectral lines will be observed"

Ive got no idea where to start
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 14, 2010

### nickjer

This site can help out for part (i): http://en.wikipedia.org/wiki/Term_symbol

I will help you with the first part of (i). You know one electron will have S=1/2, L=0 and the other has S=1/2, L=1. So S_total can be 0 or 1 (singlet and triplet). And L_total = 1 (3 states). That gives you a total of 12 states. Pauli exclusion principle doesn't apply here since the electrons can never exist in the same state.

So you can have $^{1}P_{1}$ or $^{3}P_{J}$ (where J=0,1,2). If you add up all the states for each J, you get 12 states as before.

For part (ii), the magnetic field will interact with the J_z operator and the energies will split for different m_j. In the case of $^{1}P_{1}$, J=1 (a triplet), so you will see three split levels. Do the same for the other state. Then find all the transitions between them.

Similar to what can be seen here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodzee.html#c2 (but this is a slightly more complicated example, but the picture is helpful)