What Are the Quantum Numbers for the Helium Atom in an Excited State?

[jeebs]

Hi,
I have a helium atom in the excited state of (1s,20p), and I am told that it has 4 corresponding atomic terms. I am supposed to "write down the quantum numbers of these 4 atomic terms".

As I understand it, an atomic term is specified by the ^2S+1L_J notation, where S is the spin quantum number for the whole atom, L is the orbital angular momentum quantum number for the whole atom, and J is the total angular momentum quantum number for the whole atom.

So, looking at the individual electrons, the 1s electron has spin quantum number s=1/2, and orbital angular momentum quantum number l=0.
the 20p electron has s=1/2, l=1.

I think I am right in saying that only the 20p electron contributes any orbital angular momentum to the atom, so that for the whole atom, L = l = 1, therefore the atomic term should become ^2S+1P_J.

However, this is where I start to get confused. My notes aren't that clear and there are a lot of L's, S's J's, l's, s's, j's etc. getting thrown around. How am I supposed to determine what S and J are?

I am assuming there are only 4 possible combinations of S and J. I thought of doing S = s₁+s₂ = s+s = 1/2 + 1/2 = 1, therefore M_s = -1,0,1 (not sure if this is relevant) but I was not sure about this and got the impression from my notes this was incorrect. The same goes for saying J=L+S. This would only give me the one atomic term, ³P₂, where I need 4 terms.

I'd appreciate it if someone could help me out here.
Thanks.

 

[diazona]

First of all, when you add two spin-1/2 particles, s=1 is not the only possibility. Similarly, when you add l=1 to s=1, j=2 is not the only possibility. Remember that it's not regular numerical addition when you add angular momenta; you actually get multiple results. (The math is based on group theory, but don't worry about that for now)

Anyway, the point is, figure out what other results you can get from adding two angular momenta. I find 4 states in the end when you take them all into account.

 

[jeebs]

diazona - i am aware there are 2 possibilities for the orientation of a given s, but that is due to m_s=+/-1/2, is it not? it is the capital letter quantum number S that I am interested in.
I get that for a given l you have m_l=2l+1 possibilities, etc... I still don't get this.