Total angular momentum quantum number

[learning_phys]

lets say there is an electron configuraiton of $$1s^2 2s^2 2p^2 3p^1$$

I want to find the total angular momentum quantum number, J=L+S

considering the n=1 state, there are two electrons, in the s shell which means one is spin 1/2 and the other is spin -1/2 giving a total spin of 0. The s shell has no angular momentum so L=0.

considering n=2 state, there are two electrons in the s shell which again gives us 0 total angular momentum. If we went to the p shell, there are 2 electrons in the p shell, each having L=1, so we add them together to get L=2. The two electrons do not contribute spin since their net sum is zero, S=1/2-1/2=0.

considering the n=3 state, there is 1 electron in the p shell, which means S=1/2 and L=1

J is the sum of L and S, so the total angular momentum should be J=L+S=2+1+1/2=7/2

Is this correct?

 

[learning_phys]

any ideas?