Homework Help: Modern physics, quantum numbers, subshells

1. Mar 14, 2012

fluidistic

1. The problem statement, all variables and given/known data
Find all the terms of an atom whose last subshell is np³.

2. Relevant equations
$M_L=\sum _i m_{l _i}$
$M_S=\sum _i m_{s _i}$

3. The attempt at a solution
My professor did the same exercise but with np². Basically he wrotes all the possible quantum numbers for the atom:
1)$m_l=1$, $m_s=1/2$. 2)$m_l=0$, $m_s=1/2$. 3)$m_l=-1$, $m_s=1/2$
1')$m_l=1$, $m_s=-1/2$. 2')$m_l=0$, $m_s=-1/2$. 3')$m_l=-1$, $m_s=-1/2$
Then he calculated all the possible values for $M_L$ and $M_S$. There are 15 values in total.
After this, there is an obscure step to me (he counted I don't really know what) and went to the conclusion that the solution to the problem is $^1 D ^3 P ^1 S$. Where the upper script is worth $2S+1$.
So I did the same method as him for np³ (I guess this notation means that there are 3 electrons on the subshell p or an arbitrary n?). I got 20 values for $M_L$, $M_S$. I'm stuck at doing the obscure step now. I have all possible values for $M_L$ and $M_S$.
Can someone explain me what I should do next?
Another question is... since n seems arbitrary, can I for example take $n=1$, so that $l=0$ and $m_l=0$. My professor seems to have taken n=2 for some misterious reason to me. Does someone understand why?
Edit: since there are at least 3 electrons I guess I cannot take n=1, since at least n=2. Ah... n must equal 2... ok that's what I considered, good. So I'm stuck where I pointed out.

Last edited: Mar 14, 2012