# Homework Help: Lowest energy term symbol for nitrogen

1. Oct 19, 2011

### eyearena

1. The problem statement, all variables and given/known data
Lowest energy term symbols for Nitrogen

2. Relevant equations

L=l1+l2, l1+l2-1, l1-l2

S=s1+s2, s1-s2

J=S+L, S-L

3. The attempt at a solution

So I think I'm doing this right up until finding the J value.
So the configuration of nitrogen is 1s22s22p3, so were working with 3 electrons

for the first 2e-

L`=1+1=2, 1+1-1=1, 1-1=0

coupling those to the 3rd electron

L=2+1=3, 2+1-1=2,2-1=1 so L=3,2,1

L=1+1=2,1+1-1=1, 1-1=0 so L=2,1,0

L=1-0=1 so L=1

so therefore there is 1F, 2D,3P,1S

S for the first 2e-

S=1/2 + 1/2=1

S=1/2 - 1/2=0

coupling to 3rd e-

S=1+1/2=3/2

S=0+1/2=1/2

Now for the J value I'm getting confused on which L and S values to use

ex: since there is 2 D terms how do I know which to use????????:

J= L+S, L-S

J=2+3/2=7/2 so that TS: 4D7/2

J=2-3/2= 1/2 so that TS: 4D1/2

J=2+1/2=5/2 so that TS: 2D5/2

J=2-1/2= 3/2 so that TS: 2D3/2

I feel like I'm missing something pretty elementary here and my book doesn't really show many examples for finding the term symbol for more than 1 electron that include the J values.
It said to list all possible ones, but it might mean just the lowest one (since it says that too) which means I guess I would use Hund's rule.
Despite that fact I would still like to know which how to use the L and S values to find the possible term symbols
Thank you for the help!

Last edited: Oct 19, 2011