Possible Values for Total Angular Momentum

1. Mar 15, 2010

FloridaGators

1. List all the possible values of total angular momentum for the following

1. 3P
2. 2D

2. Relevant equations
j = s + l

3. The attempt at a solution
is this problem as simple as, for 1.
for 3p, n = 3, l = 0,1,2
since it's a p orbital, l = 1
thus j = l + s, all possible values are 3/2, and 1/2
but for 2d, i just dont know... is this theoretical? there are no d orbitals at the n = 2 level right? or am i misinterpretting the symbols?

Last edited: Mar 15, 2010
2. Mar 15, 2010

nickjer

The 3 in the superscript notation for problem (1) I believe stands for 3 = 2S+1, so the spin 'S' is equal to 1.

3. Mar 16, 2010

FloridaGators

ahh! then for (1)
does that mean S = 1, and since it is a P orbital it is L = 1
Hence J = 2.

Is this all the values that J can attain?"

4. Mar 16, 2010

nickjer

J can equal |L-S|, |L-S|+1, ... L+S-1, L+S

So find the min and max J, and all values between them.

5. Mar 16, 2010

FloridaGators

ah!
so for (1)
does that mean J can equal 0 or 1
and for (2) J = 5/2 or 3/2?
is that all the values for J?
Thanks for the help by the way!

6. Mar 16, 2010

nickjer

For (1), you said S=1 and L=1, so you have for the bounds of J... J = |1-1| = 0 and J = 1+1 = 2.

So all possible values for J are 0, 1, and 2.

7. Mar 16, 2010

FloridaGators

oh ya, duh, my mistake, how about the 2nd one. the 2nd one is right though?
5/2 and 3/2?

8. Mar 16, 2010

nickjer

Yes, that looks right.