Possible Values for Total Angular Momentum

[FloridaGators]

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

1. ³P
2. ²D

Homework Equations

j = s + l

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 don't know... is this theoretical? there are no d orbitals at the n = 2 level right? or am i misinterpretting the symbols?

 

[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.

 

[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?"

 

[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.

 

[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!

 

[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.

 

[FloridaGators]

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

 

[nickjer]

Yes, that looks right.