# Spectroscopic Notation Problem

njdevils45
Moved from a technical forum, so homework template missing
Question

(a) Write down the quantum numbers for the states described in spectroscopic notation as 2S3/2, 3D2 and 5P3.
(b) Determine if any of these states are impossible, and if so, explain why. (Please note that these could describe states with more than one electron.)

My Attempt

A)

I came up with the quantum numbers for everything that I'm pretty sure is correct. Was hoping I could get a double check on this.
2S3/2 l = 0, s = 1/2, j = 3/2
3D2 l = 2, s = 1, j = 2
5P3 l = 1, s = 2, j = 3

B)
I'm almost 100% confident that 2S3/2 is impossible because when l = 0, j must = 1/2.

I'm not sure about the other two because I don't know all the rules for what s can be compared to l and j.

Any help would be greatly appreciated. Thank you!

DrClaude
Mentor
I'm almost 100% confident that 2S3/2 is impossible because when l = 0, j must = 1/2.
Not exactly. When ##L=0##, ##J=S##.

I'm not sure about the other two because I don't know all the rules for what s can be compared to l and j.
What are the rules of addition of angular momenta? In other words, given ##L## and ##S##, what are the possible values of ##J=L+S##?

kuruman
Homework Helper
Gold Member
(A) is correct
You are correct that 2S3/2 is impossible.

The rule is that the maximum value of J is L+S, the minimum value of J is |L-S| and J takes all values in between in steps of 1.

njdevils45
Not exactly. When ##L=0##, ##J=S##.

So to say that when l = 0, j must = 1/2 for the first state is correct right?

What are the rules of addition of angular momenta? In other words, given ##L## and ##S##, what are the possible values of ##J=L+S##?

Does this mean that j could only equal 1,2, or 3 for the second and third one? Therefore the value for j is possible for those two?
Is the value for s possible for the other two though? Is s allowed to be integer? I know for a fact that the values for l is possible for all three of them, and assuming that s is correct, the value for j is possible for the 2nd and third state, but are the values of s possible for the 2nd and third state?

njdevils45
(A) is correct
You are correct that 2S3/2 is impossible.

The rule is that the maximum value of J is L+S, the minimum value of J is |L-S| and J takes all values in between in steps of 1.

So for the second and third states, j is correct assuming the value for s is correct? In that case is the value for s possible for those two states?

DrClaude
Mentor
So to say that when l = 0, j must = 1/2 for the first state is correct right?
Correct.

Does this mean that j could only equal 1,2, or 3 for the second and third one? Therefore the value for j is possible for those two?
Yes on both.

Is the value for s possible for the other two though? Is s allowed to be integer? I know for a fact that the values for l is possible for all three of them, and assuming that s is correct, the value for j is possible for the 2nd and third state, but are the values of s possible for the 2nd and third state?
The spectroscopic notation is based on ##S##, the total spin of the electrons. It can have a half-integer or an integer value.

njdevils45
The spectroscopic notation is based on ##S##, the total spin of the electrons. It can have a half-integer or an integer value.

So in that case the 2nd and third states for the problem are both definitely possible?

DrClaude
Mentor
So in that case the 2nd and third states for the problem are both definitely possible?
Yes.

njdevils45
Yes.
Thank you!