Is the 52D5/2 Level of Na Atom Degenerate?

[PatF]

Homework Statement

This is a problem that was on a quiz. The quiz has already been graded and handed back and the faculty member graded very gently. (This means I passed when I think should not have.) I have thought about the answer I gave at the time and it was pretty bad. My current answer is below. Tell me if it right/wrong/stupefyingly boneheaded.

Q: "The valence electron of the Na atom is at the 5²D_5/2 level. Is this level degenerate? If so, how many folds? Give the values of all the appropriate quantum numbers for each degenerate member. Exhibit these values in tabular form with one line for each degenerate member."

Homework Equations

No equations.

The Attempt at a Solution

The above notation is spectroscopic notation telling me that the principal quantum number is 5 and the orbital angular momentum number is 2. Therefore, spin must be 1/2 since we have the subscript 5/2. In this configuration, we could have m_j equal to -5/2, -3/2,-1/2,1/2,3/2,5/2.

So, my answer should be:

A) The level is degenerate.
B) There are 6 folds.
C) The table would look as follows:

n l m_j s
5 2 -5/2 1/2
5 2 -3/2 1/2
5 2 -1/2 1/2
5 2 1/2 1/2
5 2 3/2 1/2
5 2 5/2 1/2

Is the above right or wrong?

Does anyone have a good reference for translating between quantum numbers - which I think I understand - and spectroscopic notation which is a lot more confusing?

Thanks.

 

[olgranpappy]

Homework Statement

This is a problem that was on a quiz. The quiz has already been graded and handed back and the faculty member graded very gently. (This means I passed when I think should not have.) I have thought about the answer I gave at the time and it was pretty bad. My current answer is below. Tell me if it right/wrong/stupefyingly boneheaded.

Q: "The valence electron of the Na atom is at the 5²D_5/2 level. Is this level degenerate? If so, how many folds? Give the values of all the appropriate quantum numbers for each degenerate member. Exhibit these values in tabular form with one line for each degenerate member."

Homework Equations

No equations.

The Attempt at a Solution

The above notation is spectroscopic notation telling me that the principal quantum number is 5 and the orbital angular momentum number is 2. Therefore, spin must be 1/2 since we have the subscript 5/2.

You don't have to deduce the spin since
the superscript "2" of the spectroscopic notation ${}^2D_{5/2}$ tells you that the spin is
$$2S+1=2\;,$$
I.e.,
$$S=1/2$$

In this configuration, we could have m_j equal to -5/2, -3/2,-1/2,1/2,3/2,5/2.

So, my answer should be:

A) The level is degenerate.
B) There are 6 folds.
C) The table would look as follows:

n l m_j s
5 2 -5/2 1/2
5 2 -3/2 1/2
5 2 -1/2 1/2
5 2 1/2 1/2
5 2 3/2 1/2
5 2 5/2 1/2

Is the above right or wrong?

Does anyone have a good reference for translating between quantum numbers - which I think I understand - and spectroscopic notation which is a lot more confusing?

The spectroscopic notation and the quantum numbers are related by
$${}^{(2S+1)}{\mathcal{L}}_J\;,$$
where
$\mathcal{L}$ is S or P or D or F or G etc
depending on whether the angular momentum quantum number
L is 1 or 2 or 3 or 4 or 5 etc, respectively