Help with Atomic Calcium Electron Configurations

[physicisttobe]

Homework Statement

deriving the term symbols

Relevant Equations

J= L+S

Hi everyone!
I need some help in a specific task.
It´s about this problem:
An excited state of atomic calcium has the electron configuration 1s 2 2s 2 2p6 3s 2 3p6 3d1 4f 1 . (a) Derive all the term symbols (with the appropriate specifications of S, L, and J) for the electron configuration. (b) Which term symbol corresponds to the lowest energy of this electron configuration? (c) Consider a 3 F2 level of calcium derived from a different electron configuration than that shown above. Which of the term symbols determined in part (a) can participate in spectroscopic transitions to this 3 F2 level?

I´m not sure if I my solutions are correct. So could you take a look?
First, I start with a), then I'll post b) and c). I hope that you can help me, thanks in advance!

 

[DrClaude]

What about the $S=0$ terms?

 

[physicisttobe]

What about the $S=0$ terms?

Oh, you are right, I also need to consider S=0.
But what about the other term symbols? Are they correct?

 

[DrClaude]

Oh, you are right, I also need to consider S=0.
But what about the other term symbols? Are they correct?

Yes.

 

[physicisttobe]

Thank you. I post the rest of the task a) here :

Now to question b): How exactly should I solve this problem?
My idea would be: When you draw the electron configuration you‘ll see that 3d corresponds to the lower energy, and l=2 corresponds to d orbital. This means that all term symbols with the letter D have the lowest energy? Is this consideration correct?

 

[DrClaude]

I don't know how to do b. Maybe you are to use Hund's rule, but they actually don't apply here.

 

[physicisttobe]

All right, I try to figure out how to solve b), but thank you!
And what´s about question c) ? How should I proceed here?

 

[DrClaude]

And what´s about question c) ? How should I proceed here?

Selection rules.

 

[physicisttobe]

This means Δmj = +/-1, 0 and Δl= +/- 1
This applies to these term symbols:

Is it correct?

 

[DrClaude]

This means Δmj = +/-1, 0 and Δl= +/- 1
This applies to these term symbols:
View attachment 314769
Is it correct?

No. First, you are not told about the electronic configuration of the other state, but it is reasonable to assume that $\Delta l = \pm 1$ is satisfied. Second, $\Delta m_j$ is not in play, as you are looking at transitions between terms (which include all $m_j$), not between levels.

What you need to consider are the selection rules for $\Delta L$, $\Delta J$, and $\Delta S$.

Buy the way, I did not notice that in your answer above you had terms like ⁴G and ²P (this is the problem when you submit your answer as a scan of handwritten material: it can be hard to read). These terms are not correct. Revise what the superscript number corresponds to.

 

[physicisttobe]

No. First, you are not told about the electronic configuration of the other state, but it is reasonable to assume that $\Delta l = \pm 1$ is satisfied. Second, $\Delta m_j$ is not in play, as you are looking at transitions between terms (which include all $m_j$), not between levels.

What you need to consider are the selection rules for $\Delta L$, $\Delta J$, and $\Delta S$.

I'm not sure if I understand you correctly, but then it must be the term 3G_3? Because ΔS=0, ΔL=1, Δl=1 and ΔJ=1

Buy the way, I did not notice that in your answer above you had terms like ⁴G and ²P (this is the problem when you submit your answer as a scan of handwritten material: it can be hard to read). These terms are not correct. Revise what the superscript number corresponds to.

Oh, yes you`re right, for L= 4 and S=1 it must be 3G5, 3G4, 3G3. Is it correct?

 

[DrClaude]

I'm not sure if I understand you correctly, but then it must be the term 3G_3? Because ΔS=0, ΔL=1, Δl=1 and ΔJ=1

There are many terms for which you will have transitions with ³F₂.

Oh, yes you`re right, for L= 4 and S=1 it must be 3G5, 3G4, 3G3. Is it correct?

Correct for the G terms. Make sure all the others are correct ($S=0,1$, so you should get singlet and triplet terms only).