Selection rules in electron transitions

[nomadreid]

TL;DR Summary

Do the selection rules for electron transitions imply that in photon absorption/emission, an electron can only jump between s and p, or p and d, or d and f? So, e.g., an electron jumping from shell 5 to 6, then from 6 to 7, would end up in a different orbital than an electron jumping directly from 5 to 7?

Not sure if this belongs in Chemistry or Physics.

Even less sure if I understand the selection rules for electron transition correctly; hence this question. So I would be grateful for someone to please correct the following:

Letting n and m be energy levels
An electron that absorbs a photon can only transition in one of the following ways:
from ns to mp,
from np to (ms or md),
from nd to (mp or mf)
from mf to md
and an electron that emits a photon can only transition also in those ways.

Going up a shell does not dictate whether it goes "up" or "down" in the spdf orbitals.

If the above makes any sense, then for example, if
---an electron Alice started in the 5th shell and jumped first to the 6th shell, then to the 7th shell, and
--- another electron Bob started in the 5th shell and jumped directly to the 7th shell,
the possible transitions would be

Alice
5s to 6p to 7d
5p to 6s to 7p
5p to 6d to 7p
5p to 6d to 7f
5d to 6p to 7s
5d to 6p to 7d
5d to 6f to 7d

Whereas Bob:
5s to 7p
5p to 7s
5d to 7p
5d to 7f
5f to 7d

Therefore Alice and Bob would never end up at the same place. Right? If this is correct but the reasoning is different, then why?

Finally: does the polarization of the photon have anything to do with the (correct version of) the selection rules?

Many thanks in advance, with apologies for the conceptual mess.

 

[dlgoff]

Somewhere I've got this text:

Selection rules are rather complicated.
Check out this site: https://chem.libretexts.org/Bookshe...f_Atoms/6.03:_Line_Spectra_and_the_Bohr_Model

 

[nomadreid]

Thanks, dlgoff. Upon your recommendation, I have obtained that book, and found "selection rules" in the index. I shall look into it. Also, the link you sent is a nice summary of the basic theory of transitions.