One of my homework assignments in atomic physics was the following:

Given electrons had a Spin of $S = 3/2$, what would be the number of the first 4 noble gasses (complete shells)?

The obvious expected answer is 4, 20, 56 and 120, because now one can put $4(2l+1)$ electrons on each subshell.

My problem with the question is the hypothetical nature. We are modelling physics after nature, so can we really be sure that Hund's rules would still be valid for that case? If so, why?

  • $\begingroup$ I think the exercise simply tries to establish that you understand Hund's rule, it is not trying to pretend that it is an actual law of nature or an axiom of a theory. It is neither and it breaks plenty of time even for the natural case. $\endgroup$
    – CuriousOne
    Jun 9, 2015 at 18:58

1 Answer 1


Yes, you can be sure because both $S = 1/2$ and $S = 3/2$ are fermions that must respect the Pauli exclusion principle.

  • $\begingroup$ Why would electrons still fill subshell by subshell? Wouldn't it be possible that there are exceptions from the rules (like for silver which has $[Kr]4d^{10}5s$ instead of the expected $[Kr]4d^95s^2$ configuration? Isn't it possible that electrons fill the $1p$ orbital after the $1s$ orbital in that case? $\endgroup$
    – iblue
    Jun 9, 2015 at 19:00
  • $\begingroup$ You can't be 100% sure, as you yourself've pointed out, even in the case of $S=1/2$ you have exceptions (as CuriousOne pointed in his comment, Hund's rule is not a fundamental law of nature). But I'd expect based on the solutions of energy levels for hydrogem atom with $S=3/2$ that the behavior would be quite similar. $\endgroup$ Jun 9, 2015 at 20:06

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