Day: October 21, 2015

Oh Hund

Readers who are chemists or in related fields:

I have a question where I appear to disagree with Eldest’s chemistry honors teacher.

It’s about the (ground state) electronic configurations of atoms. It’s not a problem as to which orbitals get filled first; it’s slightly more subtle. Namely, once you start filling a degenerate set of orbitals (the set of orbitals with the same n and l, having the same energy), our good buddy Hund helpfully pointed out (the maximum multiplicity rule) that first you put one electron with spin up in each orbital; only after all the orbitals with a given n,l have one spin up electron do you start putting  the second electron (now with spin down) in each orbital. For a given l, there are 2l+1 orbitals, with magnetic quantum numbers ml going from -l to l, in unit increments.

Now the question is: when you start filling the orbitals with a given l and different ml, which ml’s get filled first?

I say from highest to lowest (it has to do with maximizing the orbital angular momentum, similar to what is done with spin). Eldest’s teacher says from lowest to highest. Eldest’s book and most online resources don’t discuss this, but those that do confirm what I remember. Chemists, what say you?

Eldest came the other day with an assignment where the question was what the n, l, ml, and ms (spin up or down) of the last electron added for a given atom is. They did an example in class where they started filling up a three degenerate p orbitals (l=1) from ml=-1 and up. I said I thought it was wrong, checked online, and though he might have copied it wrong in class.  I told him to go explicitly ask his teacher today; he did, and yes, she says from lowest to highest. I am pretty sure I am right and she is wrong, but I don’t have any undergrad chem textbooks lying around to check and my trust in Wikipedia is vast but not unlimited.

Another question is what to do if the teacher is wrong. It’s easy enough to tell my kid “I am pretty sure she is wrong, but keep your head down and be prepared to learn differently in college.” The thing is that the order of filling ml’s is a relatively minor point at this level (he’s a high school sophomore); virtually nothing in his upcoming few years depends on knowing the order of filling orbitals in the right ml sequence one way or another. I also don’t want to be a douche professor parent, throwing my academic weight around and appearing to bully a high school chemistry teacher; after all, she can take it out on my kid. But if bugs me that hordes of students might learn something wrong. I will likely just let it go, though.