singlet vs. triplet

irockhard
Posts: 53
Joined: Wed Jan 23, 2008 10:40 pm

singlet vs. triplet

Postby irockhard » Thu Oct 08, 2009 1:56 pm

Can anyone explain to me why two electrons in a S state are in a singlet combination but not triplet? For example, for helium 1s^2 (where 2 is in the exponent), or for carbon (1s)^2(2s)^2(2p)2, all the electrons with S angular momentum form singlet pair. Why?

physics_auth
Posts: 160
Joined: Sat Jul 18, 2009 7:24 pm

Re: singlet vs. triplet

Postby physics_auth » Thu Oct 08, 2009 2:47 pm

irockhard wrote:Can anyone explain to me why two electrons in a S state are in a singlet combination but not triplet? For example, for helium 1s^2 (where 2 is in the exponent), or for carbon (1s)^2(2s)^2(2p)2, all the electrons with S angular momentum form singlet pair. Why?


The answer below applies to your question. I had sth different in mind ... so my answer doesn't apply here and I removed it. However, the ground state configuration of atoms is dictated both by the Pauli exclusion principle and the principle of least energy.
Last edited by physics_auth on Sun Oct 11, 2009 3:05 pm, edited 3 times in total.

kroner
Posts: 218
Joined: Fri Sep 25, 2009 1:58 am

Re: singlet vs. triplet

Postby kroner » Sun Oct 11, 2009 1:33 pm

This might be too late since it's after the test, but the Pauli exclusion principle comes into play here. The state of any pair of electrons has to be antisymmetric. If the orbital state is symmetric then the spin state has to be antisymmetric and vice versa. Both having the same orbital quantum numbers is necessarily symmetric, so the spin state has to be the antisymmetric singlet. The triplets are the symmetric spin states which are disallowed.




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