Helium has two electrons. The only configuration they can have (ground state) is spin $\frac{1}{2}$ for one and $-\frac{1}{2}$ for the other one, by the Pauli exclusion principle, which is definitely a singlet state. So I'm assuming it's something to do with excited states. If that's the case, there's an exercise in my textbook which asks for an explanation of the energy ordering of the spin triplet state of helium, but wouldn't that depend on which excited state it was in?

I have read the answers to the related question 'What causes the triplet state in helium?' and still don't understand what the 'energy ordering' would be.

  • 2
    $\begingroup$ Why do you think it has something to do with excited states? That a combined system of two spin-1/2 particles is the sum of a spin-0 singlet and a spin-1 triplet is a standard result that holds very generally. $\endgroup$
    – ACuriousMind
    Oct 31, 2016 at 12:32
  • 1
    $\begingroup$ Take a look here. $\endgroup$
    – Charlie
    Oct 31, 2016 at 12:36
  • 1
    $\begingroup$ This link should clear your doubts.....and i have to disagree with @ACuriousMind here; in the ground state, both the electrons are in the $1s$ orbital which means their spin should be antisymmetric according to the exclusion principle...meaning ground state is the singlet state in case of Helium.......for it to have a triplet state, same spins imply electron must occupy different orbitals (spatial states with different quantum numbers) $1s$ and the next energy level $2s$...which is necessarily an excited state $\endgroup$ Oct 31, 2016 at 13:22
  • 1
    $\begingroup$ My conclusion being that singlet state (ground state) has less energy than the triplet state (excited state).........it is an altogether different question though related ....that which of the excited states (triplet or singlet) is energetically more favourable...the answer is in the link posted by @Charlie $\endgroup$ Oct 31, 2016 at 13:27
  • 1
    $\begingroup$ @Muthumanimaran What was meant is that there is only one configuration IN ground state not that the only possible state IS ground state. $\endgroup$
    – user13948
    Oct 31, 2016 at 13:44

1 Answer 1


If we ignore spin-orbital coupling, helium atom's wavefunction can be represented by a product of spin part and spatial part. Triplet state is a state where spin part of the wavefunction is symmetric with respect to exchange of two electrons.

This means that the spatial part must be antisymmetric, since electrons are fermions. But this implies that there must be a node in the wavefunction — a hypersurface where the wavefunction vanishes. This can only happen in an excited state, since ground-state solution of non-symmetrized Schrödinger equation has no nodes and is always non-degenerate, so has strictly less energy. This gives you the answer about ordering of two lowest energy states with zero angular momentum.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.