# Singlet - triplet splitting in helium

1. Mar 15, 2006

### sachi

We're asked to make a rough order of magnitude estimate of this splitting.
I know that it is caused by the coulomb interaction between the electrons. Therefore I estimated the potential between them as being
V = (e^2)/(4*Pi*epsilon*a)
where a =a0/2
I've assumed that the distance between the electrons is equal to the bohr radius in Helium. The only problem is that the actual splitting between the energy levels is only going to be a fraction of this energy (as coulomb repulsion occurs for both the energy levels, but the level with the symmetric spatial part of its wavefunction will have the two electrons closer together and therefore having a higher coulomb energy of interaction). I'm having trouble coming up with an estimate for this fraction. thanks for your help.

Sachi

2. Mar 19, 2006

### Meir Achuz

"I know that it is caused by the coulomb interaction between the electrons."
No. The triplet spin state must have one electron in the n=2 state
(by Pauli). (This assumes the singlet is the ground state.)

Last edited: Mar 19, 2006
3. Apr 13, 2008

### astrosona

this is my problem too! can any one help?

i need to plot the singlet- triplet splitting energy for the $$^{1}$$S and $$^{3}$$S states corresponding to the configurations (1s,ns), n=1 to 7, and then explain why the plot is like that!!!

please help. my problem is i don't exactly know what it means? and what should i look for! i don't understand the question!

Last edited: Apr 13, 2008