# Degeneracy of hydrogen energy levels

1. May 17, 2012

### lonewolf5999

Consider a universe where the intrinsic spin of the electron is S = 5/2, but all other parameters and rules of quantum mechanics are the same. Find the degeneracy of the n=1 and n=2 levels of hydrogen.

My understanding is that electrons in an atom have 4 quantum numbers n,l,ml,ms, and different electrons can't have all 4 quantum numbers being the same. Since we have S = 5/2, we can have ms = -5/2, -3/2, -1/2, 1/2, 3/2, 5/2. For n = 1, usual rules tell us l = 0 and ml = 0, so since ms can have 6 different values, the n = 1 state has a degeneracy of 6 and can accept up to 6 electrons.

For n = 2, l = 0, the reasoning is the same as above, so that orbital also has a degeneracy of 6. For n = 2, l = 1, ml = -1, 0 or 1, and for each of these ml we can have 6 different ms, so we have a degeneracy of 18 for n = 2, l = 1 and thus a total degeneracy of 24 for n = 2.

Is this reasoning correct, or am I missing something in the problem?

Last edited: May 17, 2012
2. May 17, 2012

### vela

Staff Emeritus
Yeah, you got it.

3. May 17, 2012