I wonder how to compute statistical weight of a negative ion (anion) of hydrogen. I know that statistical weight of the electron is ge=2, of proton is also gp=2 as they both have spin equal to 1/2. Statistical weight of hydrogen atom is gH=gp×ge=4. Assuming that the electrons in negative ion are on different energy levels I get gA=gp×ge×ge=8. Is that correct?
The multiplicity of electron energy levels in the hydrogen atom is 2n^2; therefore, if the electrons are on (different) n1 and n2
levels, I think that formally the multiplicity should be calculated as 2(2n1^2)(2n2^2).
Formally, because only the ground state of H- is bound (Physical Review Letters. 38 (12): 643).
As said in Russian Wikipedia (https://ru.wikipedia.org/wiki/Гидрид-ион), hydride-ion (negative ion of hydrogen) has a pair of electrons in 1s2 state. Their spins are in opposite directions so the total spin of the electrons is 0. Hence, their statistical weight is gee=2S+1=1, and the statistical weight of the hydride-ion is that of it nucleus, i.e. g-=2.
I agree completely. I understood that your question was regarding the multiplicity when electrons are on different energy levels.
( "Assuming that the electrons in negative ion are on different energy levels I get ...")
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