Probability of occupancy in energy level as T->0 or inf.

[indie452]

an atom has 3 non-degenerate E levels, = 0, e, 2e

What is the prob of occupancy of each energy level as T-> zero and infinty and why?

for E=0
I imagine that the prob for T->0, is 1 is one or approaching one as as the temp approaches absolute zero electrons occupy the lowest state
as T->infinity, i thought at first that the prob would approach zero as i would think everything would be more likely to occupy higher levels.

but then i think i read somewhere that as T->inf. the prob for each level is equal.

for the others i thought to use Boltzmann

so for E=e...prob = (1/kT)exp[-e/kT]
E=2e...prob = (1/2kT)exp[-2e/kT]

but wouldn't this give the same answers?

 

[jbsteele]

For T->0, the probability of occupancy of each energy level is 1. This is because at absolute zero, all electrons occupy the lowest energy level due to the Pauli exclusion principle. For T->infinity, the probability of occupancy of each energy level is equal. This is because at infinite temperature, all energy levels become equally populated and thus the probability of occupancy is the same for each energy level.