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

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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?
 

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