Partition function help?

Question

How can I estimate the probability that a Hydrogen atom at room temperature is in one of its first excited states (relative to the probability of being in the ground state). "Don't forget to take degeneracy into account"

Answer 1

Let A = N * e^(-E/kT),
where
N = degeneracy of the first excited state (do they mean just the 2S state, or both the 2S and 2P states combined?)
e = 2.71828...
E = energy difference between first excited state and ground state
k = Boltzmann's constant
T = absolute temperature

Then the probability of being in one of the excited states is
A / (Ng+A)

where Ng is the degeneracy of the ground state.

Note, "A" should be a very small number, much much smaller than 1, so that the probability will be small also.