Find relative number of H atoms in n=1,2,3,4 energy levels

[xatu]

The problem:

Find the relative numbers of hydrogen atoms in the chromosphere (T=5000 K) in the n=1, 2, 3, and 4 energy levels.

Solution:

The Boltzmann distribution of energies is

$n(ε)dε=\frac{2πN}{(πkT)^{3/2}}\sqrt{ε}e^{-ε/kT}dε$

So using this I calculated the ratio to be, 1 : 5.4 x 10^-11 : 6.7 x 10^-13 : 1.5 x 10^-13.

Can anyone confirm this?

 

[TSny]

The Boltzmann distribution of energies is

$n(ε)dε=\frac{2πN}{(πkT)^{3/2}}\sqrt{ε}e^{-ε/kT}dε$

This is not applicable to this problem. You are dealing with a system that has discrete energies. See http://en.wikipedia.org/wiki/Boltzmann_distribution

 

[xatu]

Actually I used that formula, accounting for the degeneracies of the energy levels, and got the correct answer.