Instead of looking at the emission spectrum, we can also look at the absorption spectrum of hydrogen. Say some hydrogen atoms are sitting at the surface of the sun. From the interior of the sun, white light tries to come out and the atoms at the surface absorb what they can. The atoms in the ground state will now absorb the Lyman series and this will lead to dark lines if we analyze the light coming from the sun. The presence of these lines will tell us that there is hydrogen at the surface of the sun. We can also estimate the surface temperature as follows. Let T be the surface temperature. The probabilities P(n=1) and P(n=2) of an atom being at n=1 and n=2, respectively, are related by Boltzmann's formula
P(n=1)P(n=2)=4e−(E2−E1)/kT
where the factor 4 is due to the degeneracy of the n=2 level. Now only atoms in n=2 can produce the Balmer lines in the absorption spectrum. The relative strength of the Balmer and Lyman lines will tell us P(n=2)/P(n=1), from which we may infer T. Show that for T=6000 K, P(n=2)/P(n=1) is negligible and that it becomes significant only for T≃105 K. (The Boltzmann constant is k≃9×10−5 eV/K. A mnemonic is kT≃401 eV at room temperature, T=300 K.)