Q:  In order for hydrogen gas to absorb the Balmer alpha photons,
           atoms must be in the n=2 state.  How hot will the
           gas have to be in order for the number of atoms in
           n=2 to be as large as the number of atoms in the
           ground state, n=1?
           


       If one ignores the degeneracy terms gb/ga for the moment,
       all that matters is the temperature at which

               kT  =  E(2) - E(1) = 10.2 eV = 1.63 x 10^(-18) J

       Therefore
                       1.63 x 10^(-18) J
                T  =  -------------------   =  118,000 K    (approx version)
                       1.38 x 10^(-23) J/K


       If we include the degeneracy terms, g(1) = 2 and g(2) = 8,
       then the temperature drops a bit to only 85,000 Kelvin.
       That is still very hot, much hotter than the great majority
       of stars.