Q:  What is the temperature T at which
      one might expect the number of hydrogen
      atoms in the n=2 state to become
      significant?


          We have
                          -10.2 eV
               T   =   --------------
                         k *  ln(2/8)


                           -10.2 eV 
                   =  -----------------------
                      (0.000086 eV/K) * (-1.39)


                   =  86,000 Kelvin