E(dissociate H_2) = 11.1 eV

        E(ionize HI) = 13.6 eV

  
  Q:  How hot must a star be in order to produce a large
        fraction of its luminosity at these energies?


           The peak of the blackbody curve is at a wavelength

                                 0.00298 m*K                0.00298 m*K 
               lambda(peak)  =  -------------  -->   T  =  ---------------
                                      T                      lambda(peak)

 
           and the energy of a photon is

                             h*c
                 E     =   --------
                            lambda


           so we have

                            0.00298 m*K           E
                 T     =   --------------  *  ---------
                                 1               h*c 


           Plug in  E = 11.1 eV  =   1.79 x 10^(-18) J   
           and the standard values for h and c,


                 T     =     27,000   Kelvin


           In order for the peak wavelength to ionize atomic hydrogen, 
           the temperature is slightly higher:


                 T     =     33,000   Kelvin
                 



  Q:  Is the Sun hot enough?


           The photosphere of the Sun has a temperature of roughly
           T = 5800 Kelvin.  It produces very, very little high-energy
           radiation.