Q:   Estimate the speed of hydrogen atoms in the
             photosphere where T = 6000 K.

                            3 * k * T
                v  =  sqrt( --------- )
                               m


                          ( 3 * (1.38 x 10^(-23) J/K) * 6000 K )
                   =  sqrt( ---------------------------------- )
                          (         1.67 x 10^(-27) kg         )


                   =    1.2 x 10^4 m/s



  Q:   Calculate the typical size of the Doppler shift due to
             random atomic motion.

                                                 v
                 delta lambda  =   lambda  *  ( --- )
                                                 c


             So for Balmer alpha, for example,

                                                    1.2 x 10^4 m/s
                 delta lambda  =   6563 Ang  *  ( ---------------- )
                                                     3 x 10^8 m/s
  
 
                               =   0.3  Angstrom

                  

  Q:   Compare this to the equivalent and actual widths of the
                  Balmer-alpha line and the weak line in the
                  actual solar spectrum.


                    This is much less than the equivalent width
                    of strong lines such as Balmer alpha (14.6 Angstrom),
                    but comparable to the actual width of weak lines.