Q:  How long does it take a photon to travel from the core of
           the Sun to the Earth?


         In this case, we need to break the journey into two pieces:
             a) from center of Sun to outer edge of photosphere
             b) from photosphere to Earth


         In the first stage of the journey, the photon can travel only
             a very short distance before it is scattered or absorbed
             and re-emitted, so we need to use a random walk to compute
             the time it takes.


           Distance from core to photosphere    R  =  6.95 x 10^(8) m

           speed of photon                      c  =  3.0 x 10^(8) m/s

           mean free path                       l  =  0.002 m


          First, we compute the number of steps in the random walk

                          ( R ) 2        (6.95 x 10^(8) m)^2
                   N   =  (---)     =   --------------------
                          ( l )              (0.002 m)^2


                       =   1.2 x 10^(23) steps


          Now, the time required to travel all those steps is


                   t   =  (time for one step) * (number of steps)

                             0.002 m
                       =  ---------------  *  1.2 x 10^(23)
                           3 x 10^(8) m/s


                       =    8 x 10^(11) s   =  approx 25,000 years



          Since energy generated at the center of the Sun takes
          25,000 years (given our starting assumptions) to reach
          the photosphere, the Sun will continue shining and
          heating the Earth for millenia after the Wicked Witch
          waves her wand.

          She will probably be disappointed.