Your answer to b) should involve a factor 
. At any instant,
this factor represents the total number of photons received by
the particle during the preceding relaxation time 
. Because the
photons arrive randomly, this number fluctuates. What is the size of
these fluctuations? If everything else in your expression for <v>
is constant except for these fluctuations, what is 
, the
size of the fluctuations in the particle's velocity?