Classical analysis gives the differential scattering cross section for a
repulsive 
Coulomb potential to be
where 
is the distance of closest
possible approach of an alpha particle of charge ze=2e, mass M and
traveling at velocity v toward a heavy nucleus of charge Ze. Note
that, unlike the case of scattering from hard spherical reflectors,
the cross-section depends on both the velocity of the incoming
particles and the scattering angle. Using the same approach as in
(3.5), the following question:
A beam of 
-particles, of kinetic energy 5 MeV and intensity
particle/sec, is incident normally on a thin foil of thickness
cm consisting of an unknown element. Assuming
that there are 
atoms per cm 
of the
material, if at 
, 55 counts per hour are observed in a
detector area 0.25 cm 
placed at a distance of 100 cm from the
foil, which element most likely composes the film?