On average, a neutron loses 63% of its energy in an elastic collision with a hydrogen atom and 11% of its energy in an elastic collision with a carbon atom. The numbers are lower than the ones we have been using in earlier problems because most collisions are not head-on. Calculate the number of collisions, on average, needed to reduce the energy of a neutron from 2 MeV to 0.02 eV (a desirable outcome for reasons explained in Problem 129) if the neutron collides with

(a) Hydrogen atoms and

(b) Carbon atoms.