Collision between neutrons and nucleus of the moderator results in slowing down the newly born fast neutrons. Such a collision is depicted in the figure. The striking fast neutron has an initial...

Collision between neutrons and nucleus of the moderator results in slowing down the newly born fast neutrons. Such a collision is depicted in the figure. The striking fast neutron has an initial energy
E_n

and an initial momentum
p_n
. The target nucleus is initially at rest. Considering an elastic scattering, following the collision, the scattered neutron has an energy of
E'
_n

and momentum of
p'
_n

while the recoiling nucleus has an energy of
E'
_N

and momentum of
p'
_N
. Use the conservation of momentum and energy to drive a relation for energy of the scattered neutron in terms of the initial neutron energy and mass number of the target nucleus. [Hint: Find the momentum of the recoiling nucleus in terms of the momentum of the initial and the scattered neutron. Substitute for momentum terms
(p
²
= 2mE) and for the recoiling energy from the energy balance].