Chapter 43, Problem 25P

SSM (a) A neutron of mass m_n and kinetic energy K makes a head-on elastic collision with a stationary atom of mass m. Show that the fractional kinetic energy loss of the neutron is given by

$\frac{\Delta K}{K}=\frac{4m_{n}m}{{\left(m+m_n\right)}^2}$

Find $\Delta$K/K for each of the following acting as the stationary atom: (b) hydrogen, (c) deuterium, (d) carbon, and (e) lead. (f) If K = 1.00 MeV initially, how many such head-on collisions would it take to reduce the neutron’s kinetic energy to a thermal value (0.025 eV) if the stationary atoms it collides with are deuterium, a commonly used moderator? (In actual moderators, most collisions are not head-on.)