It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of pd and pc are respectively.

Case 1 : Collision of Neutron with deuterium :
e=1
Momentum conservation
mu+0=mv+2mv′ ⟹ u=v+2v′.. (1)
Newton's equation of collision
e=v′−v0−u ⟹ v′=u+v.. (2)
Solving (1) and (2), we get
v=−u3
Fractional loss in kinetic energy of neutron
Pd=12mu2−12mv212mu2 ⟹ Pd=12mu2−12m(−u3)212mu2=0.89
Case 2 : Collision of Neutron with Carbon :
Let mass of carbon = 12m
Momentum conservation
mu+0=mv+12mv′ ⟹ u=v+12v′.. (1)
Newton's equation of collision
e=v′−v0−u ⟹ v′=u+v.. (2)
Solving (1) and (2), we get
v=−11u13
Fractional loss in kinetic energy of neutron
Pc=12mu2−12mv212mu2 ⟹ Pc=12mu2−12m(−11u13)212mu2=12mu2−121121u216912mu2=144169=0.28