(a) A neutron in a nuclear reactor makes a head-on elastic collision with a carbon nucleus, which is initially at rest and has 12 times the mass of a neutron. What fraction of the neutron's initial speed is lost in the collision?

(b) Repeat part (a) if instead the neutron collides head-on with a deuteron (mass twice that of the neutron) within a heavy-water \(\left(D_{2} 0\right)\) molecule? (Carbon nuclei and deuterons can both be used as moderators in a reactor, whose purpose is to moderate their speeds, i.e. slow down neutrons, as slower neutrons are more likely to cause nuclear fission.)