In a thermal nuclear reactor, fast-moving neutrons produced during the induced fission of uranium-235 must be slowed down by a moderator to increase the probability of causing further fission.
During a head-on elastic collision between a fast neutron of mass m m\,m and a stationary moderator nucleus of mass MMM, the fraction of the neutron's initial kinetic energy transferred to the moderator nucleus, ΔEkEk\displaystyle \frac{\Delta E_{\text{k}}}{E_{\text{k}}}EkΔEk, is given by:
ΔEkEk=4mM(m+M)2 \frac{\Delta E_{\text{k}}}{E_{\text{k}}} = \frac{4mM}{(m+M)^2} EkΔEk=(m+M)24mMAssuming a neutron has a mass of 1 u1\text{ u}1 u, which of the following statements correctly compares the energy transfer per collision for deuterium (M=2 uM = 2\text{ u}M=2 u) and carbon-12 (M=12 uM = 12\text{ u}M=12 u), and identifies the superior moderator based on this mechanism?
Deuterium transfers 89\frac{8}{9}98 of the neutron's kinetic energy, while Carbon-12 transfers 48169\frac{48}{169}16948. Deuterium is a more effective moderator because its mass is closer to that of a neutron.
Deuterium transfers 19\frac{1}{9}91 of the neutron's kinetic energy, while Carbon-12 transfers 121169\frac{121}{169}169121. Carbon-12 is a more effective moderator because its larger mass allows greater momentum absorption.
Deuterium transfers 49\frac{4}{9}94 of the neutron's kinetic energy, while Carbon-12 transfers 24169\frac{24}{169}16924. Deuterium is a more effective moderator because its mass is closer to that of a neutron.
Deuterium transfers 89\frac{8}{9}98 of the neutron's kinetic energy, while Carbon-12 transfers 1213\frac{12}{13}1312. Carbon-12 is a more effective moderator because more nucleons are available to distribute the energy.
