Final answer:
In neutron scattering with beryllium and graphite, the average lethargy per collision and the number of collisions required to slow a neutron from 2 MeV to 1 eV in both systems are important factors to consider. The system that requires fewer collisions is considered a better moderator.
Step-by-step explanation:
a. The average lethargy per collision is determined by the logarithmic energy loss of the neutron. In both systems, beryllium and graphite, the average lethargy per collision can be calculated as the ratio of the change in logarithmic energy to the number of collisions. The average lethargy per collision in beryllium is computed as Δlethargy/ΔN, where Δlethargy is the change in logarithmic energy (ln(E2/E1)), and ΔN is the number of collisions required to slow the neutron down. Similarly, for graphite, the average lethargy per collision will also be Δlethargy/ΔN.
b. To determine the number of collisions required to slow a neutron from 2 MeV to 1 eV, we can use the average lethargy per collision calculated in part (a) and divide it by the change in lethargy required to reach the desired energy. The system that requires fewer collisions to slow down the neutron is considered a better moderator.