Final answer:
The average lethargy per collision in neutron scattering can be calculated using the natural logarithm of the initial and final neutron energies after each collision. Comparing the average lethargy per collision in beryllium and graphite requires specific scattering property information.
Step-by-step explanation:
In neutron scattering, the average lethargy per collision is a measure of the average logarithmic energy loss of the neutron during each collision. It can be calculated by taking the natural logarithm of the initial neutron energy divided by the final neutron energy after each collision. In the case of beryllium and graphite, the average lethargy per collision can be determined based on the specific properties of these materials.
To calculate the average lethargy per collision, we need to know the scattering cross-section and the scattering angle distribution for neutrons in beryllium and graphite. This information is typically obtained through experiments or simulations.
On average, the number of collisions required to slow a neutron from 2 MeV to 1 eV can be determined by dividing the initial neutron energy by the average energy loss per collision. The material that requires fewer collisions to slow down the neutron is considered a better moderator. However, without specific information about the scattering properties of beryllium and graphite, it is not possible to compare them in this regard.