1. The problem statement, all variables and given/known data See the image below: 2. Relevant equations In the previous part, it was proved that a particle moves through a distance x in a material without interacting with probability P given by [itex]P=\exp(-\sigma n x)[/itex] Here σ represents the cross section of the reaction between the incoming particle and the material. n represents the target (material) particles per unit volume. 3. The attempt at a solution The only thing I have figured out so far is that we need the probability of the neutron not escaping without a reaction, so there is a factor of [itex] 1- exp(- (\sigma_f + \sigma_c) nr ) [/itex] in the equation. I am not sure of where the fractional factor at the start of the equation comes from, or why the total cross section appears in the exponent.