Question 5.2: Show that when a Uranium-235 nucleus absorbs a thermal neutr......

From the cross sections shown in Table 5.6, we can see that the fission cross section for Uranium-235 is about 585 barns and that the radiative capture cross section is about 99 barns. The total absorption cross section for the thermal neutron is therefore σ_a = σ_c + σ_f = 585 barns + 99 barns = 684 barns.
The probability of the nucleus splitting apart due to fission alone is therefore P_f = σ_f/σ_a = 585/684 = 0.855, and the probability of the nucleus capturing the neutron and emitting a gamma ray is therefore P_c = σ_c/σ_a = 99/684 = 0.145. Note that if we had measured these probabilities as just as the ratio of the fission probability to the capture probability, then the values for these ratios would be P_c = σ_c/σ_f = 99/585 = 0.169 ≈ 17% and P_f = (1.0 – P_c) ≈ 83%, respectively. So the absorption of a neutron by a U-235 nucleus does not necessarily guarantee that it will split apart.