Consider a sphere consisting of pure \({ }^{235} \mathrm{U}\) (a model of a
nuclear explosive) and estimate the mean free path for fast neutrons. For fast
neutrons one may use the following data (averaged over energies)
\(\sigma_{\mathrm{f}}=1.3[\) barn \(]([1], 201) ; \eta=2.4([1], 218) ; \rho=19
\times\) \(10^{3}\left[\mathrm{~kg} \mathrm{~m}^{-3}\right]\). (a) Calculate
\(\Sigma_{f}, \lambda_{f}\) and (b) make a rough estimate of the radius
\(\mathrm{R}\) for which the leakage will be half of the neutrons produced and
argue that this will be about the critical radius; calculate the corresponding
critical mass (an accurate calculation will give \(50[\mathrm{~kg}]\) ).
