All Problems Nuclear Reactions
Problem 6.285
Thermal neutrons fall normally on the surface of a thin gold foil consisting of stable Au \(^{197}\) nuclide. The neutron flux density is \(J=1.0 \cdot 10^{10}\) part. \(/\left(\mathrm{s} \cdot \mathrm{cm}^{2}\right) .\) The mass of the foil is \(m=10 \mathrm{mg}\). The neutron capture produces beta-active Au \(^{198}\) nuclei with half-life \(T=2.7\) days. The effective capture cross-section is \(\sigma=98 \mathrm{~b} .\) Find: (a) the irradiation time after which the number of Au \(^{197}\) nuclei decreases by \(\eta=1.0 \%\) (b) the maximum number of Au \(^{198}\) nuclei that can be formed during protracted irradiation.
\(6.285 .\) (a) \(t=\eta / \sigma J=3 \cdot 10^{6}\) years; (b) \(N_{\max }=J \sigma N_{0} T / \ln 2=\) \(=1.0 \cdot 10^{13}\), where \(N_{0}\) is the number of \(\mathrm{Au}^{197}\) nuclei in the foil.