All Problems

Nuclear Reactions

Problem 6.285

Thermal neutrons fall normally on the surface of a thin gold foil consisting of stable Au 197^{197} nuclide. The neutron flux density is J=1.0⋅1010J=1.0 \cdot 10^{10} part. /(s⋅cm2)./\left(\mathrm{s} \cdot \mathrm{cm}^{2}\right) . The mass of the foil is m=10mgm=10 \mathrm{mg}. The neutron capture produces beta-active Au 198^{198} nuclei with half-life T=2.7T=2.7 days. The effective capture cross-section is σ=98 b.\sigma=98 \mathrm{~b} . Find: (a) the irradiation time after which the number of Au 197^{197} nuclei decreases by η=1.0%\eta=1.0 \% (b) the maximum number of Au 198^{198} nuclei that can be formed during protracted irradiation.

Reveal Answer
6.285.6.285 . (a) t=η/σJ=3⋅106t=\eta / \sigma J=3 \cdot 10^{6} years; (b) Nmax⁡=JσN0T/ln⁡2=N_{\max }=J \sigma N_{0} T / \ln 2= =1.0⋅1013=1.0 \cdot 10^{13}, where N0N_{0} is the number of Au197\mathrm{Au}^{197} nuclei in the foil.
Prev
Next