Thermal neutrons fall normally on the surface of a thin gold foil consisting of stable \( \mathr...

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Thermal neutrons fall normally on the surface of a thin gold foil consisting of stable \( \mathrm{Au}^{197} \) nuclide. The neutron flux density is \( J=1.0 \times 10^{10} \) 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 \( \mathrm{Au}^{198} \) nuclei with half-life \( T=2.7 \) days. The effective capture cross-section is \( \sigma=98 \mathrm{~b} \). Find: the irradiation time after which the number of \( \mathrm{Au}^{197} \) nuclei decreases by \( \eta=1.0 \% \);
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