Question

Thermal neutrons fall normally on the surface of a thin gold foil consisting of stable Au¹⁹⁷ nuclide. The neutron flux density is J = 1.0.10¹⁰ part./(s. cm²). The mass of the foil is in = 10 mg. The neutron capture produces beta-active Au¹⁸⁸ nuclei with half-life T = 2.7 days. The effective capture cross-section is σ = 98 b. Find: 

(a) the irradiation time after which the number of Au¹⁸⁷ nuclei decreases by η = 1.0%; 

(b) the maximum number of Au¹⁹⁸ nuclei that can be formed during protracted irradiation.

Answer 1

(a) Suppose N₀ = no. of Au¹⁹⁷ nuclei in the foil. Then the number of Au¹⁹⁷ nuclei transformed in time t is

For this to equal ηN₀ , we must have

(b) Rate of formation of the Au¹⁹⁸ nuclei is N₀ • J • σ per sec and rate of decay is λn, where n is the number of Au¹⁹⁸ at any instant.

because if n is smaller,  and n increase further and if n is larger and n will decrease. (Actually n_max is approached steadily as t →∞) Substitution gives using