All Problems Radioactivity
Problem 6.229
A radionuclide \(A_{1}\) with decay constant \(\lambda_{1}\) transforms into a radionuclide \(A_{2}\) with decay constant \(\lambda_{2}\). Assuming that at the initial moment the preparation contained only the radionuclide \(A_{1}\), find: (a) the equation describing accumulation of the radionuclide \(A_{2}\) with time; (b) the time interval after which the activity of radionuclide \(A_{2}\) reaches the maximum value.
6.229. (a) \(N_{2}(t)=N_{10} \frac{\lambda_{1}}{\lambda_{2}-\lambda_{1}}\left(\mathrm{e}^{-\lambda_{1} t}-\mathrm{e}^{-\lambda_{2} t}\right)\) (b) \(t_{m}=\frac{\ln \left(\lambda_{1} / \lambda_{2}\right)}{\lambda_{1}-\lambda_{j}}\)