question_answer

Show that the decay rate \['R'\] of a sample of a radionuclide is related to the number of radioactive nuclei \['N'\] at the same instant by the expression \[R=\lambda N\]  

Answer:

                By radioactive decay law, \[N={{N}_{0}}{{e}^{-\lambda t}}\] Rate of decay, \[R=-\frac{dN}{dt}=-\frac{d}{dt}({{N}_{0}}{{e}^{-\lambda t}})=\lambda {{N}_{0}}{{e}^{-\lambda t}}\] or \[R=\lambda N\].