The number of nuclei of 'A' at time, is — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

The rate equation is $\frac{dN}{dt} = \alpha - \lambda N$. Integrating from $t=0$ where $N=N_o$ yields $\ln\left(\frac{\alpha - \lambda N}{\alpha - \lambda N_o}\right) = -\lambda t$. Rearranging gives $\alpha - \lambda N = (\alpha - \lambda N_o)e^{-\lambda t}$, solving for $N$ yields $N = \frac{1}{\lambda} [\alpha - (\alpha - \lambda N_o)e^{-\lambda t}]$. Therefore, correct answer is C.