Question

Nuclei of a radioactive element $A$ are being produced at a constant rate $\alpha$. The element has a decay constant $\lambda$. At $t=0$, there are $N_0$ nuclei of the element.
Calculate the number $N$ of nuclei of $A$ at time $t$.

• A. $N=\frac{1}{\lambda }[\alpha +(\alpha -\lambda N_0\left)e^{-\lambda t}\right]$.
• B. $N=\frac{1}{\lambda }\left[\alpha /\right(\alpha -\lambda N_0\left)e^{-\lambda t}\right]$.
• C. $N=\frac{1}{\lambda }\left[\alpha \right(\alpha -\lambda N_0\left)e^{-\lambda t}\right]$.
• D. $N=\frac{1}{\lambda }[\alpha -(\alpha -\lambda N_0\left)e^{-\lambda t}\right]$.

Answer 1

The correct option is D $N=\frac{1}{\lambda }[\alpha -(\alpha -\lambda N_0\left)e^{-\lambda t}\right]$.