Question

A radioactive nucleus is being produced at a constant rate $\alpha$ per second. Its decay constant is $\lambda$. If $N_0$ are the number of nuclei at time $t=0$, then maximum number of nuclei possible are

• A. $\frac{\alpha }{\lambda }$
• B. $N_0\frac{\alpha }{\lambda }$
• C. $N_0$
• D. $\frac{\alpha }{\lambda }+N_0$

Answer 1

The correct option is A $\frac{\alpha }{\lambda }$

At any given time $t$, the governing equation is:
$\frac{dN}{dt}=\alpha -\lambda t$
when $N$ reaches a maxima.
$\frac{dN}{dt}=0$
$t=\frac{\alpha }{\lambda }$