Question

A radioactive isotope is being produced at a constant rate $x$. Half life of the radioactive substance is '$y$'. After sometime, the number of radioactive nuclei becomes constant the value of this constant is ________

Answer 1

At the stage of radioactive equilibrium, rate of formation of nuclei $=$ rate of decay of nuclei
$x=\lambda N$
$N=\frac{x}{\lambda }=\frac{x}{\left(\ln 2\right)/y}=\frac{xy}{\ln 2}$