Question

A radioactive isotope is being produced at a constant rate X. Half-life of the isotope is Y. After some time, the number of radioactive nuclei becomes constant. This constant number is

• A. $\frac{XY}{ln2}$
• B. XY
• C. XY ln 2
• D. X/Y

Answer 1

The correct option is A $\frac{XY}{ln2}$

$\begin{array}{c}\text{At the stage of radioactive equilibrium,}\\ \text{rate of formation of nuclei = rate of decay of nuclei}\\ X=\lambda N\\ N=\frac{X}{\lambda }=\frac{X}{\ln 2/Y}=\frac{XY}{\ln 2}\end{array}$