Q. The half-life period of a radioactive element $X\ $is same as the mean life time of another radioactive element Y. Initially they have the same number of atoms. Then
A) $X$ will decay faster than $Y$
B) $Y$ will decay faster than $X$
C) $Y$ and $X$ have same decay rate initially
D) $X\ $and $Y$decay at same rate always.
Explanation
(b) $T_{1/2}(X)\ = \ \tau(Y)$
$\Rightarrow \ \ \ \ \ \ \frac{0.693}{\lambda_{x}} = \frac{1}{\lambda_{\gamma}}$
$\Rightarrow \ \ \ \ \ \ \ \ \lambda_{\gamma} = \frac{\lambda_{x}}{0.693}$
$\Rightarrow \ \ \ \ {\ \ \ \lambda}_{\gamma} > \lambda_{x}$
(So, $Y$ will decay faster than $X$)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.