Q. The half life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y$. Initially both them have the same number of atoms. Then
A) $X$ and $Y$ have the same decay rate initially
B) $X$ and $Y$ decay at the same rate always
C) $Y$ will decay at a faster rate than $X$
D) $X$ will decay at a faster rate than $Y$
Explanation
(c) $\left( T_{1/2} \right)_{x} = \left( t_{mean} \right)_{y}$
$\Rightarrow \frac{0.693}{\lambda_{x}} = \frac{1}{\lambda_{y}} \Rightarrow \lambda_{x} = 0.693\lambda_{y}$ or $\lambda_{x} < \lambda_{y}$
Also rate of decay $= \lambda N$
Initially number of atoms $(N)$ of both are equal but since $\lambda_{y} > \lambda_{x}$, therefore, $y$ will decay at a faster rate than $x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.