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13.Nuclei
medium
The half life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y$. Initially both of 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 $Y$
(IIT-1999)
Solution
(c) ${({T_{1/2}})_x} = {({t_{mean}})_y}$
$ \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 $x.$
Standard 12
Physics
