The half life period of a radioactive element | vedclass

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Question

(c) ${({T_{1/2}})_x} = {({t_{mean}})_y}$

$ \Rightarrow \frac{{0.693}}{{{\lambda _x}}} = \frac{1}{{{\lambda _y}}} $

$\Rightarrow {\lambda _x} = 0

Vedclass · Accepted Answer

$Y$ will decay at a faster rate than $X$

Vedclass · Answer

(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 $x.$

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

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