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JIPMER 2017

Exam: JIPMER
Year: 2017
Subject: Physics
Chapter: Nuclear Physics

JIPMER 2017 · Physics · Nuclear Physics

The half-life period of a radioactive element X is same as the mean...

The half-life period of a radioactive element

X

is same as the mean life of another radioactive element

Y

. Initially, both of them have the same numbers of atoms then,

Options

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 $Y$

Correct answer

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

Step-by-step solution

Half life of

x=

mean life of

y

Let

\lambda_x

and

\lambda_y

be decay constants of

x and y

, then condition (1) implies

\begin{aligned} \frac{0.693}{\lambda_x} & =\frac{1}{\lambda_y} \\ \lambda_y & =\frac{\lambda_x}{0.693} \Rightarrow \lambda_y\gt\lambda_x\end{aligned}

As rate of decay

\alpha \lambda

; hence decay of

y

will be faster than that of

x

.

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