Modern Physics Ques 114
- 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
(1999, 3M)
(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 $y$
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Answer:
Correct Answer: 114.(c)
Solution:
Formula:
- $\left(t _{1 / 2}\right) _x=\left(t _{\text {mean }}\right) _y$
$\text { or } \quad \frac{0.693}{\lambda _x} =\frac{1}{\lambda _y} $
$\therefore \quad \lambda _x =0.693 \lambda _y $
$\quad \lambda _x <\lambda _y$
or 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 $x$.
BETA
