Modern Physics Ques 118
- Using a nuclear counter, the count rate of emitted particles from a radioactive source is measured. At $t=0$, it was $1600$ counts per second and $t=8$ $ s$, it was $100$ counts per second. The count rate observed as counts per second at $t=6$ $ s$ is close to
(Main 2019, 10 Jan I)
(a) $400$
(b) $200$
(c) $150$
(d) $360$
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Answer:
Correct Answer: 118.(b)
Solution:
Formula:
- Here given, at $t=0$, count rate or initial activity is
$ A _0=1600 $ $s^{-1} \text {. } $
At $t=8$ $ s$, count rate or activity is
$ A=100$ $ s^{-1} $
So, decay scheme for given sample is
$ \begin{aligned} & 1600 \stackrel{T _{1 / 2}}{\rightarrow} 800 \stackrel{T _{1 / 2}}{\rightarrow} 400 \stackrel{T _{1 / 2}}{\rightarrow} 200 \stackrel{T _{1 / 2}}{\rightarrow} 100 \\ & \text { So, } 8 s=4 T _{1 / 2} \end{aligned} $
where, $T _{1 / 2}=$ Half-life time.
$ \Rightarrow \quad T _{1 / 2}=2$ $ s $
$\therefore \quad$ From above decay scheme, we see that activity after $6$ $s$ is $ 200$ counts per second.
BETA
