Modern Physics 3 Question 2
2. 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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Solution:
- 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.
$$ \Rightarrow \quad T _{1 / 2}=2 s $$
$\therefore$ From above decay scheme, we see that activity after $6 s$ is 200 counts per second.
