Q157 / 160 · TS EAMCET 2020 (14 Sep Shift 1) · Physics

Half-life of radioactive sample is $24 \mathrm{~h}$. If a newly prepared radioactive sample shows 4 times the allowed and safe value of radio activity, the minimum time after which one can work safely with the source is

  • Correct answer
    A
    48 h
  • B
    96 h
  • C
    8 h
  • D
    72 h

Solution

Newly prepared radioactive sample shows 4 times the allowed and safe value of radioactivity, so on reaching to the allowed and safe value, its radioactivity will be reduced to $\left(\frac{1}{4}\right)$ th of the current value, $\because \quad A_t=\frac{A}{(2)^{t / t_{1 / 2}}}$ Here, $A=$ current activity, $A_t=$ final activity $=\frac{A}{4}$ $t=\text { time-taken, } t_{1 / 2}=\text { half-life }=24 \mathrm{~h}$ So, on putting the values $\begin{aligned} \frac{A}{4} & =\frac{A}{(2)^{t / t_{1 / 2}}} \Rightarrow(2)^{t / t_{1 / 2}}=4 \\ \Rightarrow(2)^{t / 24} & =(2)^2 \Rightarrow \frac{t}{24}=2 \Rightarrow t=48 \mathrm{~h} \end{aligned}$

Hence, the correct answer is option: 'A'.

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