Modern Physics Ques 146
- An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life $18$ days inside the laboratory. Tests revealed that the radiation was $64$ times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?
(2016 Adv.)
(a) $64$
(b) $90$
(c) $108.00$
(d) $120$
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Answer:
Correct Answer: 146.(c)
Solution:
Formula:
- Using the relation
$ R=R _0 (\frac{1}{2})^n $
Here, $R$ is activity of radioactive substance, $R_0$ is initial activity and $n$ is number of half-lives.
$ 1=64 (\frac{1}{2})^{n} $
Solving we get, $n=6$
Now,
$ \begin{aligned} t & =n\left(t_{12}\right) \ & =6(18\ \text{days}) & = 108 \text{ days} \end{aligned} $
BETA
