Modern Physics 3 Question 7
7. 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
(d) 120
Show Answer
Solution:
- Using the relation
$$ R=R _0 \frac{1}{2} $$
Here, $R$ is activity of radioactive substance, $R _0 \quad$ initial activity and $n$ is number of half lives.
$$ 1=64 \frac{1}{2}^{n} $$
Solving we get, $n=6$
Now,
$$ \begin{aligned} t & =n\left(t _{12}\right) \\ & =6(18 \text { days }) \\ & =108 \text { days } \end{aligned} $$
