An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive materi

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13.Nuclei

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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?

A

$64$

B

$90$

C

$108$

D

$120$

(IIT-2016)

Solution

The correct option is $C 108$

Given: $T_{1 / 2}=18$ days

Let the permissible activity after time $t$ be $R_{\circ}$

$\Rightarrow$ Initial activity of the radiation, $R=64 R_0$ (given)

Using: $\frac{0.693}{T_{1 / 2}}=2.303 \log _{10} \frac{R}{R_0}$

$\therefore \frac{0.693}{18}=2.303 \log _{10}(64)$

$\frac{0.693}{18}=2.303 \times 1.806 \Rightarrow t =108 \text { days }$

Standard 12

Physics

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