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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?

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108

120

answer is C.

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Detailed Solution

Using, $\frac{A}{A_{0}} = \frac{1}{2^{n}}$

n = number of half lives

$∴ 2^{n} = \frac{A_{0}}{A} = \frac{64}{1} = 2^{6} \Rightarrow n = 6$

$∴ T i m e = n (t_{1 / 2}) = 6 \times t_{\frac{1}{2}} = 6 \times 18 = 108 d a y s$

Hence after 108 days the laboratory can be considered safe for use

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