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?

Engineering

Physics

Radioactivity New

Question

120

108

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Rate of decay $\propto$ N

64 time higher

$N = N_{0} {(\frac{1}{2})}^{\frac{t}{time}}$

$\frac{1 N_{0}}{64} = N_{0} {(\frac{1}{2})}^{t / 18 day}$

${(\frac{1}{2})}^{6} = {(\frac{1}{2})}^{t / 18 day}$

t = 108 day