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(D) The radioactive decay follows first-order kinetics.The intensity of radiation is proportional to the amount of the radioactive substance present.L

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$12$

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(D) The radioactive decay follows first-order kinetics.The intensity of radiation is proportional to the amount of the radioactive substance present.Let the initial intensity be $I_0 = 64 	imes I_{safe}$ and the final intensity be $I = I_{safe}$.Using the relation $I = I_0 	imes (1/2)^n$,where $n$ is the number of half-lives:$I_{safe} = 64 	imes I_{safe} 	imes (1/2)^n$$1/64 = (1/2)^n$$(1/2)^6 = (1/2)^n$So,$n = 6$.The total time $t$ is given by $t = n 	imes t_{1/2}$.Given $t_{1/2} = 2 \ hr$,we have $t = 6 	imes 2 = 12 \ hr$.

$A$ freshly prepared radioactive element has a half-life of $2 \ hr$. It emits radiation whose intensity is $64$ times the permissible safe level. The minimum time after which it would be possible to work with this sample is .......... $hr$.

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