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Question

(B) The intensity of radiation is proportional to the amount of radioactive substance present.Let the initial intensity be $I_0$ and the safe level be

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) The intensity of radiation is proportional to the amount of radioactive substance present.Let the initial intensity be $I_0$ and the safe level be $I_s$.Given $I_0 = 64 	imes I_s$.Using the radioactive decay formula $I = I_0 	imes (\frac{1}{2})^n$,where $n$ is the number of half-lives.We need $I = I_s$,so $I_s = 64 	imes I_s 	imes (\frac{1}{2})^n$.$\frac{1}{64} = (\frac{1}{2})^n$.Since $64 = 2^6$,we have $(\frac{1}{2})^6 = (\frac{1}{2})^n$,which gives $n = 6$.Total time $t = n 	imes T_{1/2} = 6 	imes 2 \ hr = 12 \ hr$.

$A$ freshly prepared radioactive source of half-life $2 \ hours$ emits radiations of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with this source is ......... $hours$.

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