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Question

(B) The intensity of radiation is proportional to the number of radioactive nuclei $N$ present in the sample.Let $N_0$ be the initial number of nuclei

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(B) The intensity of radiation is proportional to the number of radioactive nuclei $N$ present in the sample.Let $N_0$ be the initial number of nuclei and $N$ be the number of nuclei after $n$ half-lives.The safe limit corresponds to $N = \frac{N_0}{128}$.Using the law of radioactive decay, the remaining fraction is given by $\frac{N}{N_0} = (\frac{1}{2})^n$.Substituting the values, we get $\frac{1}{128} = (\frac{1}{2})^n$.Since $128 = 2^7$, we have $(\frac{1}{2})^7 = (\frac{1}{2})^n$, which implies $n = 7$.Since the half-life $T_{1/2} = 1$ hour, the total time $t = n 	imes T_{1/2} = 7 	imes 1 = 7$ hours.

$A$ freshly prepared radioactive sample of half-life $1$ hour emits radiations that are $128$ times as intense as the permissible safe limit. The minimum time after which this sample can be safely used is ......... $hours$.

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