(A) The initial radioactivity $A_0$ is $4$ times the safe limit $A_s$. We need to find the time $t$ such that the activity $A_t$ becomes equal to $A_s

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(A) The initial radioactivity $A_0$ is $4$ times the safe limit $A_s$. We need to find the time $t$ such that the activity $A_t$ becomes equal to $A_s$.Given, $A_t = \frac{A_0}{2^{t/T_{1/2}}}$, where $T_{1/2} = 24 \,h$.Since $A_t = A_s$ and $A_0 = 4A_s$, we have:$A_s = \frac{4A_s}{2^{t/24}}$$2^{t/24} = 4$$2^{t/24} = 2^2$Equating the exponents:$\frac{t}{24} = 2$$t = 48 \,h$.Thus, the minimum time required is $48 \,h$.

Class 12 Physics Nuclei Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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Half-life of a radioactive sample is $24 \,h$. If a newly prepared radioactive sample shows $4$ times the allowed and safe value of radioactivity, the minimum time after which one can work safely with the source is (in $\,h$)

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A
$48$
B
$96$
C
$8$
D
$72$

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Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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Half-life of a radioactive sample is $24 \,h$. If a newly prepared radioactive sample shows $4$ times the allowed and safe value of radioactivity, the minimum time after which one can work safely with the source is (in $\,h$)

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