A radioactive sample with a half-life of 1 mo | vedclass

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(B) The activity of a radioactive sample at any time $t$ is given by $A = A_0 (1/2)^n$, where $n$ is the number of half-lives.Given, half-life $T_{1/2

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$8$

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(B) The activity of a radioactive sample at any time $t$ is given by $A = A_0 (1/2)^n$, where $n$ is the number of half-lives.Given, half-life $T_{1/2} = 1$ month.We need to find the activity $2$ months earlier, so $n = 2$ half-lives.Let $A_{initial}$ be the activity $2$ months earlier and $A_{final} = 2 \, \mu Ci$ be the activity on $1-8-1991$.Since $A_{final} = A_{initial} 	imes (1/2)^n$, we have $2 = A_{initial} 	imes (1/2)^2$.$2 = A_{initial} 	imes (1/4)$.$A_{initial} = 2 	imes 4 = 8 \, \mu Ci$.Therefore, the activity two months earlier was $8 \, \mu Ci$.

$A$ radioactive sample with a half-life of $1$ month has the label: "Activity $= 2 \, \mu Ci$ on $1-8-1991$." What will be its activity two months earlier in $\mu Ci$?

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