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Question

$R=R_{0} e^{-\lambda t}$

$\Rightarrow \frac{1}{3}=e^{-\lambda 	imes 3}=e^{-3 \lambda}$   .........$(1)$

Let activity in $9$ days be $

Vedclass · Accepted Answer

$(1/27)$ of the original value

Vedclass · Answer

$R=R_{0} e^{-\lambda t}$

$\Rightarrow \frac{1}{3}=e^{-\lambda 	imes 3}=e^{-3 \lambda}$   .........$(1)$

Let activity in $9$ days be $R'$. Then

$\frac{R^{\prime}}{R_{0}}=e^{-\lambda 	imes 9}=e^{-9 \lambda} e^{-\lambda 	imes 3}=\left(e^{-3 \lambda}ight)^{3}$

$=\left(\frac{1}{3}ight)^{3}, \quad$    from $(1)$

$=\frac{1}{27} \Rightarrow R^{\prime}=\frac{R_{0}}{27}.$

Activity of a radioactive sample decreases to $(1/3)^{rd}$ of its original value in $3\, days$. Then, in $9\, days$ its activity will become

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