QJEEM22Ch36b8: JEE Main 2022 Chemistry - Class 12 JEEM22Ch36b8 Solution: A radioactive element has a half life of 200 days. The…

Question

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A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ___________. (Nearest integer)

(Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)

Accepted Answer

\lambda=\frac{2.303}{t} \log \frac{A_{0}}{A}

\begin{aligned} \frac{0.693}{200} = \frac{2.303}{83} \log \frac{A_{0}}{A} \\ \frac{A}{A_{0}} = 0.75 \end{aligned}

Hence, percentage of original activity remaining after 83 days is

75 \%

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