JEE MAIN - Chemistry (2022 - 28th June Evening Shift - No. 16)
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)
Answer
75
Explanation
$\lambda=\frac{2.303}{t} \log \frac{A_{0}}{A}$
$$ \begin{aligned} &\frac{0.693}{200}=\frac{2.303}{83} \log \frac{A_{0}}{A} \\\\ &\frac{A}{A_{0}}=0.75 \end{aligned} $$
Hence, percentage of original activity remaining after 83 days is $75 \%$
$$ \begin{aligned} &\frac{0.693}{200}=\frac{2.303}{83} \log \frac{A_{0}}{A} \\\\ &\frac{A}{A_{0}}=0.75 \end{aligned} $$
Hence, percentage of original activity remaining after 83 days is $75 \%$
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