The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198… | JEE Main 2021 (16 Mar, Shift 2)

Q66JEE Main 2021 · 16 MAR · SHIFT 2Medium

Law of Radioactive Decay

The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198 if its atomic weight is 198 g mol ${}^{-1}$ is, (Na = 6 $\times$ 1023/mol).

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Answer: (b)

$N = \frac{1.5\times10^{-3}}{198}\times6\times10^{23} \approx 4.55\times10^{18}$ .
$\lambda = \frac{0.693}{2.7\times86400\text{ s}} \approx 2.97\times10^{-6}\text{ s}^{-1}$ .
$A = \lambda N \approx 1.35\times10^{13}$ Bq $= \frac{1.35\times10^{13}}{3.7\times10^{10}} \approx 365$ Ci.
The nearest option is (b) 357 Ci.

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