Half-life period of a radioactive element is | vedclass

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(D) For a first-order reaction,the rate constant $k$ is given by $k = \frac{0.693}{t_{1/2}}$.Given $t_{1/2} = 10.6 \ yrs$,so $k = \frac{0.693}{10.6} \

Vedclass · Accepted Answer

$70.4$

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(D) For a first-order reaction,the rate constant $k$ is given by $k = \frac{0.693}{t_{1/2}}$.Given $t_{1/2} = 10.6 \ yrs$,so $k = \frac{0.693}{10.6} \approx 0.06538 \ yrs^{-1}$.The time $t$ for $99 \%$ decomposition is calculated using $t = \frac{2.303}{k} \log \frac{a}{a-x}$.Here,$a = 100$ and $a-x = 100 - 99 = 1$.$t = \frac{2.303}{0.06538} \log \frac{100}{1} = \frac{2.303 	imes 2}{0.06538} \approx 70.45 \ yrs$.Thus,the correct option is $D$.

Half-life period of a radioactive element is $10.6 \ yrs$. How much time will it take in its $99 \ \%$ decomposition?

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