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$10 \mathrm{~g}$ of a radioactive element is disintegrated to $1 \mathrm{~g}$ in 2.303 minutes. What is the half-life (in minutes) of that radioactive element?
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Verified Answer
The correct answer is:
$0.693$
Radioactive disintegration is first order reaction
$$
\begin{aligned}
k & =\frac{2303}{t} \log \frac{a}{a-x} \\
& =\frac{2.303}{2.303} \log \frac{10}{1} \\
k & =1 \\
t_{1 / 2} & =\frac{0.693}{k}=\frac{0.693}{1} \\
& =0.693 \mathrm{~min}
\end{aligned}
$$
$$
\begin{aligned}
k & =\frac{2303}{t} \log \frac{a}{a-x} \\
& =\frac{2.303}{2.303} \log \frac{10}{1} \\
k & =1 \\
t_{1 / 2} & =\frac{0.693}{k}=\frac{0.693}{1} \\
& =0.693 \mathrm{~min}
\end{aligned}
$$
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