$10 \mathrm{~g}$ of a radioactive element is disintegrated to $1 \mathrm{~g}$ in 2.303 minutes. What is the…
$10 \mathrm{~g}$ 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?
$1 / 0.693$
$6.93$
$1$
$0.693$
Solution
Radioactive disintegration is first order reaction
$$
\begin{aligned}
k & =\frac{2303}{t} \log \frac{a}{a-x} \\
& =\frac{2.303}{2.303} \log \frac{10}{1} \\
k & =1 \\
t_{1 / 2} & =\frac{0.693}{k}=\frac{0.693}{1} \\
& =0.693 \mathrm{~min}
\end{aligned}
$$
.