Question

After $2$ hours the amount of a certain radioactive substance reduces to $1/6^{th}$ of the original amount (the decay process follows first-order kinetics). The half-life of the radioactive substance is:

• A. $15$ min
• B. $30$ min
• C. $45$ min
• D. $60$ min

Answer 1

The correct option is C $45$ min

$k=\frac{2.303}{t}log\frac{a}{a-x}$

$k=\frac{2.303}{2hr\times 60min/hr}log\frac{a}{\frac{a}{6}}$

$k=\frac{2.303}{120min}log6$

$k=0.0149/min$.
The half life period $t_{1/2}=\frac{0.693}{k}$

$t_{1/2}=\frac{0.693}{0.0149/min}$

$t_{1/2}=46.4min\simeq 45min$