Question

Half-life of radioactive substance is $3.20 \,h$. What is the time taken for a $75\%$ of substance to be used ?

• A. 6.38 h
• B. 12 h
• C. 4.18 days
• D. 1.2 days

Answer 1

Answer: (A)

The activity or decay rate $R$ of a radioactive substance is the number of decays per second.
$\therefore R=\lambda N$
or $R=\lambda N_{0}\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$
or $R=R_{0}\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$
where $R_{0}=\lambda N_{0}$
is the activity of the radioactive substance at time $t=0$. According to question,
$\frac{R}{R_{0}}=1-\frac{75}{100}=25 \%$
$\therefore \frac{25}{100}=\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$
or $\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$
or $\frac{t}{T_{1 / 2}}=2$
$\therefore t=2 T_{1 / 2}=2 \times 3.20=6.40 \,h$
or $t \approx 6.38 h$