Question

Half-life of radioactive substance is $3.20h$. 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 $\frac{t}{T_{1/2}}=2$
$\therefore t=2T_{1/2}=2\times 3.20=6.40h$
or $t\approx 6.38h$