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 day
• D. 1.2 day

Answer 1

The correct option is A 6.38 h

According to question, percentage of substance left
$\frac{R}{R_0}=1-\frac{75}{100}=25$
$\therefore \frac{25}{100}={\left(\frac{1}{2}\right)}^{t/T_{1/2}}$
or ${\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^{t/T_{1/2}}$
or $\frac{t}{T_{1/2}}=2$
$\therefore t=2T_{1/2}=2\times 3.20=6.40h$ $\approx 6.38h$