Question

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

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

Answer 1

The correct option is C $6.38$ h

Given $\frac{R}{R_0}=1-\frac{75}{100}=25$%
$\therefore \frac{25}{100}={\left(\frac{1}{2}\right)}^{\frac{t}{t_{1/2}}}$
$\Rightarrow {\left(\frac{1}{2}\right)}^2={\left(\frac{1}{2}\right)}^{\frac{t}{t_{1/2}}}\Rightarrow \frac{t}{T_{1/2}}=2$
$t=2T_{1/2}=2\times 3.20=6.40t_2$
or $t=6.38t_2$