Question

The half-life of a radioactive substance is $30$ minutes. The time (in minutes) taken between $40$% decay and $85$% decay of the same radioactive substance is

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

Answer 1

Answer: (D)

$N_0$ =Nuclei at time $t=0$

$N_1$=Remaining nuclei after $40$% decay $=(1-0.4)N_0=0.6N_0$

$N_2$=Remaining nuclei after $85$% decay

$\begin{array}{c}=\left(1-0.85\right)N_0=0.15N_0\\ \therefore \frac{N_2}{N_1}=\frac{0.15N_0}{0.6N_0}=\frac{1}{4}={\left(\frac{1}{2}\right)}^2\end{array}$

Hence, two half life is required beweeen $40$% decay and $85$% decay of radio active substance.

Time taken $=2\pi \frac{1}{2}=2\times 30=60min$