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. $60$
• B. $15$
• C. $30$
• D. $45$

Answer 1

The correct option is A $60$

We know that, $N=N_0{e}^{-\lambda t}$
For $40\%$ decay,
$N_1=N_0-\left(\frac{40}{100}\right)N_0=\left(\frac{3}{5}\right)N_0=0.6N_0$
For $85\%$ decay,
$N_2=N_0-\left(\frac{85}{100}\right)N_0=\left(\frac{3}{20}\right)N_0$$=0.15N_0$

$\frac{N_2}{N_1}=(\frac{1}{2}{)}^2$
So, two half life has passed.
Since the half-life is 30 minutes, time taken for decay from $40\%$ to $85\%$ will be $2t_{1/2}=2\times 30=60$ minutes