Explanation

(a) The activity or decay rate $R\ $of 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 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$\ \ \frac{t}{T_{1/2}} = \ 2$
$\therefore\ \ \ \ \ \ t = 2T_{1/2}\ = \ 2\ \times 3.20\ = 6.40\ h$
or t$\ \approx$ 6.38 h