Explanation

(c) From Rutherford-Soddy’s law
$N = N_{0}\left( \frac{1}{2} \right)^{n}$
Given, $N = 1 - \frac{3}{4}\ = \frac{1}{4}N_{0}\ ,\ n = \frac{t}{T}\ = \ \frac{t}{4}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{4} = \left( \frac{1}{2} \right)^{t/4}$
$\Rightarrow \ \ \ \ \ \left( \frac{1}{2} \right)^{2} = \left( \frac{1}{2} \right)^{t/4}$
$\Rightarrow \ \ \ \ \ \ \ \ \ 2\ = \frac{t}{4}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ t = 8\ months$