Explanation

(c) $\ \ \ \ N\ = \ N_{0}(1 - \ e^{- \lambda t})$
$\Rightarrow \ \ \frac{N_{0} - N}{N_{0}} = e^{- \lambda t}$
$\therefore\ \ \ \ \ \ \ \ \ \frac{1}{8} = e^{- \lambda t}$
$\Rightarrow \ \ \ \ \ \ \ 8 = e^{\lambda t}$
$\Rightarrow$ $3\ In\ 2\ = \ \lambda t$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \lambda = \frac{3\ \times \ 0.693}{15}$
Half-life period
$\ \ \ \ \ \ \ \ \ \ \ t_{1/2}\ = \ \frac{0.693}{3\ \times \ 0.693} \times \ 15$
$\ \ \ \ \ \ \ \ \ \ \ t_{1/2}\ = \ 5\ \min$