Explanation

(c)
For first order reaction ,
k=$\frac{2.303}{t_{1/2}}\log\frac{a}{\left( a - \frac{a}{2} \right)} = \frac{2.303}{t}\log\frac{a}{(a - x)}$
$\frac{2.303}{t_{1/2}}\log{2 =}\frac{2.303}{1}\log\frac{a}{a/4}$
$\frac{2.303 \times 0.3010}{t_{1/2}} = 2.303 \times \log 4$
$t_{1/2} = \frac{0.3010}{\log 4} = \frac{0.3010}{0.6020} = \frac{1}{2}h$