Explanation

(b)
$N_{2}(g) + O_{2}(g) \rightleftharpoons 2NO(g)$
$K_{c} = \frac{\lbrack NO\rbrack^{2}}{\left\lbrack N_{2} \right\rbrack\left\lbrack O_{2} \right\rbrack} = 4 \times 10^{- 4}$
$NO(g) \rightleftharpoons \frac{1}{2}N_{2}(g) + \frac{1}{2}O_{2}(g)$
$K_{c}^{'} = \frac{\left\lbrack N_{2} \right\rbrack^{\frac{1}{2}}\left\lbrack O_{2} \right\rbrack^{\frac{1}{2}}}{\lbrack NO\rbrack}$
$= \frac{1}{\sqrt{K_{c}}} = \frac{1}{\sqrt{4 \times 10^{- 4}}}$
$= \frac{1}{2 \times 10^{- 2}} = \frac{100}{2} = 50$