Explanation

(c)
_{Given,}
$N_{2} + 3H_{2} \rightleftharpoons 2NH_{3},\ K_{eq} = 1.6 \times 10^{- 5}$
$K_{eq} = \frac{\left\lbrack {NH}_{3} \right\rbrack^{2}}{\left\lbrack N_{2} \right\rbrack\left\lbrack H_{2} \right\rbrack^{3}} = 1.6 \times 10^{- 5}$ …(i)
For reaction,
$NH_{3} \rightleftharpoons \frac{1}{2}N_{2} + \frac{3}{2}H_{2}$
${K'}_{eq} = \frac{\left\lbrack N_{2} \right\rbrack^{\frac{1}{2}}\left\lbrack H_{2} \right\rbrack^{\frac{3}{2}}}{\lbrack{NH}_{3}\rbrack}$ …(ii)
On squaring both sides, Eq.(ii) becomes
$\left( K_{eq}^{'} \right)^{2} = \frac{\left\lbrack N_{2} \right\rbrack\left\lbrack H_{2} \right\rbrack^{3}}{\left\lbrack NH_{3} \right\rbrack^{2}}$ …(iii)
Eq.$(i) \times Eq.(iii)$, we get
$K_{eq} \times \left( K_{eq}^{'} \right)^{2} = 1$
$1.6 \times 10^{- 5} \times \left( K_{eq}^{'} \right)^{2} = 1$
$K_{eq}^{'} = \frac{1}{\sqrt{1.6 \times 10^{- 5}}} = \frac{1000}{4} = 250$