$P _0[1-\alpha] \quad P _0 \alpha \quad \frac{ P _0 \alpha}{2} \quad \text { partial pr. at eq }$

$P _0\left[1+\frac{\alpha}{2}\right]=1$

$K _{ p }=\frac{\left( P _{ H _2}\right)\left( P _{ O _2}\right)^{1 / 2}}{ P _{ H _2 O }}$

$\frac{\left( P _0 \alpha\right)\left(\frac{ P _0 \alpha}{2}\right)^{1 / 2}}{ P _0[1-\alpha]}=2 \times 10^{-3}$

since $\alpha$ is negligible w.r.t 1 so $P _0=1$ and $1-\alpha \approx 1$

$\frac{\alpha \sqrt{\alpha}}{\sqrt{2}}=2 \times 10^{-3}$

$\alpha^{3 / 2}=2^{3 / 2} \times 10^{-3}$

$\alpha=2^{3 / 2 \times 2 / 3} \times 10^{-3 \times 2 / 3}$

$\alpha=2 \times 10^{-2} \quad \% \alpha=2 \%$