Sol. $$ \begin{aligned} & \mathrm{H}_2 \mathrm{O}(\mathrm{~g}) \rightarrow \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \\ & \mathrm{P}_0[1-\alpha]_{\sim} \mathrm{P}_0 \alpha \frac{\mathrm{P}_0 \alpha}{2} \\ & \mathrm{P}_0\left[1+\frac{\alpha}{2}\right]=1 \\ & \mathrm{~K}_{\mathrm{p}}=\frac{\left(\mathrm{P}_{\mathrm{H}_2}\right)\left(\mathrm{P}_{\mathrm{O}_2}\right)^{1 / 2}}{\mathrm{P}_{\mathrm{H}_2}} \\ & \frac{\left(\mathrm{P}_0 \alpha\right)\left(\frac{\mathrm{P}_0 \alpha}{2}\right)^{1 / 2}}{\mathrm{P}_0[1-\alpha]}=2 \times 10^{-3} \end{aligned} $$ partial pr. since $\alpha$ is negligible w.r.t 1 so $\mathrm{P}_0=1$ and $1-\alpha \approx 1$ $$ \begin{aligned} & \frac{\alpha \sqrt{\alpha}}{\sqrt{2}}=2 \times 10^{-3} \\ & \alpha^{3 / 2}=2^{3 / 2} \times 10^{-3} \\ & \alpha=2^{3 / 2 \times 2 / 3} \times 10^{-3 \times 2 / 3} \\ & \alpha=2 \times 10^{-2} \end{aligned} $$