Water decomposes at 2300K H _ 2 O(g) → H _ 2 (g) + (1)/(2) O _ 2...

Decomposition of water gives:
${H}_{2}O\left(g\right) ⇌ {H}_{2}\left(g\right) + \dfrac{1}{2}{O}_{2}\left(g\right)$

${P}_{0}\left[1 - \alpha\right]{P}_{0}\alpha\dfrac{{P}_{0}\alpha}{2}$ partial pr. at eq.

Thus, ${P}_{0}\left[1 + \dfrac{\alpha}{2}\right] = 1 \ldots \left(1\right)$

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

$\dfrac{\left({P}_{0}\alpha\right){\left(\dfrac{{P}_{0}\alpha}{2}\right)}^{1 / 2}}{{P}_{0}\left[1 - \alpha\right]} = 2 \times {10}^{- 3}$

since $\alpha$ is negligible w.r.t 1 thus, $1 - \alpha \approx 1$

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

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

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

$⇒ \alpha = 2 \times {10}^{- 2},$