Explanation:

The phenomenon described is a photochemical decomposition reaction. When white silver chloride ($\text{AgCl}$) is exposed to sunlight, it undergoes decomposition due to the energy from light (photons). This reaction breaks down silver chloride into elemental silver ($\text{Ag}$) and chlorine gas ($\text{Cl}_2$). The elemental silver formed is grey, which causes the white silver chloride to appear grey. The chemical equation for this reaction is: $2\text{AgCl(s)} \xrightarrow{\text{Sunlight}} 2\text{Ag(s)} + \text{Cl}_2\text{(g)}$. Option (A) is correct because the formation of metallic silver is responsible for the grey color change. Option (B) is incorrect; Silver oxide ($\text{Ag}_2\text{O}$) is a different compound and is not formed by the photodecomposition of $\text{AgCl}$. Option (C) is incorrect; Silver nitrate ($\text{AgNO}_3$) is a soluble salt and a reactant in the preparation of $\text{AgCl}$, not a product of its decomposition. Option (D) is incorrect; Silver hydroxide ($\text{AgOH}$) is unstable and decomposes to silver oxide and water, and is not formed here.