At \(\mathrm{T}(\mathrm{K})\) in a saturated solution of \(\mathrm{MgCO}_3\) and \(\mathrm{Ag}_2 \mathrm{CO}_3\), if the concentration of \(\mathrm{Mg}^{2+}\) ion is \(3.2 \times 10^{-5} \mathrm{M}\), then the concentration of \(\mathrm{Ag}^{+}\)ion in the solution will be [Given: \(\mathrm{K}_{\mathrm{sp}}\left(\mathrm{MgCO}_3\right)=1.6 \times 10^{-6}\) and \(\mathrm{K}_{\mathrm{sp}}\left(\mathrm{Ag}_2 \mathrm{CO}_3\right)=8.0 \times 10^{-12}\) at \(\mathrm{T}(\mathrm{K})\) ]

1. A \(\sqrt{1.3} \times 10^{-7} \mathrm{M}\)
2. B \(\sqrt{1.5} \times 10^{-6} \mathrm{M}\)
3. C \(\sqrt{1.6} \times 10^{-6} \mathrm{M}\)
4. D \(\sqrt{1.6} \times 10^{-5} \mathrm{M}\)