Answer:
Option B
Explanation:
For the given centration of the cell, the cell reactions are $M \rightarrow M^{2+}$ at left hand electrode
$M^{2+} \rightarrow M$ at right hand electrode
$\Rightarrow$ $M^{2+}$(RHS elecrode)
$\rightarrow M^{2+}$ (LHS elelctrode)
$E^{0}=0$
Applying Nernst equation
$E_{cell}=0.059=0-\frac{0.059}{2}$
$\log\frac{[M^{2+}]at LHS electrode}{0.001}$
$\Rightarrow$ $\log\frac{[M^{2+}]at LHS electrode}{0.001}=-2$
$\Rightarrow$ $[M^{2+}]$ at LHS electrode
=$10^{-2} \times 0.001=10^{-5} M$
The solubility equilibria for $MX_{2}$ is
$MX_{2}\rightleftarrows M^{2+}(aq)+2X^{-}(aq)$
Solubility product , $K_{sp}=[M^{2+}][X^{-}]^{2}$
= $10^{-5} \times (2 \times 10^{-5})^{2}=4 \times 10^{-15}$
[$ \because $ In satuarated solution of $MX_{2}$,$[X^{-}]$=2$[M^{2}]]$