The solubility of $\mathrm{AgCN}$ in a buffer solution of $\mathrm{pH}=3$ is $x$. The value of $x$ is:

[Assume: No cyano complex is formed:$\mathrm{Ksp}\left(\mathrm{AgCN}\right)=22\times {10}^{-16}$and $\left.\mathrm{Ka}\left(\mathrm{HCN}\right)=6.2\times {10}^{-10}\right]$

 Let us assume solubility of $\mathrm{AgCN}$ is $\mathrm{M}$ in a buffer of $\mathrm{pH}=3$

$AgCN\left(\mathrm{s}\right)\rightleftharpoons {\mathrm{Ag}}^{+}\left(\mathrm{s}\right)+{\mathrm{CN}}^{-}\left(\mathrm{s}\right)$

$[\mathrm{Ag}{]}^{+}=\mathrm{a},[\mathrm{HCN}]=a$

For weak $\mathrm{HCN}$,

${\mathrm{K}}_{\mathrm{sp}}$ $=\frac{\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{CN}}^{-}\right]}{\left[\mathrm{HCN}\right]}$

$6.2\times {10}^{-10}$ =$\frac{{10}^{-3}\left[{\mathrm{CN}}^{-}\right]}{\mathrm{a}}$

$\left[{\mathrm{CN}}^{-}\right]$  $=6.2\times {10}^{-7}\times \mathrm{a}$

For $\mathrm{AgCN}$

${\mathrm{K}}_{\mathrm{sp}}$  $=\left[{\mathrm{Ag}}^{+}\right]\left[{\mathrm{CN}}^{-}\right]$

$2.2\times {10}^{-16}$ $=\mathrm{a}\times 6.2\times {10}^{-10}\times \mathrm{a}$

$a^2$  $=\frac{2.2\times {10}^{-16}}{6.2\times {10}^{-10}}$

$a^2$  $=3.55\times {10}^{-10}$

a  $=1.88\times {10}^{-5}$

 $=1.9\times {10}^{-5}$

Therefore, the correct option is (B).