A plating works wants to recover silver from a waste solution that holds $[\text{Cu}^{2+}] = 0.100\ \text{mol L}^{-1}$ and $[\text{Ag}^+] = 0.0500\ \text{mol L}^{-1}$ at $298\ \text{K}$. The solution is electrolysed between platinum electrodes, and the potential of the cathode is lowered very slowly. Silver deposits first. The aim is to remove as much silver as possible before any copper comes out. The volume stays fixed, and the copper ion concentration does not change while silver deposits. Take $E^\circ(\text{Ag}^+/\text{Ag}) = 0.80\ \text{V}$, $E^\circ(\text{Cu}^{2+}/\text{Cu}) = 0.34\ \text{V}$ and $\dfrac{2.303RT}{F} = 0.059\ \text{V}$, and ignore any overpotential. What is $[\text{Ag}^+]$ left in the solution at the moment copper just begins to deposit?