For the given cell: {Cu(s)|Cu^{2+}(C_1\ M)\|Cu^{2+}(C_2\ M)|Cu(s)} change in Gibbs energy ( G) is negative, if:

Strategy: For a concentration cell with identical electrodes, $\Delta G$ is negative (spontaneous) if $E_{\text{cell}}$ is positive. Apply the Nernst Equation where $E°_{\text{cell}} = 0$.

Step 1: Cell reaction Anode: $\ce{Cu \rightarrow Cu^{2+}(C_1) + 2e^-}$ Cathode: $\ce{Cu^2+(C2) + 2e^- \rightarrow Cu}$ Net: $\ce{Cu^{2+}(C_2) \rightarrow Cu^{2+}(C_1)}$

Step 2: Condition for spontaneity $E_{\text{cell}} = -\frac{0.059}{2} \log\frac{C_1}{C_2}$ For $E_{\text{cell}} > 0$: $\log(C_1/C_2) < 0 \implies C_1 < C_2$.

Step 3: Evaluate options Among given options, $C_2 = \sqrt{2}C_1$ satisfies $C_2 > C_1$.

$\boxed{\text{Answer: (d) } C_2 = \sqrt{2} C_1}$