A solution containing `1 mol` per litre of each `Cu(NO_(3))_(2), AgNO_(3),` ` Hg_(2)(NO_(3))_(2)` and `Mg(NO_(3))_(2)` ​is being electrolyzed by using inert electrodes. The values of standard electrode potentials in volts `(` reduction potential `)` are
`Ag^(o+)|Ag=+0.80, Hg_(2)^(2+)|2Hg=+0.79`
`Cu^(2+)|Cu=+0.34,Mg^(2+)|Mg=-2.37`.
With increasing voltage, the sequence of deposition of metals at the cathode will be
(a)A g , H g , C u , M g
(b) M g , C u , H g , A g
(c) A g , H g , C u , M g
(d) C u , H g , A g , M g

Options

A. `Ag,Hg,Cu,Mg`
B. `Mg,Cu,Hg,Ag`
C. `Ag,Hg,Cu,Mg`
D. `Cu,Hg,Ag,Mg`

Explanation

To determine the sequence of deposition of metals at the cathode during the electrolysis of the given solutions, we will analyze the standard electrode potentials provided for each metal ion. The standard reduction potential indicates how easily a metal ion can gain electrons and be reduced to its metallic form. The higher the reduction potential, the more favorable the reduction reaction, and thus the more easily the metal will deposit at the cathode.

### Step-by-Step Solution:

1. **List the Standard Electrode Potentials:**
- \( \text{Ag}^+ + e^- \rightarrow \text{Ag} \) : \( E^\circ = +0.80 \, \text{V} \)
- \( \text{Hg}_2^{2+} + 2e^- \rightarrow 2\text{Hg} \) : \( E^\circ = +0.79 \, \text{V} \)
- \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \) : \( E^\circ = +0.34 \, \text{V} \)
- \( \text{Mg}^{2+} + 2e^- \rightarrow \text{Mg} \) : \( E^\circ = -2.37 \, \text{V} \)

2. **Rank the Metals by Their Reduction Potentials:**
- The highest reduction potential is for silver (\(+0.80 \, \text{V}\)), followed by mercury (\(+0.79 \, \text{V}\)), then copper (\(+0.34 \, \text{V}\)), and finally magnesium (\(-2.37 \, \text{V}\)).
- Therefore, the order of deposition based on the standard reduction potentials is:
- Silver (Ag)
- Mercury (Hg)
- Copper (Cu)
- Magnesium (Mg)

3. **Conclusion:**
- As the voltage increases during electrolysis, the sequence of deposition of metals at the cathode will be:
- **Silver (Ag), Mercury (Hg), Copper (Cu), Magnesium (Mg)**

### Final Answer:
The correct option is (a) Ag, Hg, Cu, Mg.