A solution containing one mole per litre each of `Cu(NO_(3))_(2),AgNO_(3),Hg(NO_(3))_(2)` and `Mg(NO_(3))_(2)` is being electrolysed by using inerty electrodes. The values of the standard oxidation potentials in vlts are `Ag//Ag^(+)=-0.8V,Ag//Hg^(2+)=-79V,Cu//Cu^(2+)=-0.34V,Mg//Mg^(2+)=2.37V`. The order in which metals will be formed at cathode will be-

Options

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

Explanation

To determine the order in which metals will be formed at the cathode during the electrolysis of the given solution, we need to analyze the standard reduction potentials of the metal ions involved. The reduction potential indicates the tendency of a species to gain electrons (be reduced) and form the corresponding metal.

### Step-by-Step Solution:

1. **Identify the Standard Reduction Potentials**:
The standard reduction potentials (E°) for the metal ions are given as follows:
- For Ag⁺ + e⁻ → Ag: E° = +0.8 V
- For Hg²⁺ + 2e⁻ → Hg: E° = +0.79 V
- For Cu²⁺ + 2e⁻ → Cu: E° = +0.34 V
- For Mg²⁺ + 2e⁻ → Mg: E° = -2.37 V

2. **Convert Oxidation Potentials to Reduction Potentials**:
Since the question provides oxidation potentials, we need to convert them to reduction potentials. The reduction potential is the negative of the oxidation potential:
- E°(Ag) = +0.8 V (already in reduction form)
- E°(Hg) = +0.79 V (already in reduction form)
- E°(Cu) = +0.34 V (already in reduction form)
- E°(Mg) = -2.37 V (already in reduction form)

3. **Rank the Metals by Their Reduction Potentials**:
The higher the reduction potential, the greater the tendency for the metal to be reduced (deposited at the cathode):
- Ag: +0.8 V
- Hg: +0.79 V
- Cu: +0.34 V
- Mg: -2.37 V (this will not deposit as it has a negative potential)

4. **Determine the Order of Deposition**:
Based on the reduction potentials, the order in which metals will be deposited at the cathode is:
- First: Ag (highest potential)
- Second: Hg
- Third: Cu
- Mg will not deposit due to its negative potential.

5. **Final Order of Metals**:
Therefore, the final order of metals formed at the cathode during electrolysis is:
- Ag > Hg > Cu

### Conclusion:
The order in which metals will be formed at the cathode is **Ag, Hg, Cu**.