A solution containing one mole per litre of each `Cu(NO_(3))_(2), AgNO_(3), Hg_(2)(NO_(3))_(2)` is being electrolysed by using inert electrodes. The values of standard electrode potentials in volts (reduction potentials) are
`Ag^(+)//Ag = +0.80 V, HG_(2)^(2+)//Hg = +0.79 V`
`Cu^(+)//Cu = +0.34 V, Mg^(2+)//Mg = -2.37 V`
With increasing valtage, the sequence of deposition of metals on the cathode will be

Options

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

Explanation

To determine the sequence of deposition of metals on the cathode during the electrolysis of a solution containing `Cu(NO3)2`, `AgNO3`, and `Hg2(NO3)2`, we need to analyze the standard electrode potentials provided for each metal ion. The standard electrode potentials indicate how easily a metal ion can be reduced to its metallic form. The higher the potential, the more favorable the reduction reaction.

### Step-by-Step Solution:

1. **Identify the Standard Electrode Potentials:**
- For `Ag^+ + e^- → Ag`, E° = +0.80 V
- For `Hg2^2+ + 2e^- → 2Hg`, E° = +0.79 V
- For `Cu^2+ + 2e^- → Cu`, E° = +0.34 V
- For `Mg^2+ + 2e^- → Mg`, E° = -2.37 V

2. **Rank the Metals by Their Standard Electrode Potentials:**
- The metals can be ranked from highest to lowest standard reduction potential:
- Ag: +0.80 V
- Hg: +0.79 V
- Cu: +0.34 V
- Mg: -2.37 V

3. **Consider the Feasibility of Deposition:**
- The metals with higher standard reduction potentials will deposit first when the voltage is increased.
- However, since the standard reduction potential of magnesium is negative (-2.37 V), it indicates that magnesium will not be deposited under normal electrolysis conditions. The reduction potential of water (which is higher than that of magnesium) will take precedence over magnesium.

4. **Determine the Sequence of Deposition:**
- Based on the above analysis, the sequence of deposition of metals on the cathode, with increasing voltage, will be:
- First: Ag (Silver)
- Second: Hg (Mercury)
- Third: Cu (Copper)
- Therefore, the final sequence is Ag, Hg, Cu.

5. **Conclusion:**
- The sequence of deposition of metals on the cathode is: **Ag, Hg, Cu**.