The metal that cannot be obtained by the electrolysis of an aqueous solution of its salt is:

To decide which metal cannot be deposited at the cathode when we perform electrolysis of an aqueous solution of its salt, we must compare the ease of reduction of the metal ion with that of water. A species that has a higher (more positive) reduction potential gets reduced in preference to a species that has a lower (more negative) reduction potential.

First, we recall the standard reduction potentials (all values in volts, at 25 °C, 1 M):

$$\text{Ag}^+ + e^- \rightarrow \text{Ag},\; E^\circ = +0.80$$

$$\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu},\; E^\circ = +0.34$$

$$\text{Cr}^{3+} + 3e^- \rightarrow \text{Cr},\; E^\circ = -0.74$$

$$\text{Ca}^{2+} + 2e^- \rightarrow \text{Ca},\; E^\circ = -2.87$$

The competing cathodic reaction in any aqueous solution is the reduction of water to hydrogen gas:

$$2\,\text{H}_2\text{O} + 2e^- \rightarrow \text{H}_2 + 2\,\text{OH}^-,$$

with $$E^\circ = -0.83\text{ V}.$$

The rule we now apply is simple: the half-reaction with the higher potential occurs preferentially. We compare each metal’s potential with that of water:

• For silver: $$+0.80 \gt -0.83,$$ so $$\text{Ag}^+$$ is reduced more easily than water; silver will be deposited.

• For copper: $$+0.34 \gt -0.83,$$ so $$\text{Cu}^{2+}$$ also wins over water; copper will be deposited.

• For chromium: $$-0.74 \gt -0.83,$$ the reduction of $$\text{Cr}^{3+}$$ is still slightly easier than that of water; chromium, though with difficulty, can be deposited from a specially buffered aqueous bath.

• For calcium: $$-2.87 \lt -0.83,$$ meaning $$\text{Ca}^{2+}$$ is much harder to reduce than water. During electrolysis of any aqueous calcium salt, water will always be reduced first, giving hydrogen gas. Calcium metal can therefore never be obtained from an aqueous solution; it must be produced from the molten (fused) salt.

Thus, out of the four metals listed, calcium is the one that cannot be obtained by electrolysis of an aqueous solution of its salt.

Hence, the correct answer is Option 2.