`Cu_((aq.))^+` has less stable nature than `Cu_((aq.))^(2+)` but `Fe_((aq.))^(3+)` is more stable than `Fe_((aq.))^(2+)`.
Half-filled and completely filled, sub-shell are more stable.

Options

A. If both assertion and reason are true and the reason is the correct explanation of assertion
B. If both assertion and reason are true and the reason is not the correct explanation of assertion
C. If assertion is false but reason is true
D. If assertion is true but the reason is false

Answer

To solve the question regarding the stability of the copper and iron ions, we will analyze the electronic configurations and the factors affecting their stability step by step.

### Step 1: Write the electronic configurations of the relevant ions.

1. **Copper (Cu)**:
- Atomic number = 29
- Ground state configuration: \( [Ar] 3d^{10} 4s^1 \)
- For \( Cu^+ \):
- Loses one electron from \( 4s \):
- Configuration: \( [Ar] 3d^{10} \)
- For \( Cu^{2+} \):
- Loses one more electron from \( 3d \):
- Configuration: \( [Ar] 3d^9 \)

2. **Iron (Fe)**:
- Atomic number = 26
- Ground state configuration: \( [Ar] 3d^6 4s^2 \)
- For \( Fe^{2+} \):
- Loses two electrons (first from \( 4s \), then from \( 3d \)):
- Configuration: \( [Ar] 3d^6 \)
- For \( Fe^{3+} \):
- Loses one more electron from \( 3d \):
- Configuration: \( [Ar] 3d^5 \)

### Step 2: Analyze the stability of \( Cu^+ \) and \( Cu^{2+} \).

- **Stability of \( Cu^+ \)**:
- Configuration: \( [Ar] 3d^{10} \) (completely filled)
- Generally, completely filled subshells are stable, but in this case, we also consider the electrode potential.

- **Stability of \( Cu^{2+} \)**:
- Configuration: \( [Ar] 3d^9 \) (not completely filled)
- The standard electrode potential for \( Cu^+ \) to \( Cu \) is +0.52 V, while for \( Cu^{2+} \) to \( Cu \) it is +0.34 V.
- A lower electrode potential indicates that \( Cu^{2+} \) is more stable than \( Cu^+ \).

### Step 3: Analyze the stability of \( Fe^{2+} \) and \( Fe^{3+} \).

- **Stability of \( Fe^{2+} \)**:
- Configuration: \( [Ar] 3d^6 \) (not half-filled)

- **Stability of \( Fe^{3+} \)**:
- Configuration: \( [Ar] 3d^5 \) (half-filled)
- Half-filled subshells are generally more stable due to symmetry and exchange energy.

### Conclusion:

- **Assertion**: \( Cu^+ \) has less stable nature than \( Cu^{2+} \) is true, as \( Cu^{2+} \) is more stable due to lower electrode potential.
- **Assertion**: \( Fe^{3+} \) is more stable than \( Fe^{2+} \) is also true, due to the half-filled \( 3d^5 \) configuration.

### Final Statement:

Both the assertion and the reason are true, but the reason (half-filled and completely filled subshells are more stable) does not correctly explain the assertion regarding copper ions.