Statement I: The ionization energy of `Na^(2+)` is less than that of `Na^(+)` .
Statement II: `Na^(+)` has an inert gas configuration.

Options

A. If both Statement I and Statement II are true and Statement II is the correct explanation of Statement I.
B. If both Statement I and Statement II are true but Statement II is not the correct explanation for Statement I.
C. If Statement I is true but Statement II is false.
D. If Statement I is false but Statement II is true.

Answer

To analyze the statements provided in the question, we will evaluate each one step by step.

### Step 1: Analyze Statement I
**Statement I:** The ionization energy of `Na^(2+)` is less than that of `Na^(+)`.

1. **Understanding Ionization Energy:** Ionization energy is the energy required to remove an electron from an atom or ion.
2. **Electronic Configuration of `Na^(+)`:** Sodium (Na) has an atomic number of 11. When it loses one electron to form `Na^(+)`, its electronic configuration becomes:
- `Na`: 1s² 2s² 2p⁶ 3s¹
- `Na^(+)`: 1s² 2s² 2p⁶ (which is the same as the configuration of Neon, a noble gas).
3. **Electronic Configuration of `Na^(2+)`:** When `Na^(+)` loses another electron to form `Na^(2+)`, its electronic configuration becomes:
- `Na^(2+)`: 1s² 2s² 2p⁵.
4. **Comparison of Ionization Energies:** Since `Na^(+)` has a noble gas configuration (which is stable), removing an electron from it (to form `Na^(2+)`) requires more energy than removing an electron from `Na` (which has a less stable configuration). Therefore, the ionization energy of `Na^(2+)` is actually greater than that of `Na^(+)`.

**Conclusion for Statement I:** This statement is **false**.

### Step 2: Analyze Statement II
**Statement II:** `Na^(+)` has an inert gas configuration.

1. **Inert Gas Configuration:** An inert gas configuration refers to a completely filled electron shell, which is very stable.
2. **Electronic Configuration of `Na^(+)`:** As established earlier, the electronic configuration of `Na^(+)` is:
- `Na^(+)`: 1s² 2s² 2p⁶.
3. **Comparison with Noble Gas Configuration:** This configuration is identical to that of Neon (Ne), which is indeed an inert gas.

**Conclusion for Statement II:** This statement is **true**.

### Final Conclusion
- **Statement I:** False
- **Statement II:** True

Thus, the correct option is that Statement I is false and Statement II is true.

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