In which of the following the stabiliy of two oxidation states is correctly represented?

Options

A. `Fe^(2+) gt Fe^(3+)`
B. `Ti^(3+) gt Ti^(4+)`
C. `Mn^(2+) gt Mn^(3+)`
D. `Cu^(+) gt Cu^(2+)`

Explanation

To determine the stability of the oxidation states of the given ions, we need to analyze their electronic configurations and apply the principles of stability related to half-filled and fully filled subshells. Here’s a step-by-step solution:

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

1. **Fe²⁺**:
- Atomic number of Fe = 26
- Electronic configuration: [Ar] 3d⁶

2. **Fe³⁺**:
- Remove one electron from Fe²⁺
- Electronic configuration: [Ar] 3d⁵

3. **Ti³⁺**:
- Atomic number of Ti = 22
- Electronic configuration: [Ar] 3d²

4. **Ti⁴⁺**:
- Remove two electrons from Ti³⁺
- Electronic configuration: [Ar] 3d⁰

5. **Mn²⁺**:
- Atomic number of Mn = 25
- Electronic configuration: [Ar] 3d⁵

6. **Mn³⁺**:
- Remove one electron from Mn²⁺
- Electronic configuration: [Ar] 3d⁴

7. **Cu⁺**:
- Atomic number of Cu = 29
- Electronic configuration: [Ar] 3d¹⁰

8. **Cu²⁺**:
- Remove one electron from Cu⁺
- Electronic configuration: [Ar] 3d⁹

### Step 2: Analyze the stability of oxidation states

- **Fe²⁺ vs Fe³⁺**:
- Fe³⁺ has a half-filled 3d⁵ configuration, which is more stable than the 3d⁶ configuration of Fe²⁺.
- **Conclusion**: Fe³⁺ is more stable than Fe²⁺.

- **Ti³⁺ vs Ti⁴⁺**:
- Ti⁴⁺ has an empty 3d⁰ configuration, which is less stable compared to Ti³⁺ with 3d².
- **Conclusion**: Ti³⁺ is more stable than Ti⁴⁺.

- **Mn²⁺ vs Mn³⁺**:
- Mn²⁺ has a half-filled 3d⁵ configuration, which is more stable than the 3d⁴ configuration of Mn³⁺.
- **Conclusion**: Mn²⁺ is more stable than Mn³⁺.

- **Cu⁺ vs Cu²⁺**:
- Cu²⁺ has a 3d⁹ configuration, which is less stable than the fully filled 3d¹⁰ configuration of Cu⁺.
- **Conclusion**: Cu⁺ is more stable than Cu²⁺.

### Step 3: Determine the correct option

From the analysis, we conclude:
- The correct order of stability is:
- Mn²⁺ > Mn³⁺
- Fe³⁺ > Fe²⁺
- Cu⁺ > Cu²⁺
- Ti³⁺ > Ti⁴⁺

Thus, the correct answer is the option that states Mn²⁺ is more stable than Mn³⁺.

### Final Answer:
The correct option is **C**: Mn²⁺ > Mn³⁺.

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