Which of the following have highest magnetic moment ?

Options

A. `Fe^(2+)`
B. `Mn^(+)`
C. `Fe^(3+)`
D. `Fe^(+)`

Answer

To determine which of the given ions has the highest magnetic moment, we will calculate the magnetic moment (μ) for each ion using the formula:

\[ \mu = \sqrt{n(n + 2)} \]

where \( n \) is the number of unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Ions and Their Electronic Configurations**:
- **Fe²⁺**: Iron has an atomic number of 26. Its electronic configuration is \( \text{[Ar]} 3d^6 4s^2 \). For Fe²⁺, we remove two electrons (from the 4s orbital), giving us \( \text{[Ar]} 3d^6 \).
- **Mn²⁺**: Manganese has an atomic number of 25. Its electronic configuration is \( \text{[Ar]} 3d^5 4s^2 \). For Mn²⁺, we remove one electron from the 4s orbital, resulting in \( \text{[Ar]} 3d^5 \).
- **Fe³⁺**: For Fe³⁺, we remove three electrons (two from 4s and one from 3d), resulting in \( \text{[Ar]} 3d^5 \).
- **Fe⁺**: For Fe⁺, we remove one electron from the 4s orbital, giving us \( \text{[Ar]} 3d^6 4s^1 \).

2. **Count the Unpaired Electrons**:
- **Fe²⁺ (3d⁶)**: The configuration is \( 3d^6 \) which has 4 unpaired electrons.
- **Mn²⁺ (3d⁵)**: The configuration is \( 3d^5 \) which has 5 unpaired electrons.
- **Fe³⁺ (3d⁵)**: The configuration is \( 3d^5 \) which has 5 unpaired electrons.
- **Fe⁺ (3d⁶ 4s¹)**: The configuration is \( 3d^6 4s^1 \) which has 4 unpaired electrons.

3. **Calculate the Magnetic Moment for Each Ion**:
- **Fe²⁺**:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.89 \, \text{BM} \]
- **Mn²⁺**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \text{BM} \]
- **Fe³⁺**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \text{BM} \]
- **Fe⁺**:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.89 \, \text{BM} \]

4. **Compare the Magnetic Moments**:
- Fe²⁺: 4.89 BM
- Mn²⁺: 5.92 BM
- Fe³⁺: 5.92 BM
- Fe⁺: 4.89 BM

5. **Conclusion**:
The ions with the highest magnetic moment are Mn²⁺ and Fe³⁺, both having a magnetic moment of approximately 5.92 BM.

### Final Answer:
**Mn²⁺ and Fe³⁺ have the highest magnetic moment.**