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 follow these steps:

### Step 1: Understand Magnetic Moment
The magnetic moment (μ) is a measure of the tendency of an object to align with a magnetic field. The formula to calculate the magnetic moment for transition metal ions is given by:

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

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

### Step 2: Analyze Each Ion
We will analyze each ion provided in the options to find the number of unpaired electrons.

#### Option 1: Fe²⁺
- **Electronic Configuration of Fe**: \( [Ar] 4s^2 3d^6 \)
- **For Fe²⁺**: Remove 2 electrons from the 4s orbital.
- **Configuration**: \( [Ar] 3d^6 \)
- **Unpaired Electrons**: 4 (as per Hund's rule)
- **Magnetic Moment**:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.9 \text{ Bohr magneton} \]

#### Option 2: Mn²⁺
- **Electronic Configuration of Mn**: \( [Ar] 4s^2 3d^5 \)
- **For Mn²⁺**: Remove 1 electron from the 4s orbital.
- **Configuration**: \( [Ar] 4s^1 3d^5 \)
- **Unpaired Electrons**: 6 (1 from 4s and 5 from 3d)
- **Magnetic Moment**:
\[ \mu = \sqrt{6(6 + 2)} = \sqrt{48} \approx 6.9 \text{ Bohr magneton} \]

#### Option 3: Fe³⁺
- **For Fe³⁺**: Remove 3 electrons (2 from 4s and 1 from 3d).
- **Configuration**: \( [Ar] 3d^5 \)
- **Unpaired Electrons**: 5
- **Magnetic Moment**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.9 \text{ Bohr magneton} \]

#### Option 4: Fe⁺
- **For Fe⁺**: Remove 1 electron (1 from 4s).
- **Configuration**: \( [Ar] 4s^1 3d^6 \)
- **Unpaired Electrons**: 5 (1 from 4s and 4 from 3d)
- **Magnetic Moment**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.9 \text{ Bohr magneton} \]

### Step 3: Compare Magnetic Moments
Now we compare the calculated magnetic moments:
- Fe²⁺: \( \approx 4.9 \) Bohr magneton
- Mn²⁺: \( \approx 6.9 \) Bohr magneton
- Fe³⁺: \( \approx 5.9 \) Bohr magneton
- Fe⁺: \( \approx 5.9 \) Bohr magneton

### Conclusion
The ion with the highest magnetic moment is **Mn²⁺** with a magnetic moment of approximately **6.9 Bohr magneton**.

### Final Answer
**Mn²⁺ has the highest magnetic moment.**

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