If Hund's rule is not followed , magnetic moment of `Fe^(2+) , Mn^(o+) ` and Cr all having `24` electron will be in order

Options

A. `Fe^(2+) lt Mn^(+) lt Cr`
B. `Fe^(2+) = Cr lt Mn^(+2)`
C. `Fe^(+2)=Mn lt Cr`
D. `Mn^(+)=Cr lt Fe^(+2)`

Explanation

To solve the problem of determining the order of magnetic moments for Fe²⁺, Mn⁺, and Cr, all having 24 electrons, we will follow these steps:

### Step 1: Determine the electronic configurations
1. **Fe²⁺ (Iron)**: Iron has an atomic number of 26. The electron configuration of neutral Fe is [Ar] 3d⁶ 4s². For Fe²⁺, we remove two electrons (typically from the 4s orbital first), leading to:
\[ \text{Fe}^{2+} : [Ar] 3d^6 \]

2. **Mn⁺ (Manganese)**: Manganese has an atomic number of 25. The electron configuration of neutral Mn is [Ar] 3d⁵ 4s². For Mn⁺, we remove one electron from the 4s orbital:
\[ \text{Mn}^{+} : [Ar] 3d^5 \]

3. **Cr (Chromium)**: Chromium has an atomic number of 24. The electron configuration of neutral Cr is [Ar] 3d⁵ 4s¹. Since Cr is an exception, we have:
\[ \text{Cr} : [Ar] 3d^5 4s^1 \]

### Step 2: Count the number of unpaired electrons
1. **Fe²⁺**: The 3d⁶ configuration can be filled as follows:
- 3d: ↑↓ ↑↓ ↑ ↑ ↑ (4 unpaired electrons)
Thus, Fe²⁺ has **4 unpaired electrons**.

2. **Mn⁺**: The 3d⁵ configuration can be filled as follows:
- 3d: ↑ ↑ ↑ ↑ ↑ (5 unpaired electrons)
Thus, Mn⁺ has **5 unpaired electrons**.

3. **Cr**: The 3d⁵ 4s¹ configuration can be filled as follows:
- 3d: ↑ ↑ ↑ ↑ ↑ (5 unpaired electrons)
- 4s: ↑ (1 unpaired electron)
Thus, Cr has **6 unpaired electrons**.

### Step 3: Calculate the magnetic moment
The magnetic moment (μ) is calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

1. **Fe²⁺**:
\[ \mu_{Fe^{2+}} = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.89 \, \mu_B \]

2. **Mn⁺**:
\[ \mu_{Mn^{+}} = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \mu_B \]

3. **Cr**:
\[ \mu_{Cr} = \sqrt{6(6 + 2)} = \sqrt{48} \approx 6.93 \, \mu_B \]

### Step 4: Order the magnetic moments
Now we can order the magnetic moments based on the calculated values:
- **Fe²⁺**: 4.89 μ_B
- **Mn⁺**: 5.92 μ_B
- **Cr**: 6.93 μ_B

Thus, the order of magnetic moments is:
\[ \text{Fe}^{2+} < \text{Mn}^{+} < \text{Cr} \]

### Final Answer
The order of magnetic moments for Fe²⁺, Mn⁺, and Cr is:
\[ \text{Fe}^{2+} < \text{Mn}^{+} < \text{Cr} \]