Maximum magnetic moment is shown by

Options

A. `3d^8`
B. `3d^7`
C. `3d^9`
D. `3d^5`

Explanation

To determine which configuration has the maximum magnetic moment, we need to analyze the number of unpaired electrons in the d-orbitals of the transition metals. The magnetic moment can be calculated using the formula:

\[ \text{Magnetic Moment} = \sqrt{n(n + 2)} \]

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

### Step-by-Step Solution:

1. **Identify the d-electron configurations**: We will consider the common d-electron configurations for transition metals, specifically focusing on 3d series:
- 3d⁵
- 3d⁶
- 3d⁷
- 3d⁸
- 3d⁹

2. **Determine the number of unpaired electrons for each configuration**:
- **3d⁵**: All five electrons are unpaired. Therefore, \( n = 5 \).
- **3d⁶**: There are 4 unpaired electrons (1 pair). Therefore, \( n = 4 \).
- **3d⁷**: There are 3 unpaired electrons (2 pairs). Therefore, \( n = 3 \).
- **3d⁸**: There are 2 unpaired electrons (3 pairs). Therefore, \( n = 2 \).
- **3d⁹**: There is 1 unpaired electron (4 pairs). Therefore, \( n = 1 \).

3. **Calculate the magnetic moment for each configuration**:
- **For 3d⁵**:
\[ \text{Magnetic Moment} = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \]
- **For 3d⁶**:
\[ \text{Magnetic Moment} = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.90 \]
- **For 3d⁷**:
\[ \text{Magnetic Moment} = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \]
- **For 3d⁸**:
\[ \text{Magnetic Moment} = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.83 \]
- **For 3d⁹**:
\[ \text{Magnetic Moment} = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73 \]

4. **Compare the magnetic moments**:
- 3d⁵: 5.92
- 3d⁶: 4.90
- 3d⁷: 3.87
- 3d⁸: 2.83
- 3d⁹: 1.73

5. **Conclusion**: The configuration with the maximum magnetic moment is **3d⁵**, which has 5 unpaired electrons and a magnetic moment of approximately 5.92.