The magnetic nature of elements depends on the presence of unpaired electrons. Identify the configuration of transition element which shows highest magnetic moment.

Options

A. `3d^7`
B. `3d^5`
C. `3d^8`
D. `3d^2`

Explanation

To determine the configuration of the transition element that shows the highest magnetic moment, we need to analyze the number of unpaired electrons in each given electronic configuration. The magnetic moment is directly related to the number of unpaired electrons, with more unpaired electrons resulting in a higher magnetic moment.

### Step-by-Step Solution:

1. **Identify the Configurations**: We have four configurations to analyze:
- Option 1: 3d⁷
- Option 2: 3d⁵
- Option 3: 3d⁸
- Option 4: 3d⁹

2. **Determine the Number of Unpaired Electrons**:
- **For 3d⁷**:
- The filling order is: ↑ ↑ ↑ ↑ (first 5 electrons are unpaired) and then the next two electrons will pair up.
- Thus, there are 3 unpaired electrons.
- **For 3d⁵**:
- All five electrons are unpaired: ↑ ↑ ↑ ↑ ↑.
- Thus, there are 5 unpaired electrons.
- **For 3d⁸**:
- The filling order is: ↑ ↑ ↑ ↑ (first 5 electrons are unpaired) and then the next three electrons will pair up.
- Thus, there are 2 unpaired electrons.
- **For 3d⁹**:
- The filling order is: ↑ ↑ ↑ ↑ (first 5 electrons are unpaired) and then the next four electrons will pair up.
- Thus, there are 1 unpaired electron.

3. **Calculate the Magnetic Moment**:
- The formula for calculating the magnetic moment (μ) is:
\[ μ = \sqrt{n(n + 2)} \text{ Bohr magnetons} \]
- **For 3d⁷** (3 unpaired electrons):
\[ μ = \sqrt{3(3 + 2)} = \sqrt{15} \text{ Bohr magnetons} \]
- **For 3d⁵** (5 unpaired electrons):
\[ μ = \sqrt{5(5 + 2)} = \sqrt{35} \text{ Bohr magnetons} \]
- **For 3d⁸** (2 unpaired electrons):
\[ μ = \sqrt{2(2 + 2)} = \sqrt{8} \text{ Bohr magnetons} \]
- **For 3d⁹** (1 unpaired electron):
\[ μ = \sqrt{1(1 + 2)} = \sqrt{3} \text{ Bohr magnetons} \]

4. **Compare the Magnetic Moments**:
- 3d⁷: μ = √15
- 3d⁵: μ = √35
- 3d⁸: μ = √8
- 3d⁹: μ = √3

5. **Conclusion**: The configuration with the highest magnetic moment is 3d⁵, which has 5 unpaired electrons.

### Final Answer:
The configuration of the transition element that shows the highest magnetic moment is **3d⁵** (Option 2).

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