The maximum magnetic moment is shown by the ion with electronic configuration

Options

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

Explanation

To determine which ion shows the maximum magnetic moment based on its electronic configuration, we will analyze the given configurations step by step.

### Step 1: Understand the Magnetic Moment Formula
The magnetic moment (μ) is calculated using the formula:
\[ \mu = \sqrt{N(N + 2)} \]
where \(N\) is the number of unpaired electrons.

### Step 2: Analyze Each Electronic Configuration

1. **For 3D8:**
- Configuration: 3D has 8 electrons.
- Distribution: The electrons will fill as follows: ↑↓ ↑↓ ↑↓ ↑ ↑ (2 paired in first three orbitals and 2 unpaired in the last).
- Unpaired Electrons: 2
- Magnetic Moment Calculation:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{2 \times 4} = \sqrt{8} \]

2. **For 3D5:**
- Configuration: 3D has 5 electrons.
- Distribution: All electrons will be unpaired: ↑ ↑ ↑ ↑ ↑.
- Unpaired Electrons: 5
- Magnetic Moment Calculation:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \]

3. **For 3D7:**
- Configuration: 3D has 7 electrons.
- Distribution: 3 paired and 4 unpaired: ↑↓ ↑↓ ↑↓ ↑ ↑.
- Unpaired Electrons: 3
- Magnetic Moment Calculation:
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{3 \times 5} = \sqrt{15} \]

4. **For 3D9:**
- Configuration: 3D has 9 electrons.
- Distribution: 4 paired and 5 unpaired: ↑↓ ↑↓ ↑↓ ↑↑ ↑.
- Unpaired Electrons: 1
- Magnetic Moment Calculation:
\[ \mu = \sqrt{1(1 + 2)} = \sqrt{1 \times 3} = \sqrt{3} \]

### Step 3: Compare the Magnetic Moments
- **3D8:** μ = √8
- **3D5:** μ = √35 (maximum)
- **3D7:** μ = √15
- **3D9:** μ = √3

### Conclusion
The ion with the electronic configuration 3D5 shows the maximum magnetic moment, which is √35.

### Final Answer
**The ion with electronic configuration 3D5 shows the maximum magnetic moment.**

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