Which one of the following show highest magnetic moment?

Options

A. `V^(3+)`
B. `Cr^(3+)`
C. `Fe^(3+)`
D. `Co^(3+)`

Explanation

To determine which ion shows the highest magnetic moment among the given options, we will calculate the magnetic moment for each ion based on their electronic configurations and the number of unpaired electrons. The formula for calculating the magnetic moment (μ) is:

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

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

### Step-by-Step Solution:

1. **Calculate the magnetic moment for V³⁺ (Vanadium ion)**:
- Electronic configuration: \( \text{Ar} \, 3d^2 \, 4s^0 \)
- Number of unpaired electrons (\(n\)): 2
- Magnetic moment calculation:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{2 \times 4} = \sqrt{8} \approx 2.82 \, \text{Bohr magneton} \]

2. **Calculate the magnetic moment for Cr³⁺ (Chromium ion)**:
- Electronic configuration: \( \text{Ar} \, 3d^3 \, 4s^0 \)
- Number of unpaired electrons (\(n\)): 3
- Magnetic moment calculation:
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{3 \times 5} = \sqrt{15} \approx 3.87 \, \text{Bohr magneton} \]

3. **Calculate the magnetic moment for Fe³⁺ (Iron ion)**:
- Electronic configuration: \( \text{Ar} \, 3d^5 \, 4s^0 \)
- Number of unpaired electrons (\(n\)): 5
- Magnetic moment calculation:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \approx 5.92 \, \text{Bohr magneton} \]

4. **Calculate the magnetic moment for Co³⁺ (Cobalt ion)**:
- Electronic configuration: \( \text{Ar} \, 3d^6 \, 4s^0 \)
- Number of unpaired electrons (\(n\)): 4
- Magnetic moment calculation:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{4 \times 6} = \sqrt{24} \approx 4.89 \, \text{Bohr magneton} \]

### Conclusion:
After calculating the magnetic moments for all four ions, we find:
- V³⁺: 2.82 Bohr magneton
- Cr³⁺: 3.87 Bohr magneton
- Fe³⁺: 5.92 Bohr magneton
- Co³⁺: 4.89 Bohr magneton

The ion with the highest magnetic moment is **Fe³⁺**, with a magnetic moment of approximately **5.92 Bohr magneton**.