Which of the following transition metal ions has highest magnetic moment ?

Options

A. `Cu^(2+)`
B. `Ni^(2+)`
C. `Co^(2+)`
D. `Fe^(2+)`

Explanation

To determine which transition metal ion has the highest magnetic moment, we need to analyze the number of unpaired electrons in each ion. The magnetic moment (μ) can be calculated using the formula:

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

where \(n\) is the number of unpaired electrons. The more unpaired electrons an ion has, the higher its magnetic moment will be.

### Step-by-Step Solution:

1. **Identify the transition metal ions**: The ions we need to analyze are:
- Copper (Cu²⁺)
- Nickel (Ni²⁺)
- Cobalt (Co²⁺)
- Iron (Fe²⁺)

2. **Determine the electronic configuration of each ion**:
- **Copper (Cu²⁺)**:
- Atomic number of Cu = 29
- Ground state configuration: [Ar] 3d¹⁰ 4s¹
- After losing 2 electrons (from 4s and 3d): Configuration = 3d⁹
- **Nickel (Ni²⁺)**:
- Atomic number of Ni = 28
- Ground state configuration: [Ar] 3d⁸ 4s²
- After losing 2 electrons: Configuration = 3d⁸
- **Cobalt (Co²⁺)**:
- Atomic number of Co = 27
- Ground state configuration: [Ar] 3d⁷ 4s²
- After losing 2 electrons: Configuration = 3d⁷
- **Iron (Fe²⁺)**:
- Atomic number of Fe = 26
- Ground state configuration: [Ar] 3d⁶ 4s²
- After losing 2 electrons: Configuration = 3d⁶

3. **Count the number of unpaired electrons in each ion**:
- **Cu²⁺ (3d⁹)**:
- Configuration: ↑↓ ↑↓ ↑↓ ↑↓ ↑
- Unpaired electrons: 1
- **Ni²⁺ (3d⁸)**:
- Configuration: ↑↓ ↑↓ ↑↓ ↑ ↑
- Unpaired electrons: 2
- **Co²⁺ (3d⁷)**:
- Configuration: ↑↓ ↑↓ ↑↓ ↑ ↑ ↑
- Unpaired electrons: 3
- **Fe²⁺ (3d⁶)**:
- Configuration: ↑↓ ↑↓ ↑↓ ↑ ↑ ↑ ↑
- Unpaired electrons: 4

4. **Calculate the magnetic moment for each ion**:
- **Cu²⁺**:
- \(n = 1\) → \(\mu = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73\)
- **Ni²⁺**:
- \(n = 2\) → \(\mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83\)
- **Co²⁺**:
- \(n = 3\) → \(\mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87\)
- **Fe²⁺**:
- \(n = 4\) → \(\mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.89\)

5. **Conclusion**:
- The ion with the highest magnetic moment is **Fe²⁺** with 4 unpaired electrons and a magnetic moment of approximately 4.89.

### Final Answer:
**Fe²⁺ has the highest magnetic moment among the given transition metal ions.**