Which of the following shows maximum magnetic moment?

Options

A. `Mg^(2+)`
B. `Ti^(3+)`
C. `V^(3+)`
D. `Fe^(2+)`

Explanation

To determine which of the given ions shows the maximum magnetic moment, we need to calculate 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 there are, the higher the magnetic moment.

### Step-by-Step Solution:

1. **Identify the Ions**: We need to analyze the following ions:
- Mg²⁺
- Ti³⁺
- V³⁺
- Fe²⁺

2. **Determine Electron Configurations**:
- **Mg²⁺**:
- Atomic number of Mg = 12
- Electron configuration: 1s² 2s² 2p⁶ 3s²
- For Mg²⁺, it loses 2 electrons from the 3s subshell:
- Configuration: 1s² 2s² 2p⁶ (all electrons are paired)
- Unpaired electrons (n) = 0

- **Ti³⁺**:
- Atomic number of Ti = 22
- Electron configuration: [Ar] 4s² 3d²
- For Ti³⁺, it loses 3 electrons (2 from 4s and 1 from 3d):
- Configuration: [Ar] 3d¹
- Unpaired electrons (n) = 1

- **V³⁺**:
- Atomic number of V = 23
- Electron configuration: [Ar] 4s² 3d³
- For V³⁺, it loses 3 electrons (2 from 4s and 1 from 3d):
- Configuration: [Ar] 3d²
- Unpaired electrons (n) = 2

- **Fe²⁺**:
- Atomic number of Fe = 26
- Electron configuration: [Ar] 4s² 3d⁶
- For Fe²⁺, it loses 2 electrons from 4s:
- Configuration: [Ar] 3d⁶
- Unpaired electrons (n) = 4

3. **Calculate Magnetic Moments**:
- For **Mg²⁺**:
\[ \mu = \sqrt{0(0 + 2)} = 0 \]
- For **Ti³⁺**:
\[ \mu = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73 \, \text{BM} \]
- For **V³⁺**:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2.83 \, \text{BM} \]
- For **Fe²⁺**:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.89 \, \text{BM} \]

4. **Compare the Magnetic Moments**:
- Mg²⁺: 0 BM
- Ti³⁺: 1.73 BM
- V³⁺: 2.83 BM
- Fe²⁺: 4.89 BM

5. **Conclusion**: The ion with the maximum magnetic moment is **Fe²⁺**, with a magnetic moment of approximately 4.89 BM.

### Final Answer:
**Fe²⁺ shows the maximum magnetic moment.**