Which of the following ion has the maximum magnetic moment?

Options

A. `Mn^(2+)`
B. `Fe^(2+)`
C. `Ti^(2+)`
D. `Cr^(2+)`

Explanation

To determine which ion has the maximum magnetic moment, we need to calculate the number of unpaired electrons in each of the given ions. 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 greater its magnetic moment will be.

### Step-by-Step Solution:

1. **Identify the Ions and Their Electronic Configurations:**
- **Mn²⁺**: The electronic configuration is \( \text{Ar} \, 3d^5 \, 4s^0 \)
- **Fe²⁺**: The electronic configuration is \( \text{Ar} \, 3d^6 \, 4s^0 \)
- **Ti²⁺**: The electronic configuration is \( \text{Ar} \, 3d^2 \, 4s^0 \)
- **Cr²⁺**: The electronic configuration is \( \text{Ar} \, 3d^4 \, 4s^0 \)

2. **Count the Unpaired Electrons:**
- **Mn²⁺ (3d⁵)**: There are 5 unpaired electrons.
- **Fe²⁺ (3d⁶)**: There are 4 unpaired electrons.
- **Ti²⁺ (3d²)**: There are 2 unpaired electrons.
- **Cr²⁺ (3d⁴)**: There are 4 unpaired electrons.

3. **Compare the Number of Unpaired Electrons:**
- Mn²⁺: 5 unpaired electrons
- Fe²⁺: 4 unpaired electrons
- Ti²⁺: 2 unpaired electrons
- Cr²⁺: 4 unpaired electrons

4. **Determine the Ion with the Maximum Magnetic Moment:**
- Since Mn²⁺ has the highest number of unpaired electrons (5), it will have the maximum magnetic moment.

### Conclusion:
The ion with the maximum magnetic moment is **Mn²⁺**.

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