Which of the following ions has the highest magnetic moment

Options

A. `Ti^(3+)`
B. `Sc^(3+)`
C. `Mn^(2+)`
D. `Zn^(2+)`

Answer

To determine which 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 greater its magnetic moment will be.

### Step-by-Step Solution:

1. **Identify the Ions and Their Electronic Configurations:**
- **Titanium (Ti) +3:**
- Atomic number of Ti = 22
- Electronic configuration of Ti = [Ar] 3d² 4s²
- For Ti +3, we remove 3 electrons (2 from 4s and 1 from 3d):
- Configuration: [Ar] 3d¹
- Unpaired electrons = 1

- **Scandium (Sc) +3:**
- Atomic number of Sc = 21
- Electronic configuration of Sc = [Ar] 3d¹ 4s²
- For Sc +3, we remove 3 electrons (2 from 4s and 1 from 3d):
- Configuration: [Ar] 3d⁰
- Unpaired electrons = 0

- **Manganese (Mn) +2:**
- Atomic number of Mn = 25
- Electronic configuration of Mn = [Ar] 3d⁵ 4s²
- For Mn +2, we remove 2 electrons (2 from 4s):
- Configuration: [Ar] 3d⁵
- Unpaired electrons = 5

- **Zinc (Zn) +2:**
- Atomic number of Zn = 30
- Electronic configuration of Zn = [Ar] 3d¹⁰ 4s²
- For Zn +2, we remove 2 electrons (2 from 4s):
- Configuration: [Ar] 3d¹⁰
- Unpaired electrons = 0

2. **Count the Unpaired Electrons:**
- Ti +3: 1 unpaired electron
- Sc +3: 0 unpaired electrons
- Mn +2: 5 unpaired electrons
- Zn +2: 0 unpaired electrons

3. **Determine the Ion with the Highest Magnetic Moment:**
- The ion with the highest number of unpaired electrons is Mn +2, which has 5 unpaired electrons.

4. **Conclusion:**
- Therefore, the ion with the highest magnetic moment is **Mn +2**.

### Final Answer:
The ion with the highest magnetic moment is **Mn +2**.

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