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 can be calculated using the formula:

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

where \( n \) is the number of unpaired electrons. Let's evaluate each ion step by step.

### Step 1: Analyze Ti³⁺ (Titanium ion)
1. **Find the electronic configuration of Ti (Titanium)**:
- Atomic number of Ti = 22
- Electronic configuration: \( [Ar] 3d^2 4s^2 \)

2. **Determine the configuration for Ti³⁺**:
- Ti³⁺ means we remove 3 electrons. The first two will be removed from the 4s orbital, and one from the 3d orbital.
- Remaining configuration: \( 3d^1 4s^0 \)

3. **Count unpaired electrons**:
- Number of unpaired electrons = 1

### Step 2: Analyze Sc³⁺ (Scandium ion)
1. **Find the electronic configuration of Sc (Scandium)**:
- Atomic number of Sc = 21
- Electronic configuration: \( [Ar] 3d^1 4s^2 \)

2. **Determine the configuration for Sc³⁺**:
- Sc³⁺ means we remove 3 electrons. The first two will be removed from the 4s orbital, and one from the 3d orbital.
- Remaining configuration: \( 3d^0 4s^0 \)

3. **Count unpaired electrons**:
- Number of unpaired electrons = 0

### Step 3: Analyze Mn²⁺ (Manganese ion)
1. **Find the electronic configuration of Mn (Manganese)**:
- Atomic number of Mn = 25
- Electronic configuration: \( [Ar] 3d^5 4s^2 \)

2. **Determine the configuration for Mn²⁺**:
- Mn²⁺ means we remove 2 electrons, both from the 4s orbital.
- Remaining configuration: \( 3d^5 4s^0 \)

3. **Count unpaired electrons**:
- Number of unpaired electrons = 5 (since all 5 electrons in the 3d subshell are unpaired)

### Step 4: Analyze Zn²⁺ (Zinc ion)
1. **Find the electronic configuration of Zn (Zinc)**:
- Atomic number of Zn = 30
- Electronic configuration: \( [Ar] 3d^{10} 4s^2 \)

2. **Determine the configuration for Zn²⁺**:
- Zn²⁺ means we remove 2 electrons, both from the 4s orbital.
- Remaining configuration: \( 3d^{10} 4s^0 \)

3. **Count unpaired electrons**:
- Number of unpaired electrons = 0

### Conclusion
Now we summarize the number of unpaired electrons for each ion:
- Ti³⁺: 1 unpaired electron
- Sc³⁺: 0 unpaired electrons
- Mn²⁺: 5 unpaired electrons
- Zn²⁺: 0 unpaired electrons

The ion with the highest magnetic moment is Mn²⁺, which has 5 unpaired electrons.

### Final Answer
The ion with the highest magnetic moment is **Mn²⁺ (option 3)**.

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