Which one of the following ions has the highest magnetic moment ?

Options

A. `Mn^(2+)`
B. `Zn^(2+)`
C. `Ca^(2+)`
D. `K^+`

Answer

To determine which ion has the highest magnetic moment, we will follow these steps:

### Step 1: Understand the Concept of Magnetic Moment
The magnetic moment (μ) of an ion is calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons in the ion.

### Step 2: Identify the Ions and Their Electron Configurations
We will analyze the ions provided in the question:

1. **Manganese Ion (Mn²⁺)**:
- Atomic number of Manganese (Mn) = 25
- Ground state electron configuration: \( [Ar] 3d^5 4s^2 \)
- For Mn²⁺, it loses 2 electrons (from 4s), resulting in \( [Ar] 3d^5 \).
- Number of unpaired electrons = 5.

2. **Zinc Ion (Zn²⁺)**:
- Atomic number of Zinc (Zn) = 30
- Ground state electron configuration: \( [Ar] 3d^{10} 4s^2 \)
- For Zn²⁺, it loses 2 electrons (from 4s), resulting in \( [Ar] 3d^{10} \).
- Number of unpaired electrons = 0.

3. **Calcium Ion (Ca²⁺)**:
- Atomic number of Calcium (Ca) = 20
- Ground state electron configuration: \( [Ar] 4s^2 \)
- For Ca²⁺, it loses 2 electrons (from 4s), resulting in \( [Ar] \).
- Number of unpaired electrons = 0.

4. **Potassium Ion (K⁺)**:
- Atomic number of Potassium (K) = 19
- Ground state electron configuration: \( [Ar] 4s^1 \)
- For K⁺, it loses 1 electron (from 4s), resulting in \( [Ar] \).
- Number of unpaired electrons = 0.

### Step 3: Calculate the Magnetic Moment for Each Ion
Now we will calculate the magnetic moment for each ion using the formula:

1. **For Mn²⁺**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \approx 5.91 \, \text{Bohr Magneton} \]

2. **For Zn²⁺**:
\[ \mu = \sqrt{0(0 + 2)} = \sqrt{0} = 0 \, \text{Bohr Magneton} \]

3. **For Ca²⁺**:
\[ \mu = \sqrt{0(0 + 2)} = \sqrt{0} = 0 \, \text{Bohr Magneton} \]

4. **For K⁺**:
\[ \mu = \sqrt{0(0 + 2)} = \sqrt{0} = 0 \, \text{Bohr Magneton} \]

### Step 4: Compare the Magnetic Moments
- Mn²⁺: 5.91 Bohr Magneton
- Zn²⁺: 0 Bohr Magneton
- Ca²⁺: 0 Bohr Magneton
- K⁺: 0 Bohr Magneton

### Conclusion
The ion with the highest magnetic moment is **Mn²⁺** with a magnetic moment of approximately 5.91 Bohr Magneton.