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 can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons in the ion.

### Step 2: Analyze Each Ion
We will analyze the given ions to find the number of unpaired electrons in each.

1. **Manganese (Mn²⁺)**:
- Atomic number of Mn = 25
- Electronic configuration: \( [Ar] 4s^2 3d^5 \)
- For Mn²⁺, we remove 2 electrons from the 4s orbital:
- Configuration of Mn²⁺: \( 3d^5 \)
- Number of unpaired electrons (n) = 5 (since all 5 electrons in the d-orbitals are unpaired).

2. **Zinc (Zn²⁺)**:
- Atomic number of Zn = 30
- Electronic configuration: \( [Ar] 4s^2 3d^{10} \)
- For Zn²⁺, we remove 2 electrons from the 4s orbital:
- Configuration of Zn²⁺: \( 3d^{10} \)
- Number of unpaired electrons (n) = 0 (all electrons are paired).

3. **Calcium (Ca²⁺)**:
- Atomic number of Ca = 20
- Electronic configuration: \( [Ar] 4s^2 \)
- For Ca²⁺, we remove 2 electrons from the 4s orbital:
- Configuration of Ca²⁺: \( [Ar] \)
- Number of unpaired electrons (n) = 0 (all electrons are paired).

4. **Potassium (K⁺)**:
- Atomic number of K = 19
- Electronic configuration: \( [Ar] 4s^1 \)
- For K⁺, we remove 1 electron from the 4s orbital:
- Configuration of K⁺: \( [Ar] \)
- Number of unpaired electrons (n) = 0 (all electrons are paired).

### Step 3: Calculate the Magnetic Moment for Each Ion
Using the formula \( \mu = \sqrt{n(n + 2)} \):

1. **For Mn²⁺**:
- \( n = 5 \)
- \( \mu = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \, \text{Bohr magneton} \)

2. **For Zn²⁺**:
- \( n = 0 \)
- \( \mu = \sqrt{0(0 + 2)} = \sqrt{0} = 0 \, \text{Bohr magneton} \)

3. **For Ca²⁺**:
- \( n = 0 \)
- \( \mu = \sqrt{0(0 + 2)} = \sqrt{0} = 0 \, \text{Bohr magneton} \)

4. **For K⁺**:
- \( n = 0 \)
- \( \mu = \sqrt{0(0 + 2)} = \sqrt{0} = 0 \, \text{Bohr magneton} \)

### Step 4: Conclusion
Among the ions analyzed, Mn²⁺ has the highest magnetic moment of \( \sqrt{35} \, \text{Bohr magneton} \) due to having 5 unpaired electrons. Therefore, the ion with the highest magnetic moment is:

**Answer: Mn²⁺**