Which of the following ion has maximum value of magnetic moment `

Options

A. `Cu^(+2)`
B. `Mn^(+3)`
C. `Fe^(+3)`
D. `V^(+3)`

Answer

To determine which ion has the maximum value of magnetic moment, we will follow these steps:

### Step 1: Understand the formula for magnetic moment
The magnetic moment (μ) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

### Step 2: Identify the electronic configurations of the ions
We will analyze the electronic configurations of the given ions to find the number of unpaired electrons.

1. **Copper (Cu²⁺)**:
- Atomic number of Cu = 29
- Ground state configuration: [Ar] 4s¹ 3d¹⁰
- For Cu²⁺, we remove 2 electrons:
- 1 from 4s and 1 from 3d
- Configuration: [Ar] 3d⁹
- Unpaired electrons in 3d⁹ = 1

2. **Manganese (Mn³⁺)**:
- Atomic number of Mn = 25
- Ground state configuration: [Ar] 4s² 3d⁵
- For Mn³⁺, we remove 3 electrons:
- 2 from 4s and 1 from 3d
- Configuration: [Ar] 3d⁴
- Unpaired electrons in 3d⁴ = 4

3. **Iron (Fe³⁺)**:
- Atomic number of Fe = 26
- Ground state configuration: [Ar] 4s² 3d⁶
- For Fe³⁺, we remove 3 electrons:
- 2 from 4s and 1 from 3d
- Configuration: [Ar] 3d⁵
- Unpaired electrons in 3d⁵ = 5

4. **Vanadium (V³⁺)**:
- Atomic number of V = 23
- Ground state configuration: [Ar] 4s² 3d³
- For V³⁺, we remove 3 electrons:
- 2 from 4s and 1 from 3d
- Configuration: [Ar] 3d²
- Unpaired electrons in 3d² = 2

### Step 3: Calculate the magnetic moments
Now we can calculate the magnetic moments for each ion using the number of unpaired electrons:

1. **Cu²⁺**:
- \( n = 1 \)
- \( \mu = \sqrt{1(1 + 2)} = \sqrt{3} \)

2. **Mn³⁺**:
- \( n = 4 \)
- \( \mu = \sqrt{4(4 + 2)} = \sqrt{24} = 2\sqrt{6} \)

3. **Fe³⁺**:
- \( n = 5 \)
- \( \mu = \sqrt{5(5 + 2)} = \sqrt{35} \)

4. **V³⁺**:
- \( n = 2 \)
- \( \mu = \sqrt{2(2 + 2)} = \sqrt{8} = 2\sqrt{2} \)

### Step 4: Compare the magnetic moments
Now we compare the calculated magnetic moments:
- Cu²⁺: \( \sqrt{3} \)
- Mn³⁺: \( 2\sqrt{6} \)
- Fe³⁺: \( \sqrt{35} \)
- V³⁺: \( 2\sqrt{2} \)

### Conclusion
The ion with the maximum magnetic moment is **Fe³⁺** with 5 unpaired electrons.

---