The pair having similar magnetic moment is

Options

A. `Ti^(3+),V^(3+)`
B. `Cr^(3+),Mn^(2+)`
C. `Mn^(2+),Fe^(3+)`
D. `Fe^(2+),Mn^(2+)`

Answer

To determine the pair having similar magnetic moments, we will calculate the magnetic moment (μ) for each pair based on the number of unpaired electrons (n) using the formula:

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

### Step-by-Step Solution:

1. **Identify the pairs to analyze**:
- Pair 1: Ti³⁺ and V³⁺
- Pair 2: Cr³⁺ and Mn²⁺
- Pair 3: Mn²⁺ and Fe³⁺
- Pair 4: Fe²⁺ and Mn²⁺

2. **Calculate for Ti³⁺ and V³⁺**:
- Titanium (Ti) has an electronic configuration of [Ar] 3d² 4s².
- For Ti³⁺, the configuration becomes 3d¹ (1 unpaired electron).
- Vanadium (V) has an electronic configuration of [Ar] 3d³ 4s².
- For V³⁺, the configuration becomes 3d² (2 unpaired electrons).
- Calculate μ:
- For Ti³⁺:
\[ \mu = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73 \]
- For V³⁺:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.83 \]
- **Conclusion**: This pair does not have similar magnetic moments.

3. **Calculate for Cr³⁺ and Mn²⁺**:
- Chromium (Cr) has an electronic configuration of [Ar] 3d⁵ 4s¹.
- For Cr³⁺, the configuration becomes 3d³ (3 unpaired electrons).
- Manganese (Mn) has an electronic configuration of [Ar] 3d⁵ 4s².
- For Mn²⁺, the configuration becomes 3d⁵ (5 unpaired electrons).
- Calculate μ:
- For Cr³⁺:
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \]
- For Mn²⁺:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \]
- **Conclusion**: This pair does not have similar magnetic moments.

4. **Calculate for Mn²⁺ and Fe³⁺**:
- We already know Mn²⁺ has 5 unpaired electrons (μ ≈ 5.92).
- Iron (Fe) has an electronic configuration of [Ar] 3d⁶ 4s².
- For Fe³⁺, the configuration becomes 3d⁵ (5 unpaired electrons).
- Calculate μ:
- For Fe³⁺:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \]
- **Conclusion**: This pair has similar magnetic moments.

5. **Calculate for Fe²⁺ and Mn²⁺**:
- We already know Mn²⁺ has 5 unpaired electrons (μ ≈ 5.92).
- For Fe²⁺, the configuration becomes 3d⁶ (4 unpaired electrons).
- Calculate μ:
- For Fe²⁺:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.90 \]
- **Conclusion**: This pair does not have similar magnetic moments.

### Final Answer:
The pair having similar magnetic moment is **Mn²⁺ and Fe³⁺**.