Which of the following pairs will have effective magnetic moment equal ?

Options

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

Answer

To determine which pairs of ions have the same effective magnetic moment, we need to calculate the number of unpaired electrons for each ion in the given pairs and then use the formula for effective magnetic moment.

### Step-by-Step Solution:

1. **Understand the Formula for Effective Magnetic Moment:**
The effective magnetic moment (μ) is given by the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

2. **Identify the Ions in Each Pair:**
We need to analyze the given pairs of ions to find their electronic configurations and the number of unpaired electrons.

3. **Calculate Unpaired Electrons for Each Ion:**
- **Pair 1: Vanadium (V³⁺) and Scandium (Sc³⁺)**
- Vanadium (atomic number 23):
- Configuration: [Ar] 4s² 3d³
- V³⁺: [Ar] 3d² → 2 unpaired electrons.
- Scandium (atomic number 21):
- Configuration: [Ar] 4s² 3d¹
- Sc³⁺: [Ar] 3d⁰ → 0 unpaired electrons.
- **Result:** Not equal.

- **Pair 2: Titanium (Ti²⁺) and Scandium (Sc²⁺)**
- Titanium (atomic number 22):
- Configuration: [Ar] 4s² 3d²
- Ti²⁺: [Ar] 3d² → 2 unpaired electrons.
- Scandium (Sc²⁺): [Ar] 4s² 3d¹ → 1 unpaired electron.
- **Result:** Not equal.

- **Pair 3: Chromium (Cr³⁺) and Manganese (Mn²⁺)**
- Chromium (atomic number 24):
- Configuration: [Ar] 4s² 3d⁴
- Cr³⁺: [Ar] 3d³ → 3 unpaired electrons.
- Manganese (atomic number 25):
- Configuration: [Ar] 4s² 3d⁵
- Mn²⁺: [Ar] 3d⁵ → 5 unpaired electrons.
- **Result:** Not equal.

- **Pair 4: Chromium (Cr²⁺) and Iron (Fe²⁺)**
- Chromium (Cr²⁺):
- Configuration: [Ar] 4s² 3d⁴ → 4 unpaired electrons.
- Iron (atomic number 26):
- Configuration: [Ar] 4s² 3d⁶
- Fe²⁺: [Ar] 3d⁶ → 4 unpaired electrons.
- **Result:** Equal.

4. **Conclusion:**
The only pair with equal effective magnetic moments is **Chromium (Cr²⁺) and Iron (Fe²⁺)**, both having 4 unpaired electrons.

### Final Answer:
The pair that has effective magnetic moment equal is **Chromium (Cr²⁺) and Iron (Fe²⁺)**.