How many of the following ions have same spin only magnetic moment.
`Ni^(2+)`, `Fe^(2+)`, `Cu^(2+)`, `Cr^(3+)`, `V^(3+)`

Answer

To determine how many of the given ions have the same spin-only magnetic moment, we need to follow these steps:

### Step 1: Determine the electronic configurations of the ions.

1. **Ni²⁺ (Nickel ion)**:
- Atomic number of Ni = 28
- Electronic configuration of Ni = [Ar] 3d⁸ 4s²
- For Ni²⁺, we remove 2 electrons from the 4s orbital:
- Configuration: [Ar] 3d⁸

2. **Fe²⁺ (Iron ion)**:
- Atomic number of Fe = 26
- Electronic configuration of Fe = [Ar] 3d⁶ 4s²
- For Fe²⁺, we remove 2 electrons from the 4s orbital:
- Configuration: [Ar] 3d⁶

3. **Cu²⁺ (Copper ion)**:
- Atomic number of Cu = 29
- Electronic configuration of Cu = [Ar] 3d¹⁰ 4s¹
- For Cu²⁺, we remove 1 electron from the 4s and 1 from the 3d:
- Configuration: [Ar] 3d⁹

4. **Cr³⁺ (Chromium ion)**:
- Atomic number of Cr = 24
- Electronic configuration of Cr = [Ar] 3d⁵ 4s¹
- For Cr³⁺, we remove 1 electron from the 4s and 2 from the 3d:
- Configuration: [Ar] 3d³

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

### Step 2: Count the number of unpaired electrons in each ion.

1. **Ni²⁺ (3d⁸)**:
- Configuration: 3d⁸ has 2 unpaired electrons.

2. **Fe²⁺ (3d⁶)**:
- Configuration: 3d⁶ has 4 unpaired electrons.

3. **Cu²⁺ (3d⁹)**:
- Configuration: 3d⁹ has 1 unpaired electron.

4. **Cr³⁺ (3d³)**:
- Configuration: 3d³ has 3 unpaired electrons.

5. **V³⁺ (3d²)**:
- Configuration: 3d² has 2 unpaired electrons.

### Step 3: Identify ions with the same number of unpaired electrons.

- **Ni²⁺**: 2 unpaired electrons
- **Fe²⁺**: 4 unpaired electrons
- **Cu²⁺**: 1 unpaired electron
- **Cr³⁺**: 3 unpaired electrons
- **V³⁺**: 2 unpaired electrons

### Conclusion:

The ions with the same number of unpaired electrons are:
- **Ni²⁺** and **V³⁺** (both have 2 unpaired electrons).

Thus, there are **2 ions** that have the same spin-only magnetic moment.