Which of the following gaseous ion contains maximum number of unpaired electrons ?

Options

A. `Fe^(2+)`
B. `Co^(3+)`
C. `Co^(2+)`
D. `Fe^(3+)`

Explanation

To determine which of the given gaseous ions contains the maximum number of unpaired electrons, we will analyze the electronic configurations of the ions in question. Let's assume the ions are Fe²⁺, Co³⁺, Co²⁺, and Ac³⁺.

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

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

2. **Co³⁺ (Cobalt in +3 oxidation state)**:
- Atomic number of Co = 27
- Ground state configuration: [Ar] 4s² 3d⁷
- For Co³⁺, we remove three electrons (two from 4s and one from 3d):
- Configuration: [Ar] 3d⁶

3. **Co²⁺ (Cobalt in +2 oxidation state)**:
- For Co²⁺, we remove two electrons (both from 4s):
- Configuration: [Ar] 3d⁷

4. **Ac³⁺ (Actinium in +3 oxidation state)**:
- Atomic number of Ac = 89
- Ground state configuration: [Rn] 7s² 6d¹
- For Ac³⁺, we remove three electrons (two from 7s and one from 6d):
- Configuration: [Rn] 6d¹

### Step 2: Determine the number of unpaired electrons for each ion.

1. **Fe²⁺ (3d⁶)**:
- Filling the 3d orbitals according to Hund's rule:
- Configuration: ↑↓ ↑ ↑ ↑ ↑ (4 unpaired electrons)

2. **Co³⁺ (3d⁶)**:
- Configuration: ↑↓ ↑ ↑ ↑ ↑ (4 unpaired electrons)

3. **Co²⁺ (3d⁷)**:
- Configuration: ↑↓ ↑ ↑ ↑ ↑ ↑ (3 unpaired electrons)

4. **Ac³⁺ (6d¹)**:
- Configuration: ↑ (1 unpaired electron)

### Step 3: Compare the number of unpaired electrons.

- Fe²⁺: 4 unpaired electrons
- Co³⁺: 4 unpaired electrons
- Co²⁺: 3 unpaired electrons
- Ac³⁺: 1 unpaired electron

### Conclusion:

Both Fe²⁺ and Co³⁺ have the maximum number of unpaired electrons, which is 4. Therefore, the answer to the question is that both Fe²⁺ and Co³⁺ contain the maximum number of unpaired electrons.

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