Atomic number of Mn. Fe and Co are 25, 26 and 27 respectively. Which of the following inner orbital octahedral complex ions are diamagnetic ?

Options

A. `[Co(NH_(3))_(6)]^(3+)`
B. `[Mn(CN)_(6)]^(3-)`
C. `[Fe(CN)_(6)]^(4-)`
D. `[Fe(CN)_(6)]^(3-)`

Explanation

To determine which of the given inner orbital octahedral complex ions are diamagnetic, we will analyze each complex based on the oxidation states of the central metal ions and their electron configurations.

### Step-by-Step Solution:

1. **Identify the Oxidation States**:
- For each complex ion, determine the oxidation state of the central metal ion (Mn, Fe, Co) based on the charges of the ligands.

2. **Determine Electron Configuration**:
- Using the atomic numbers of Mn (25), Fe (26), and Co (27), find the electron configuration for the metal ions in their respective oxidation states.

3. **Fill the d-Orbitals**:
- For inner orbital complexes, we will assume low-spin configurations. Fill the d-orbitals according to Hund's rule and the Pauli exclusion principle.

4. **Count Unpaired Electrons**:
- After filling the d-orbitals, count the number of unpaired electrons. If there are no unpaired electrons, the complex is diamagnetic.

5. **Identify Diamagnetic Complexes**:
- Based on the count of unpaired electrons, identify which complexes are diamagnetic.

### Detailed Steps:

#### 1. For Cobalt Complex:
- **Oxidation State**: Let the oxidation state of Co be \( x \). Given the complex has a charge of +3 and ammonia is neutral, we have:
\[ x + 0 = +3 \implies x = +3 \]
- **Electron Configuration**: Cobalt in +3 state has the configuration \( [Ar] 3d^6 \).
- **Filling d-Orbitals**:
- In a low-spin configuration, the d-orbitals fill as follows:
- \( t_{2g}^6 \) (all paired)
- \( e_g^0 \)
- **Unpaired Electrons**: 0 (All paired)
- **Conclusion**: This complex is **diamagnetic**.

#### 2. For Manganese Complex:
- **Oxidation State**: Let the oxidation state of Mn be \( x \). Given the complex has a charge of +3 and cyanide is -1:
\[ x - 3 = +3 \implies x = +3 \]
- **Electron Configuration**: Manganese in +3 state has the configuration \( [Ar] 3d^4 \).
- **Filling d-Orbitals**:
- In a low-spin configuration, the d-orbitals fill as follows:
- \( t_{2g}^4 \) (2 paired, 2 unpaired)
- \( e_g^0 \)
- **Unpaired Electrons**: 2 (Two unpaired)
- **Conclusion**: This complex is **paramagnetic**.

#### 3. For Iron (II) Complex:
- **Oxidation State**: Let the oxidation state of Fe be \( x \). Given the complex has a charge of +2 and the ligands total -6:
\[ x - 6 = -4 \implies x = +2 \]
- **Electron Configuration**: Iron in +2 state has the configuration \( [Ar] 3d^6 \).
- **Filling d-Orbitals**:
- In a low-spin configuration, the d-orbitals fill as follows:
- \( t_{2g}^6 \) (all paired)
- \( e_g^0 \)
- **Unpaired Electrons**: 0 (All paired)
- **Conclusion**: This complex is **diamagnetic**.

#### 4. For Iron (III) Complex:
- **Oxidation State**: Let the oxidation state of Fe be \( x \). Given the complex has a charge of +3 and the ligands total -6:
\[ x - 6 = -3 \implies x = +3 \]
- **Electron Configuration**: Iron in +3 state has the configuration \( [Ar] 3d^5 \).
- **Filling d-Orbitals**:
- In a low-spin configuration, the d-orbitals fill as follows:
- \( t_{2g}^5 \) (5 unpaired)
- \( e_g^0 \)
- **Unpaired Electrons**: 5 (All unpaired)
- **Conclusion**: This complex is **paramagnetic**.

### Final Answer:
The complexes that are diamagnetic are:
- **Cobalt Complex** (1st option)
- **Iron (II) Complex** (3rd option)

Thus, the answer is **1 and 3**.