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 the electronic configurations of manganese (Mn), iron (Fe), and cobalt (Co) and their respective complex ions.

### Step-by-Step Solution:

1. **Identify the Atomic Numbers and Electronic Configurations:**
- Manganese (Mn) has an atomic number of 25:
- Electronic configuration: \( [Ar] 4s^2 3d^5 \)
- Iron (Fe) has an atomic number of 26:
- Electronic configuration: \( [Ar] 4s^2 3d^6 \)
- Cobalt (Co) has an atomic number of 27:
- Electronic configuration: \( [Ar] 4s^2 3d^7 \)

2. **Analyze Each Complex Ion:**
- **Cobalt (III) Complex: \( Co(NH_3)_6^{3+} \)**
- Oxidation state of Co: +3
- Remove 3 electrons: \( [Ar] 3d^6 \)
- In an inner orbital octahedral complex, \( NH_3 \) is a strong field ligand, leading to pairing of electrons:
- Configuration: \( (3d)^{6} \) → All electrons paired.
- **Result:** Diamagnetic (no unpaired electrons).

- **Manganese (III) Complex: \( Mn(CN)_6^{3-} \)**
- Oxidation state of Mn: +3
- Remove 3 electrons: \( [Ar] 3d^4 \)
- \( CN^- \) is also a strong field ligand, leading to pairing:
- Configuration: \( (3d)^{4} \) → 2 unpaired electrons.
- **Result:** Paramagnetic (2 unpaired electrons).

- **Iron (II) Complex: \( Fe(CN)_6^{4-} \)**
- Oxidation state of Fe: +2
- Remove 2 electrons: \( [Ar] 3d^6 \)
- \( CN^- \) as a strong field ligand causes pairing:
- Configuration: \( (3d)^{6} \) → All electrons paired.
- **Result:** Diamagnetic (no unpaired electrons).

- **Iron (III) Complex: \( Fe(CN)_6^{3-} \)**
- Oxidation state of Fe: +3
- Remove 3 electrons: \( [Ar] 3d^5 \)
- \( CN^- \) as a strong field ligand:
- Configuration: \( (3d)^{5} \) → 5 unpaired electrons.
- **Result:** Paramagnetic (5 unpaired electrons).

3. **Conclusion:**
- The diamagnetic complex ions are:
- \( Co(NH_3)_6^{3+} \)
- \( Fe(CN)_6^{4-} \)

### Summary of Results:
- **Diamagnetic Complexes:**
- \( Co(NH_3)_6^{3+} \)
- \( Fe(CN)_6^{4-} \)
- **Paramagnetic Complexes:**
- \( Mn(CN)_6^{3-} \)
- \( Fe(CN)_6^{3-} \)