Explain the following: (i)
[CoF_(6)]^(3-)` is paramgnetic but `[Co(CN)_(6)]^(3-)` is diamagnetic .

Options

A. paramagnetic and undergoes `sp^(3) d^(2)` hybridisation
B. diamagnetic and undergoes `d^(2) sp^(3)` hybridisation
C. paramagnetic and undergoes `sp^(3) d` hybridisation
D. diamagnetic and undergoes `sp^(3)` hybridisation .

Explanation

To explain why \([CoF_6]^{3-}\) is paramagnetic while \([Co(CN)_6]^{3-}\) is diamagnetic, we need to analyze the electronic configurations and the nature of the ligands involved in both complexes.

### Step-by-Step Solution:

1. **Identify the Oxidation State of Cobalt**:
- In both complexes, cobalt is in the +3 oxidation state. The electronic configuration of cobalt (Co) in its elemental form is \([Ar] 3d^7 4s^2\).
- Upon losing three electrons (two from 4s and one from 3d), the configuration becomes \(3d^6\).

2. **Determine the Nature of the Ligands**:
- **Fluoride (\(F^-\))**: This is a weak field ligand, which does not cause significant pairing of electrons.
- **Cyanide (\(CN^-\))**: This is a strong field ligand, which causes pairing of electrons in the d-orbitals.

3. **Electron Configuration in the Complexes**:
- For \([CoF_6]^{3-}\):
- The \(3d^6\) configuration will have unpaired electrons because the weak field ligand (fluoride) does not promote pairing. The arrangement in the \(d\) orbitals will be:
- \(t_{2g}^4 e_g^2\) (4 unpaired electrons).
- Thus, \([CoF_6]^{3-}\) is **paramagnetic** due to the presence of unpaired electrons.

- For \([Co(CN)_6]^{3-}\):
- The strong field ligand (cyanide) will cause the \(3d^6\) electrons to pair up. The arrangement will be:
- \(t_{2g}^6 e_g^0\) (all electrons paired).
- Thus, \([Co(CN)_6]^{3-}\) is **diamagnetic** because there are no unpaired electrons.

4. **Hybridization**:
- The hybridization for \([CoF_6]^{3-}\) is \(d^2sp^3\) due to the weak field ligands.
- The hybridization for \([Co(CN)_6]^{3-}\) is \(d^2sp^3\) as well, but the strong field nature of \(CN^-\) leads to electron pairing.

### Conclusion:
- \([CoF_6]^{3-}\) is paramagnetic because it has unpaired electrons, while \([Co(CN)_6]^{3-}\) is diamagnetic due to the absence of unpaired electrons.