To determine which of the given complexes are not correctly matched with the hybridization of their central metal ion, we will analyze each complex one by one.
### Step 1: Analyze `[Ni(CO)4]`
- **Metal Ion**: Nickel (Ni)
- **Oxidation State**: In `[Ni(CO)4]`, CO is a neutral ligand, so Ni remains in the 0 oxidation state.
- **Electronic Configuration**: Ni has an atomic number of 28, so its electronic configuration is `[Ar] 3d^8 4s^2`.
- **Hybridization**: Since CO is a strong field ligand, it will cause pairing of electrons. The 4s and 3d orbitals will hybridize to form `sp^3` hybridization.
- **Conclusion**: The hybridization of `[Ni(CO)4]` is correctly matched as `sp^3`.
### Step 2: Analyze `[Ni(CN)4]^(2-)`
- **Metal Ion**: Nickel (Ni)
- **Oxidation State**: In `[Ni(CN)4]^(2-)`, CN is a -1 ligand. Therefore, for the complex to be neutral, Ni must be in the +2 oxidation state.
- **Electronic Configuration**: Ni in +2 state has the configuration `[Ar] 3d^8`.
- **Hybridization**: CN is a strong field ligand, leading to pairing of electrons. The 3d orbitals will hybridize with the 4s orbital to form `dsp^2` hybridization.
- **Conclusion**: The hybridization of `[Ni(CN)4]^(2-)` is incorrectly matched as `sp^3`, it should be `dsp^2`.
### Step 3: Analyze `[CoF6]^(3-)`
- **Metal Ion**: Cobalt (Co)
- **Oxidation State**: In `[CoF6]^(3-)`, F is a -1 ligand. Therefore, Co must be in the +3 oxidation state.
- **Electronic Configuration**: Co in +3 state has the configuration `[Ar] 3d^6`.
- **Hybridization**: Fluorine is a weak field ligand, so there will be no pairing. The 3d, 4s, and 4p orbitals will hybridize to form `sp^3d^2` hybridization.
- **Conclusion**: The hybridization of `[CoF6]^(3-)` is incorrectly matched as `d^2sp^3`, it should be `sp^3d^2`.
### Step 4: Analyze `[Fe(CN)6]^(3-)`
- **Metal Ion**: Iron (Fe)
- **Oxidation State**: In `[Fe(CN)6]^(3-)`, CN is a -1 ligand. Therefore, Fe must be in the +3 oxidation state.
- **Electronic Configuration**: Fe in +3 state has the configuration `[Ar] 3d^5`.
- **Hybridization**: CN is a strong field ligand, leading to pairing of electrons. The 3d orbitals will hybridize with the 4s orbital to form `d^2sp^3` hybridization.
- **Conclusion**: The hybridization of `[Fe(CN)6]^(3-)` is incorrectly matched as `sp^3d^2`, it should be `d^2sp^3`.
### Final Conclusion
From the analysis:
- (a) `[Ni(CO)4]` is correctly matched as `sp^3`.
- (b) `[Ni(CN)4]^(2-)` is incorrectly matched as `sp^3` (should be `dsp^2`).
- (c) `[CoF6]^(3-)` is incorrectly matched as `d^2sp^3` (should be `sp^3d^2`).
- (d) `[Fe(CN)6]^(3-)` is incorrectly matched as `sp^3d^2` (should be `d^2sp^3`).
Thus, the complexes that are not correctly matched with their hybridization are (b), (c), and (d).
### Answer
The correct option is (b), (c), and (d) are not correctly matched with the hybridization of their central metal ion.
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