Step 1: Understanding the Concept:
Hybridization depends on the coordination number (CN) and the field strength of ligands.
CN = 4 results in \(sp^3\) (tetrahedral) or \(dsp^2\) (square planar).
CN = 6 results in \(d^2sp^3\) (inner orbital octahedral) or \(sp^3d^2\) (outer orbital octahedral).
Strong field ligands (SFL) like \(CO, CN^-, NH_3\) cause electron pairing, while weak field ligands (WFL) like \(F^-\) do not.
Step 2: Detailed Explanation:
1. \([Ni(CO)_4]\): Ni is in 0 state (\(3d^8 4s^2\)). \(CO\) is a strong ligand, it forces \(4s\) electrons into \(3d\), resulting in a \(3d^{10}\) configuration. This leaves \(4s\) and \(4p\) vacant \(\implies sp^3\) (d).
2. \([Ni(CN)_4]^{2-\):} \(Ni^{2+}\) is \(3d^8\). \(CN^-\) is a strong ligand, pairs electrons in \(3d\), leaving one \(3d\), one \(4s\), and two \(4p\) vacant \(\implies dsp^2\) (c).
3. \([Co(NH_3)_6]^{3+\):} \(Co^{3+}\) is \(3d^6\). \(NH_3\) is a strong ligand here, pairs all 6 electrons into 3 orbitals. Two inner \(3d\), one \(4s\), and three \(4p\) vacant \(\implies d^2sp^3\) (b).
4. \([CoF_6]^{3-}\): \(Co^{3+}\) is \(3d^6\). \(F^-\) is a weak ligand, no pairing. Uses outer \(4d\) orbitals \(\implies sp^3d^2\) (a).
Step 3: Final Answer:
The matching is 1-d, 2-c, 3-b, 4-a, which is option (C).