Step 1: Determine the geometry of each complex. (a) [Co(NH\(_3\))\(_6\)]\(^{3+}\):
Co atomic number = 27. Co\(^{3+}\) configuration: [Ar] 3d\(^6\).
NH\(_3\) is a strong field ligand, so it will cause pairing of electrons. The 6 electrons will occupy three d-orbitals.
Hybridization involves two empty 3d orbitals, one 4s, and three 4p orbitals, leading to d\(^2\)sp\(^3\) hybridization.
The geometry for coordination number 6 is Octahedral.
So, a \(\rightarrow\) ii.
(b) [NiCl\(_4\)]\(^{2-}\):
Ni atomic number = 28. Ni\(^{2+}\) configuration: [Ar] 3d\(^8\).
Cl\(^-\) is a weak field ligand. No pairing of electrons will occur.
Hybridization involves one 4s and three 4p orbitals, as the 3d orbitals are not empty. This leads to sp\(^3\) hybridization.
The geometry for sp\(^3\) hybridization is Tetrahedral.
So, b \(\rightarrow\) iii.
(c) [Ni(CN)\(_4\)]\(^{2-}\):
Ni\(^{2+}\) configuration: [Ar] 3d\(^8\).
CN\(^-\) is a strong field ligand. It will force the two unpaired electrons in the 3d orbitals to pair up, leaving one 3d orbital empty.
Hybridization involves the one empty 3d orbital, one 4s, and two 4p orbitals, leading to dsp\(^2\) hybridization.
The geometry for dsp\(^2\) hybridization is Square planar.
So, c \(\rightarrow\) iv.
(d) [Fe(CO)\(_5\)]:
Fe atomic number = 26. Fe(0) configuration: [Ar] 3d\(^6\) 4s\(^2\).
CO is a strong field ligand. In the complex, the 8 valence electrons of Fe rearrange and pair up in the 3d orbitals.
The complex has coordination number 5. The hybridization is dsp\(^3\).
The geometry for coordination number 5 (dsp\(^3\)) is Trigonal bipyramidal.
So, d \(\rightarrow\) i.
Step 2: Compile the matches.
The correct matches are: a \(\rightarrow\) ii, b \(\rightarrow\) iii, c \(\rightarrow\) iv, d \(\rightarrow\) i. Step 3: Final Answer.
This combination corresponds to option (A).