Step 1: Understanding the Concept:
The geometry of a coordination complex is primarily dictated by its Coordination Number (CN) and the hybridization of the central metal, which is influenced by the field strength of the ligands.
Step 2: Key Formula or Approach:
Determine the coordination number from the formula. For CN=6, the geometry is Octahedral. For CN=5, it's Trigonal Bipyramidal. For CN=4, use Valence Bond Theory (strong vs weak ligands) to distinguish between Tetrahedral ($sp^3$) and Square Planar ($dsp^2$).
Step 3: Detailed Explanation:
(a) [Co(NH$_{3}$)$_{6}$]$^{3+$:} CN =
6. With six ligands, the only possible symmetric geometry is Octahedral. (a $\rightarrow$ ii)
(b) [NiCl$_{4}$]$^{2-$:} CN =
4. The $Cl^{-}$ ion is a weak field ligand, so it does not force electron pairing in the $Ni^{2+}$ ($d^8$) ion. The hybridization utilizes outer orbitals ($sp^3$), resulting in a Tetrahedral geometry. (b $\rightarrow$ iii)
(c) [Ni(CN)$_{4}$]$^{2-$:} CN =
4. The $CN^{-}$ ion is a very strong field ligand, forcing electron pairing. This frees up an inner d-orbital, leading to $dsp^2$ hybridization and a Square planar geometry. (c $\rightarrow$ iv)
(d) [Fe(CO)$_{5}$]: CN =
5. With five ligands, the characteristic geometry is Trigonal bipyramidal ($dsp^3$ hybridization). (d $\rightarrow$ i)
Step 4: Final Answer:
The correct matching sequence is a-ii, b-iii, c-iv, d-i.