An octahedral complex is formed when hybrid orbitals of the following types are involved:

A. sp3

B. dsp2

C. d2sp3

D. None of these

To determine which hybrid orbitals are involved in the formation of an octahedral complex, we need to consider the geometry and electron configuration of the central metal atom. An octahedral complex typically has six ligands symmetrically arranged around a central metal ion, leading to a specific hybridization pattern.

Understanding Octahedral Geometry

In an octahedral arrangement, the ligands are positioned at the corners of an octahedron. This geometry arises when the central metal ion undergoes hybridization to accommodate six electron pairs, which can be either bonding pairs with ligands or lone pairs.

Types of Hybridization

Let's analyze the options provided:

• A. sp3: This hybridization involves the mixing of one s orbital and three p orbitals, resulting in four equivalent sp3 hybrid orbitals. This configuration leads to a tetrahedral geometry, not octahedral.
• B. dsp2: This hybridization involves one d orbital, one s orbital, and two p orbitals, forming four equivalent dsp2 hybrid orbitals. This arrangement is characteristic of square planar complexes, which also do not exhibit octahedral geometry.
• C. d2sp3: This hybridization involves two d orbitals, one s orbital, and three p orbitals. The combination of these orbitals produces six equivalent d2sp3 hybrid orbitals, which perfectly aligns with the octahedral geometry.
• D. None of these: This option implies that none of the previous hybridizations are suitable for octahedral complexes, which is not accurate since d2sp3 is indeed appropriate.

Conclusion on Hybridization

Based on the analysis, the correct answer is C. d2sp3. This hybridization allows for the formation of six equivalent orbitals that can effectively bond with six ligands, resulting in the characteristic octahedral shape.

Examples of Octahedral Complexes

Common examples of octahedral complexes include octahedral complexes of transition metals such as [Fe(CN)6]4- and [Co(NH3)6]3+. In these complexes, the central metal ion utilizes d2sp3 hybridization to form strong bonds with the surrounding ligands, leading to the stable octahedral structure.

In summary, when considering the formation of octahedral complexes, the d2sp3 hybridization is the key to understanding how the geometry and bonding arise in these coordination compounds.