To identify the complex exhibiting \(d^2sp^3\) hybridization, we must first grasp the concept of hybridization and then apply it to each provided option.
Hybridization Explained: Hybridization is the atomic orbital combination process that yields new hybrid orbitals. The resultant hybridization type dictates the molecule's geometry.
1. [Co(NH3)6]3+
- Cobalt (Co) in this complex is in the +3 oxidation state.
- Cobalt's electronic configuration is [Ar] 3d7 4s2. For Co3+, this simplifies to [Ar] 3d6.
- The Co3+ ion undergoes \(d^2sp^3\) hybridization, utilizing its 3d, 4s, and 4p orbitals to construct the octahedral complex.
2. SF6
- In SF6, the sulfur atom is bonded to six fluorine atoms.
- Sulfur achieves six bonds via \(sp^3d^2\) hybridization, resulting in an octahedral geometry.
3. BrF5
- In BrF5, the central bromine atom is bonded to five fluorine atoms and possesses one lone pair.
- This molecule demonstrates \(sp^3d^2\) hybridization, leading to a square pyramidal shape.
4. [PtCl4]2-
- In this scenario, platinum (Pt) forms four coordinate bonds with chlorine atoms.
- The complex adopts \(dsp^2\) hybridization, yielding a square planar geometry, characteristic of Pt2+'s d8 electron count.
Therefore, [Co(NH3)6]3+ is the correct answer due to its formation of \(d^2sp^3\) hybridization.