Which statement is wrong?

The correct answer is option 3. \(sp^3d\) hybrid orbitals are all at \(90^o\) to one another.

Let us delve into the details to clarify why statement (3) is incorrect regarding \(sp^3d\) hybrid orbitals:

Understanding \(sp^3d\) Hybridization:

Definition of \(sp^3d\) Hybridization:

\(sp^3d\) hybridization involves the mixing of one \(s\) orbital, three \(p\) orbitals, and one \(d\) orbital of an atom to form a set of five hybrid orbitals. These hybrid orbitals are used by the atom to bond with other atoms to form molecules.

Arrangement of \(sp^3d\) Hybrid Orbitals:

The resulting \(sp^3d\) hybrid orbitals arrange themselves in space according to the geometry of the molecule. They orient themselves to minimize repulsion between electron pairs and maximize bonding efficiency.

Geometry and Angles:

Unlike simple geometries like tetrahedral (\(sp^3\)) or linear (\(sp\)), \(sp^3d\) hybridization typically results in more complex molecular geometries. The angles between \(sp^3d\) hybrid orbitals depend on the specific molecule's geometry, which is determined by the arrangement of atoms around the central atom. These angles are influenced by factors such as lone pairs of electrons and the repulsion between electron pairs.

Incorrectness of Statement (3):

Statement (3) suggests that \(sp^3d\) hybrid orbitals are all at \(90^\circ\) to one another, which implies a regular geometric arrangement similar to a cube or other symmetrical shape. However, \(sp^3d\) hybridization does not result in such a regular arrangement where all hybrid orbitals are exactly at \(90^\circ\) angles to each other. The angles between \(sp^3d\) hybrid orbitals are determined by the molecular geometry, which could be trigonal bipyramidal, see-saw, square pyramidal, or octahedral, depending on the number of bonding pairs and lone pairs around the central atom.

Conclusion:

Given these points, the correct analysis shows that statement (3) is incorrect because \(sp^3d\) hybrid orbitals do not arrange themselves at \(90^\circ\) angles to each other. Instead, their spatial arrangement depends on the overall geometry of the molecule, which is influenced by the number of bonding pairs and lone pairs around the central atom. Therefore, the incorrect statement among the options provided is Option (3): \(sp^3d\) hybrid orbitals are all at \(90^o\) to one another.

This statement does not accurately describe the geometry or spatial arrangement of \(sp^3d\) hybrid orbitals in molecules.