Question

The d orbitals involve in \[ds{{p}^{2}}\] hybridisation is:
A. \[{{d}_{xy}}\]
B. \[{{d}_{{{z}^{2}}}}\]
C. \[{{d}_{{{x}^{2}}-{{y}^{2}}}}\]
D. \[{{d}_{xz}}\]

Answer 1

Hint: We should recall the concept of hybridisation. We should know that choice of ‘d’ orbital for a particular type of hybridization depends on the spatial orientation of the orbital and the geometry of the molecule or ion which the hybridized orbitals are expected to form.

Step by step answer:
We know that the \[{{d}_{{{x}^{2}}-{{y}^{2}}}}\] orbital lies in the xy plane with its lobes directed along the x axis and y axis. The lobes of the \[{{p}_{x}}\] and \[{{p}_{y}}\] orbitals are also directed along the same x,y axis. The \[ds{{p}^{2}}\]hybridization favours a planar geometry in which the four hybridized orbitals lie in the equatorial xy plane, as in. \[IC{{l}^{4-}}\text{ }or\text{ }Xe{{F}_{4}}\]. So, the \[{{d}_{{{x}^{2}}-{{y}^{2}}}}\] orbital is used in \[ds{{p}^{2}}\] hybridization, along with the s, \[{{p}_{x}}\] and \[{{p}_{y}}\] orbitals to form a square planar geometry.
And we should know that the \[{{d}_{{{z}^{2}}}}\] orbital has its main lobes along the z axis, and its cylindrical collar around the same axis. We know that the \[s{{p}^{3}}d\] hybridization favours either a trigonal bipyramidal geometry using the \[{{d}_{{{z}^{2}}}}\] orbital or a square pyramidal geometry using the \[{{d}_{{{x}^{2}}-{{y}^{2}}}}\] orbital. In forming a stable trigonal pyramid, the two axial bonds above and below the equatorial xy plane have to be almost equally strong as the three equatorial bonds, as in \[PC{{l}_{5}}\]. So, the \[{{d}_{{{z}^{2}}}}\] orbital is used, along with the’s’ and the three 'p' orbitals, to form three equatorial bonds and two equally strong axial bonds for a trigonal bipyramid.
So from our discussion, now we know that our correct answer is option C.

Note: It will be interesting for us to know that the idea that atoms form covalent bonds by sharing pairs of electrons was first proposed by G. N. Lewis in 1902. It was in 1927 that Walter Heitler and Fritz London showed how the sharing of pairs of electrons holds a covalent molecule together. The Heitler-London model of covalent bonds was the basis of the valence-bond theory. The last major step in the evolution of this theory was the suggestion by Linus Pauling that atomic orbitals mix to form hybrid orbitals, such as the \[sp,\text{ }s{{p}^{2}},\text{ }s{{p}^{3}},\text{ }ds{{p}^{3}},\text{ }and\text{ }{{d}^{2}}s{{p}^{3}}\] orbitals.