Question

In $s{{p}^{3}}{{d}^{3}}$ hybridisation, which orbitals are involved?
(A) ${{d}_{{{x}^{2}}-{{y}^{2}}}},{{d}_{{{z}^{2}}}},{{d}_{xy}}$
(B) ${{d}_{xy}},{{d}_{yz}},{{d}_{zx}}$
(C) ${{d}_{{{x}^{2}}-{{y}^{2}}}},{{d}_{xy}},{{d}_{xz}}$
(D) ${{d}_{{{z}^{2}}}},{{d}_{yz}},{{d}_{zx}}$

Answer 1

Hint: In order to get the desired geometry, the orbitals involved in overlapping must be chosen such that the planes or axis along which the bond formation is involved are considered in order to attain a stable structure.

Complete step by step solution:
It is given that the molecule has $s{{p}^{3}}{{d}^{3}}$ hybridisation. That is, there is overlapping in the atomic orbitals of one s-orbital, three p-orbital and three d-orbitals such that the seven hybridised orbitals are similar in energy (degenerate).
From the VSEPR theory, it is seen that the molecule with $s{{p}^{3}}{{d}^{3}}$ hybridisation has pentagonal bipyramidal geometry. In this, there are five bonds formed in the X-Y plane and the remaining two, one above and one below the plane along the Z-axis.
As we know, the s-orbital being non-directional is found in the plane. The p- subshell having three orbitals, are directed along the X-, Y-, Z-axis respectively.
Whereas, the d-subshell has five orbitals. The ${{d}_{xy}},{{d}_{yz}},{{d}_{zx}}$- orbitals have their lobes placed in between their named axes. The remaining two orbitals, that is, the ${{d}_{{{x}^{2}}-{{y}^{2}}}}$ orbitals has its lobes present on the X-Y plane and the ${{d}_{{{z}^{2}}}}$ orbitals having a unique shape has its lobes lie both along the Z-axis and in the X-Y plane.
So, the given geometry can be attained only with the s, ${{p}_{x}},{{p}_{y}}$, ${{d}_{{{x}^{2}}-{{y}^{2}}}}$,${{d}_{xy}}$ orbitals lying in the X-Y plane and the ${{p}_{z}}$ and ${{d}_{{{z}^{2}}}}$ orbitals lying perpendicular to the X-Y plane along the Z-axis.

Therefore, in $s{{p}^{3}}{{d}^{3}}$ hybridisation, the d-orbitals involved are option (A) ${{d}_{{{x}^{2}}-{{y}^{2}}}},{{d}_{{{z}^{2}}}},{{d}_{xy}}$.

Note: While choosing the orbitals involved in the hybridisation, the stable geometry of the molecule will help us to determine the plane or axis along which the bonds are being formed.