In an octahedral structure, the pair of d orbitals involved in $d^2sp^3$ hybridization is :-
A
$d_{xz}, d_{x^2-y^2}$
B
$d_{z^2}, d_{xz}$
C
$d_{xy}, d_{yz}$
D
$d_{x^2-y^2}, d_{z^2}$
The answer is D.
Solution
In an octahedral complex the six ligands approach the metal along the $\pm x$, $\pm y$ and $\pm z$ axes. The hybrid orbitals must point along these axes. Among the d orbitals, only $d_{x^2-y^2}$ (lobes along x and y axes) and $d_{z^2}$ (lobes along the z axis) point along the axes. $d_{xy}$, $d_{yz}$ and $d_{xz}$ have their lobes between the axes, so they are not used. So in $d^2sp^3$ hybridization the two d orbitals are $d_{x^2-y^2}$ and $d_{z^2}$ (together with one s and three p orbitals).
Conceptd orbitals used in octahedral hybridisation
Valence bond theory in past papers
5 questions from this chapter have appeared across 5 exam years.