If a molecule $M{{X}_{3}}$ has zero dipole moment, the sigma bonding orbital used by $M$ are
(A) $s{{p}^{3}}d$−hybrid
(B) $sp$−hybrid
(C) $s{{p}^{3}}{{d}^{2}}$−hybrid
(D) $s{{p}^{2}}$−hybrid

Hint: In any system where there is a charge separation, a dipole moment arises. The difference in electronegativity between two atoms that are chemically linked generates dipole moments. It is a vector quantity, that is, it has both magnitude and direction. Non-polar molecules are those that have zero dipole moment. These are not arranged symmetrically.

Complete Step by Step Answer:
If a molecule with the formula $M{{X}_{3}}$ has zero dipole moment, then it must be in the shape of a triangular planar. The metal $M$ shows $s{{p}^{2}}$−hybridization such that the three $s{{p}^{2}}$−hybridised orbital of $M$is bonded to three $X$atoms with a sigma bond. These three bonds lie at an angle of ${{120}^{o}}$ to each other, and the direction of the dipole moment is from $M$ to$X$.

An example of this type of molecule is $B{{F}_{3}}$ such that $B$is bonded to three $F$ and has a net zero dipole moment. Thus, if a molecule $M{{X}_{3}}$has zero dipole moment, the sigma bonding orbital used by $M$are $s{{p}^{2}}$−hybrid.
Correct Option: (D) $s{{p}^{2}}$−hybrid.

Note: The molecule with the formula $M{{X}_{3}}$ having zero dipole moment must be planar. The dipole moment of all three $M-X$ bonds is the same. However, the two $M-X$bonds which are opposite in direction to the third $M-X$ bond will cancel out its dipole moment and, hence, result in zero dipole moment.