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The trigonal bipyramidal geometry results from hybridization
(A) $ds{{p}^{3}}$ or $s{{p}^{3}}d$
(B) $ds{{p}^{2}}$ or $s{{p}^{2}}d$
(C) ${{d}^{2}}s{{p}^{3}}$ or $s{{p}^{3}}{{d}^{2}}$
(D) ${{d}^{3}}s{{p}^{2}}$ or ${{d}^{2}}s{{p}^{3}}$

Answer
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Hint: Hybridization is the idea of combining the two atomic orbitals to form a new type of hybridised orbital. This mixing creates hybrid orbitals with entirely different energies and shapes. A triangular bipyramidal with one atom in the middle and five additional atoms at each of its corners is known as a trigonal bipyramidal. All five atoms are not identical. Three of these atoms are equatorial and the remaining two are axial.

Complete Step by Step Answer:
The trigonal bipyramidal geometry results from the hybridization$ds{{p}^{3}}$ or$s{{p}^{3}}d$. An example of a trigonal bipyramidal molecule is$PC{{l}_{5}}$. Its structure is as shown below:

The three equatorial $P-Cl$ bonds lie in one plane. The other two axial $P-Cl$bonds lie out of the plane, one of which lies above the plane and the other below the plane. The angle between equatorial bonds is ${{120}^{o}}$ whereas the angle between axial bonds and equatorial bonds is${{90}^{o}}$. Five $s{{p}^{3}}d$ orbitals of phosphorus and $p$ orbitals of chlorine atoms overlap in$PC{{l}_{5}}$. The $p$ orbitals are completely filled. They combine to create five $P-Cl$ sigma bonds.
Correct Option: (A) $ds{{p}^{3}}$ or $s{{p}^{3}}d$.

Note: he axial bonds are longer than the equatorial bonds. The reason for this is that axial bond pairs experience a stronger repulsive interaction than equatorial bond pairs; hence they are often a little longer. Because of this, it makes the $PC{{l}_{5}}$ molecule somewhat more reactive than the equatorial bonds.