Trigonal bipyramidal geometry is characteristic of molecules with five electron domains around the central atom, such as $PC{l}_5$. In this geometry, there are two distinct types of positions for the atoms/ligands:

1. Axial positions: Two positions along the vertical axis, 180° apart from each other.
2. Equatorial positions: Three positions in a horizontal plane, 120° apart from each other.

Let's analyze the right angles (90°) present:

• Each axial bond forms a 90° angle with each of the three equatorial bonds. Since there are two axial bonds, this accounts for $2\times 3=6$ right angles.
• The angles between the equatorial bonds are 120°, so there are no 90° angles within the equatorial plane.

Therefore, the total number of right angles in a trigonal bipyramidal geometry is 6.

Option Analysis:

• A) 3: This is incorrect. There are more than 3 right angles.
• B) 12: This is incorrect. This number would imply 4 right angles per axial bond, which is not the case.
• C) 6: This is correct. Each of the two axial bonds forms a 90° angle with each of the three equatorial bonds, totaling 6 right angles.
• D) 9: This is incorrect. This would imply 4.5 right angles per axial bond, which is not possible.

Correct Answer: (C)