Concept: An octahedral molecule has a central atom (M) bonded to six surrounding atoms (X) arranged at the vertices of an octahedron. The bond angles in an ideal octahedral geometry are primarily $90^{\circ }$ and $180^{\circ }$.

Why (A) is correct:

In a regular octahedral geometry, the central atom M is at the center, and the six X atoms are positioned along the three mutually perpendicular axes (x, y, and z axes). Each axis has two X atoms, one on each side of the central M atom.

Consider the X atoms along one axis. Let's say X1 and X2 are along the x-axis. The bond angle between X1-M-X2 is $180^{\circ }$.

Similarly, for the y-axis, if X3 and X4 are along it, the bond angle X3-M-X4 is $180^{\circ }$.

And for the z-axis, if X5 and X6 are along it, the bond angle X5-M-X6 is $180^{\circ }$.

Since there are three such pairs of X atoms lying on opposite sides of the central atom along three mutually perpendicular axes, there are 3 X-M-X bonds at $180^{\circ }$.

Option Analysis:

• A) 3: This is correct, as explained above. There are three pairs of diametrically opposite X atoms, each forming a $180^{\circ }$ bond angle with the central atom.
• B) 2: This is incorrect. There are three such bonds, not two.
• C) 6: This is incorrect. Six refers to the total number of X atoms or the number of M-X bonds, not the number of $180^{\circ }$ X-M-X bonds.
• D) 4: This is incorrect. There are three such bonds, not four.

Correct Answer: (A)