Which of the following octahedral complexes do not show geometrical isomerism?

MA₅B

The correct answer is option 3. MA₅B.

Geometrical isomerism in octahedral complexes occurs when there are multiple ways to arrange the ligands around the central metal ion in different spatial configurations. Let's analyze each type of complex to see if they can form geometrical isomers:

1. \(MA_3B_3\):

This complex has three A ligands and three B ligands. There are two distinct ways to arrange the ligands:

Facial (fac) isomer: The three A ligands and three B ligands each occupy adjacent positions, forming faces of the octahedron.

Meridional (mer) isomer: The three A ligands and three B ligands each occupy positions along a meridian, spanning opposite sides of the octahedron.

Because there are two distinct arrangements, \(MA_3B_3\) shows geometrical isomerism.

2. \(MA_4B_2\):

This complex has four A ligands and two B ligands. The two B ligands can be arranged in two ways:

Cis isomer: The two B ligands are adjacent to each other.

Trans isomer: The two B ligands are opposite each other.

Because these two arrangements are possible, \(MA_4B_2\) shows geometrical isomerism.

3. \(MA_5B\):

This complex has five A ligands and one B ligand. There is only one way to arrange the single B ligand among the five A ligands in an octahedral geometry. The B ligand can only occupy one position, while the five A ligands fill the remaining positions. Since there are no alternative arrangements, \(MA_5B\) does not show geometrical isomerism.

4. \(MA_2B_4\):

This complex has two A ligands and four B ligands. The two A ligands can be arranged in two ways:

Cis isomer: The two A ligands are adjacent to each other.

Trans isomer: The two A ligands are opposite each other.

Because these two arrangements are possible, \(MA_2B_4\) shows geometrical isomerism.

The octahedral complex \(MA_5B\) does not show geometrical isomerism because there is only one way to position the single B ligand among the five A ligands. In an octahedral geometry, this unique arrangement does not allow for any alternative spatial configurations.