Cis-trans isomerism is found in square planar complexes of which of the following molecular formula?

MA₂B₂

The correct answer is option 3. \(MA_2B_2\).

Cis-trans isomerism, also known as geometrical isomerism, is a form of stereoisomerism where the relative positions of ligands around a central metal atom differ, leading to different spatial arrangements. This type of isomerism is possible in square planar complexes where two types of ligands can be arranged differently around the central metal ion.

Let us analyze each option for the possibility of cis-trans isomerism in a square planar geometry:

1. \(MA_4\):

This complex has four identical ligands (A) around the central metal ion (M). Since all ligands are the same, there is no possibility of different spatial arrangements leading to cis-trans isomerism.

2. \(MA_3B\):

This complex has three identical ligands (A) and one different ligand (B) around the central metal ion (M). Since there is only one different ligand, there are no distinct alternative arrangements that would lead to cis-trans isomerism.

3. \(MA_2B_2\):

This complex has two identical ligands (A) and two other identical ligands (B) around the central metal ion (M). There are two possible spatial arrangements:

Cis isomer: The two A ligands are adjacent to each other, and the two B ligands are also adjacent.

Trans isomer: The two A ligands are opposite each other, and the two B ligands are also opposite.

These different spatial arrangements make MA2B2 capable of exhibiting cis-trans isomerism.

4. \(MAB_3\):

This complex has one ligand of type A and three identical ligands of type B around the central metal ion (M). With only one different ligand (A), there are no distinct alternative arrangements leading to cis-trans isomerism.

The square planar complex \(MA_2B_2\) exhibits cis-trans isomerism because it has two pairs of different ligands that can be arranged in different spatial configurations around the central metal ion.

Therefore, the correct answer is \(MA_2B_2\).