Stereoisomers are those isomers that have the same molecular formula and chemical bonds but they have different spatial arrangements of atoms. As already mentioned, stereoisomerism involves two types of isomerism viz., geometrical isomerism and optical isomerism. These are discussed below:

1. Geometrical isomerism

Geometrical isomerism arises in heteroleptic complexes due to ligands occupying different positions around the central ion. The ligands occupy positions either adjacent to one another or opposite to one another. These are referred to as cis-form (ligands occupy adjacent positions) and trans- form (ligands occupy opposite positions). This type of isomerism is, therefore, also referred to as cis-trans isomerism. This type of isomerism is very common in coordination compounds. This is due to different coordination numbers varying from 2 to 9, commonly encountered in these compounds.

2. Optical isomerism

There are certain substances that can rotate the plane of polarised light. These are called optically active substances. The isomers which rotate the plane of polarised light equally but in opposite directions are called optically active isomers. These are also called enantiomers or enantiomorphs. The isomer which rotates the plane of polarised light to the right is called dextro rotatory designated as (d) and the one which rotates the plane of polarized light to the left is called laevo rotatory designated as (l). A 1 : 1 equilibrium mixture of d and l isomers gives a net zero rotation and is also called racemic mixture. The d and l isomers are mirror images of each other just as left hand is mirror image of the right hand. These mirror image compounds are non-superimposable on each other and do not possess the plane of symmetry. These optical isomers also possess the property of chirality (handedness). The essential condition for a substance to show optical activity is that the substance should not have a plane of symmetry in its structure. The optical isomers have identical physical and chemical properties. They differ only in the direction in which they rotate the plane of polarised light

A coordination complex of type MX₂Y₂ (M = meal ion, X and Y are monodentate ligands) can have either a tetrahedral or a square planar geometry. The maximum number of possible isomers in these two cases are, respectively,

1 and 2

The correct answer is option 1. 1 and 2.

Let us delve into the reasoning behind the number of possible isomers for the coordination complex \( \text{MX}_2\text{Y}_2 \) in both tetrahedral and square planar geometries.

Tetrahedral Geometry

In a tetrahedral geometry, the central metal ion (M) is surrounded by four ligands in a shape where the angles between any two bonds are approximately 109.5 degrees. Here, \( X \) and \( Y \) are monodentate ligands.

Symmetry Consideration: Due to the high symmetry of the tetrahedral shape, any arrangement of two \( X \) ligands and two \( Y \) ligands will be identical. No matter how you swap the positions of \( X \) and \( Y \) ligands, you will always get the same spatial arrangement.

Therefore, there is only one unique way to arrange \( \text{X}_2 \) and \( \text{Y}_2 \) around the metal center in a tetrahedral complex, leading to 1 possible isomer.

Square Planar Geometry

In a square planar geometry, the central metal ion (M) is surrounded by four ligands arranged at 90-degree angles in a plane, forming a square. Here, the arrangement of ligands can lead to different spatial isomers.

Cis Isomer: In the cis isomer, the two \( X \) ligands are adjacent to each other, and the two \( Y \) ligands are also adjacent to each other.

Trans Isomer: In the trans isomer, the two \( X \) ligands are opposite each other, and the two \( Y \) ligands are also opposite each other.

Thus, for a square planar complex \( \text{MX}_2\text{Y}_2 \), there are two distinct spatial arrangements of the ligands, resulting in 2 possible isomers: cis and trans.

To summarize:

In tetrahedral geometry, \( \text{MX}_2\text{Y}_2 \) can only have 1 isomer due to its high symmetry.

In square planar geometry, \( \text{MX}_2\text{Y}_2 \) can have 2 isomers: cis and trans.

Therefore, the correct answer is 1 and 2.