A coordination complex of type `MX_(2)Y_(2)` (M-metal ion: X, Y-monodentate lingads), can have either a tetrahedral or a square planar geometry. The maximum number of posible isomers in these two cases are respectively:

Options

A. 1 and 2
B. 2 and 1
C. 1 and 3
D. 3 and 2

Explanation

To solve the problem of determining the maximum number of possible isomers for the coordination complex of type \( MX_2Y_2 \) with tetrahedral and square planar geometries, we can break down the solution step by step.

### Step 1: Understanding the Coordination Complex
The coordination complex is of the form \( MX_2Y_2 \), where:
- \( M \) is the metal ion.
- \( X \) and \( Y \) are monodentate ligands.

### Step 2: Analyzing Tetrahedral Geometry
In a tetrahedral geometry, the ligands are arranged around the central metal ion in a way that they occupy the corners of a tetrahedron.

- For the complex \( MX_2Y_2 \):
- The two \( X \) ligands and two \( Y \) ligands can be arranged in only one way due to the symmetry of the tetrahedral structure.

Thus, the maximum number of isomers in tetrahedral geometry is **1**.

### Step 3: Analyzing Square Planar Geometry
In a square planar geometry, the ligands are arranged around the central metal ion in a square plane.

- For the complex \( MX_2Y_2 \):
- We can have two distinct arrangements:
1. **Cis Isomer**: Both \( X \) ligands are adjacent to each other, and both \( Y \) ligands are adjacent to each other.
2. **Trans Isomer**: The \( X \) ligands are opposite each other, and the \( Y \) ligands are opposite each other.

Thus, the maximum number of isomers in square planar geometry is **2**.

### Final Answer
The maximum number of possible isomers for the coordination complex \( MX_2Y_2 \) is:
- **1 isomer for tetrahedral geometry**
- **2 isomers for square planar geometry**

### Summary of Isomers
- Tetrahedral: 1 isomer
- Square Planar: 2 isomers