For the square planar complex [M(a) (b) (c ) (d)] (where M = central meatal and a, b, c and d are monodentate ligands), the number of possible geometrical isomers are

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine the number of possible geometrical isomers for the square planar complex [M(a)(b)(c)(d)], where M is the central metal and a, b, c, and d are monodentate ligands, we can follow these steps:

### Step 1: Understand the Geometry
The complex is square planar, which means that the coordination number is 4. In square planar complexes, geometrical isomerism can occur due to the arrangement of ligands around the central metal atom.

**Hint 1:** Recall that square planar complexes can exhibit geometrical isomers due to the different possible arrangements of ligands.

### Step 2: Identify the Ligands
We have four different monodentate ligands: A, B, C, and D. Since all ligands are different, we can arrange them in various ways around the central metal.

**Hint 2:** Consider how many unique arrangements can be made with four different ligands in a square planar geometry.

### Step 3: Fix One Ligand
To simplify the counting of isomers, we can fix one ligand in a position. For instance, let’s fix ligand A in one position. The remaining three ligands (B, C, D) can occupy the other three positions.

**Hint 3:** Fixing one ligand helps in reducing the complexity of counting isomers.

### Step 4: Count the Arrangements
With A fixed, we can arrange B, C, and D in the remaining three positions. The arrangements can be visualized as follows:
1. A at the top, B at one side, C at the other side, and D at the bottom.
2. A at the top, B at one side, D at the other side, and C at the bottom.
3. A at the top, C at one side, B at the other side, and D at the bottom.
4. A at the top, C at one side, D at the other side, and B at the bottom.
5. A at the top, D at one side, B at the other side, and C at the bottom.
6. A at the top, D at one side, C at the other side, and B at the bottom.

However, due to symmetry in square planar complexes, some of these arrangements will be identical.

**Hint 4:** Remember that some arrangements may look different but are actually the same due to the symmetrical nature of the square planar geometry.

### Step 5: Determine Unique Isomers
After analyzing the arrangements, we find that there are three unique geometrical isomers:
1. A-B-C-D
2. A-B-D-C
3. A-C-B-D

Thus, the total number of geometrical isomers for the complex [M(a)(b)(c)(d)] is **3**.

**Final Answer:** The number of possible geometrical isomers is **3**.