The total No. of isomers possible for the complex `[Co (e n)_(2)Cl_(2)]` is :-

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To determine the total number of isomers for the complex \([Co(en)_2Cl_2]\), we can follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The complex \([Co(en)_2Cl_2]\) has a coordination number of 6 because it contains two bidentate ethylenediamine (en) ligands and two monodentate chloride (Cl) ligands. The geometry of such a complex is octahedral.

**Hint:** Remember that the coordination number indicates how many ligand atoms are bonded to the central metal atom.

### Step 2: Determine Possible Geometrical Isomers
In an octahedral complex, we can have geometrical isomers, specifically cis and trans forms.

- **Cis Isomer:** In the cis configuration, the two ethylenediamine ligands are adjacent to each other.
- **Trans Isomer:** In the trans configuration, the two ethylenediamine ligands are opposite each other.

**Hint:** Visualize the octahedral structure to help differentiate between cis and trans configurations.

### Step 3: Analyze Optical Isomerism
The cis isomer can exhibit optical isomerism because it lacks a plane of symmetry. This means that the cis isomer can exist in two forms: the D (dextrorotatory) form and the L (levorotatory) form.

- **Optical Isomers of Cis:** The cis isomer has two optical isomers (D and L).
- **Optical Isomers of Trans:** The trans isomer does not have optical isomers because it has a plane of symmetry.

**Hint:** Remember that optical isomers are non-superimposable mirror images and require the absence of symmetry.

### Step 4: Count Total Isomers
Now, we can summarize the isomers:
- **Cis Isomer:** 2 (D and L forms)
- **Trans Isomer:** 1

Thus, the total number of isomers is:
\[ \text{Total Isomers} = 2 \text{ (cis)} + 1 \text{ (trans)} = 3 \]

**Hint:** Keep track of both geometrical and optical isomers to ensure you count all possible variations.

### Conclusion
The total number of isomers possible for the complex \([Co(en)_2Cl_2]\) is **3**.

**Final Answer:** 3