The possible geometric isomers of the complex , `[Co(en) Br_2Cl_2]^(-)` is :

Options

A. 2
B. 3
C. 4
D. 6

Explanation

To determine the possible geometric isomers of the complex \([Co(en)Br_2Cl_2]^-\), we need to analyze the coordination geometry and the ligands involved.

### Step-by-Step Solution:

1. **Identify the Coordination Number and Geometry**:
- The cobalt complex has a coordination number of 6 due to the presence of two bidentate ligands (ethylenediamine, en) and four monodentate ligands (two bromides and two chlorides).
- The geometry of a coordination complex with a coordination number of 6 is octahedral.

2. **Identify the Ligands**:
- The ligands in the complex are:
- Ethylenediamine (en) - a bidentate ligand that occupies two coordination sites.
- Two bromide ions (Br) - monodentate ligands.
- Two chloride ions (Cl) - monodentate ligands.

3. **Determine Possible Arrangements**:
- Since en is a bidentate ligand, it will occupy two adjacent positions in the octahedral geometry. The remaining four positions will be occupied by the two bromides and two chlorides.
- The geometric isomers can be categorized based on the relative positions of the bromides and chlorides.

4. **Construct the Isomers**:
- **Isomer 1**: Place the two bromides trans to each other and the two chlorides trans to each other.
- **Isomer 2**: Place the two chlorides trans to each other and the two bromides trans to each other.
- **Isomer 3**: Place one bromide and one chloride adjacent to each other, and the other bromide and chloride adjacent to each other.
- **Isomer 4**: Place the two bromides adjacent to each other and the two chlorides adjacent to each other.

5. **Count the Isomers**:
- After constructing the arrangements, we find that there are a total of 4 distinct geometric isomers.

### Final Answer:
The possible geometric isomers of the complex \([Co(en)Br_2Cl_2]^-\) are **4**.