`[Co(NH_(3))Cl(en)_(2)]^(2+)` exist which isomerism ?

Options

A. trans-isomer will show optical isomerism .
B. cis-isomer will show optical isomerism .
C. Both trans and cis-isomers will show optical isomerism .
D. Neither cis nor trans-isomer will show optical isomerism .

Explanation

To determine the types of isomerism exhibited by the coordination compound \([Co(NH_3)Cl(en)_2]^{2+}\), we will analyze the ligands and their arrangements around the central metal ion, cobalt (Co).

### Step-by-Step Solution:

1. **Identify the Ligands**:
- The complex contains:
- 1 monodentate ligand: Chloride ion (Cl)
- 2 bidentate ligands: Ethylenediamine (en)
- 3 monodentate ligands: Ammonia (NH3)

2. **Determine the Coordination Number**:
- Cobalt has a coordination number of 6 because it is surrounded by 2 bidentate ligands (each contributing 2 coordination sites) and 1 monodentate ligand (contributing 1 coordination site).

3. **Possible Geometries**:
- With a coordination number of 6, the geometry of the complex is octahedral.

4. **Cis-Trans Isomerism**:
- In octahedral complexes, cis and trans isomerism is possible.
- The cis isomer has the two bidentate ligands adjacent to each other, while in the trans isomer, they are opposite each other.

5. **Optical Isomerism**:
- The cis isomer can exhibit optical isomerism because it lacks a plane of symmetry, allowing for non-superimposable mirror images.
- The trans isomer does not exhibit optical isomerism because it has a plane of symmetry.

6. **Conclusion**:
- The coordination compound \([Co(NH_3)Cl(en)_2]^{2+}\) exhibits:
- **Cis-Trans Isomerism**: due to the arrangement of the bidentate ligands.
- **Optical Isomerism**: only in the cis form.

### Final Answer:
The coordination compound \([Co(NH_3)Cl(en)_2]^{2+}\) exhibits **cis-trans isomerism** and **optical isomerism** (only in the cis form).

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