Which one of the following complexes shows optical isomerism ?
(en=ethylenediamine)

Options

A. trans `[Co(en)_2 Cl_2] Cl`
B. `[Co(NH_3)_4Cl_2]Cl`
C. `[Co(NH_3)_3 Cl_3]`
D. cis `[Co(em)_2 Cl_2]Cl`

Explanation

To determine which complex shows optical isomerism, we need to analyze the given complexes based on their structures and symmetry properties. Optical isomerism occurs when a molecule can exist in two non-superimposable mirror images, which typically happens when there is no plane of symmetry or center of symmetry in the molecule.

### Step-by-Step Solution:

1. **Identify the complexes**: The question provides several complexes, including those with cobalt (Co) and ligands like ethylenediamine (en) and chloride (Cl).

2. **Analyze the first complex**:
- The complex is given as trans-[Co(en)₂Cl₂]⁺.
- In this configuration, the two ethylenediamine ligands are opposite each other (trans), and the two chloride ligands are also opposite each other.
- Since this complex has a plane of symmetry, it cannot have optical isomers. Thus, it does not show optical isomerism.

3. **Analyze the second complex**:
- The complex is [Co(NH₃)₄Cl₂]⁺.
- This complex can exist in both cis and trans forms.
- However, both cis and trans forms will have a plane of symmetry, so this complex also does not show optical isomerism.

4. **Analyze the third complex**:
- The complex is [Co(NH₃)₃Cl₃].
- This complex can exhibit facial (fac) and meridional (mer) isomerism.
- Both fac and mer forms will have a plane of symmetry, so this complex does not show optical isomerism.

5. **Analyze the fourth complex**:
- The complex is cis-[Co(en)₂Cl₂]⁺.
- In this configuration, the two ethylenediamine ligands are adjacent to each other (cis), and the two chloride ligands are also adjacent.
- This arrangement does not have a plane of symmetry, making it optically active. Therefore, it can exist in two non-superimposable mirror images (D and L forms).

6. **Conclusion**: The only complex that shows optical isomerism is **cis-[Co(en)₂Cl₂]⁺**.

### Final Answer:
The complex that shows optical isomerism is **cis-[Co(en)₂Cl₂]⁺**.

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