Which one of the following complexes shows optical isomerism ?

Options

A. `cis[Co(en)_(2)"Cl"_(2)]"Cl" `
B. `trans[Co(en)_(2)"Cl"_(2)]"Cl" `
C. `[Co(NH_(3))_(4)"Cl"_(2)]"Cl"`
D. `[Co("NH"_(3))_(3)"Cl"_(3)]`

Answer

To determine which of the given complexes shows optical isomerism, we need to analyze each complex based on the criteria for optical isomerism. Optical isomerism occurs when a molecule has a chiral center, meaning it cannot be superimposed on its mirror image. This typically requires the presence of four different ligands around a central metal atom.

### Step-by-Step Solution:

1. **Identify the Complexes:**
We have four coordination complexes to analyze. Let's denote them as:
- A: [Co(en)₂Cl₂] (cis)
- B: [Co(en)₂Cl₂] (trans)
- C: [Co(NH₃)₄Cl₂]
- D: [Co(NH₃)Cl₃]

2. **Analyze Complex A: [Co(en)₂Cl₂] (cis):**
- This complex has two bidentate ethylene diamine (en) ligands and two chloride (Cl) ligands.
- The cis arrangement means that the two en ligands are adjacent to each other.
- Since there is no plane of symmetry, this complex can exist in two non-superimposable mirror images (enantiomers).
- **Conclusion:** Complex A shows optical isomerism.

3. **Analyze Complex B: [Co(en)₂Cl₂] (trans):**
- This is the trans isomer of the same complex as A.
- In the trans arrangement, the two en ligands are opposite each other.
- There is a plane of symmetry in this structure, meaning it cannot exist in two non-superimposable forms.
- **Conclusion:** Complex B does not show optical isomerism.

4. **Analyze Complex C: [Co(NH₃)₄Cl₂]:**
- This complex has four ammonia (NH₃) ligands and two chloride (Cl) ligands.
- Regardless of how the ligands are arranged, there will always be a plane of symmetry present due to the arrangement of identical ligands.
- **Conclusion:** Complex C does not show optical isomerism.

5. **Analyze Complex D: [Co(NH₃)Cl₃]:**
- This complex has three chloride ligands and one ammonia ligand.
- Similar to Complex C, there will be a plane of symmetry present in this arrangement as well.
- **Conclusion:** Complex D does not show optical isomerism.

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