Which of the following compounds show optical isomerism?
I. `cis -[Co(NH_(3))_(4) Cl_(2)]^(+) `
II. Trans - `[Co(en)_(2) Cl_(2)]^(+)`
III. Cis - `[Co(en)_(2) cl_(2)]^(+)`
IV. `[Co(en)_(3)]^(3+)`
Choose the correct answer form the codes given below.

Options

A. I and II
B. II and III
C. III and IV
D. I, III and IV

Explanation

To determine which of the given compounds show optical isomerism, we need to analyze the structures of each compound and check for symmetry. Optical isomerism occurs in chiral compounds, which lack an internal plane of symmetry.

### Step-by-Step Solution:

1. **Identify the Compounds:**
- I. `cis -[Co(NH₃)₄Cl₂]⁺`
- II. `trans - [Co(en)₂Cl₂]⁺`
- III. `cis - [Co(en)₂Cl₂]⁺`
- IV. `[Co(en)₃]³⁺`

2. **Analyze Compound I: `cis -[Co(NH₃)₄Cl₂]⁺`:**
- This compound has a square planar geometry. The presence of two identical ligands (Cl) and four identical ligands (NH₃) creates a plane of symmetry.
- **Conclusion:** This compound does not show optical isomerism.

3. **Analyze Compound II: `trans - [Co(en)₂Cl₂]⁺`:**
- In this compound, the trans configuration also leads to a symmetrical arrangement. The two Cl ligands are opposite each other, creating a plane of symmetry.
- **Conclusion:** This compound does not show optical isomerism.

4. **Analyze Compound III: `cis - [Co(en)₂Cl₂]⁺`:**
- The cis configuration means that the two Cl ligands are adjacent. This arrangement disrupts symmetry, resulting in a chiral molecule.
- **Conclusion:** This compound shows optical isomerism.

5. **Analyze Compound IV: `[Co(en)₃]³⁺`:**
- This compound has three bidentate ethylenediamine (en) ligands. The arrangement is such that it lacks any plane of symmetry, making it chiral.
- **Conclusion:** This compound shows optical isomerism.

### Final Answer:
The compounds that show optical isomerism are:
- III. `cis - [Co(en)₂Cl₂]⁺`
- IV. `[Co(en)₃]³⁺`

Thus, the correct answer is option **C (III and IV)**.

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