Which of the following does not show optical activity ?

Options

A. `[Co(NH_(3))_(4)Cl_(2)]`
B. `[Cr(o x)_(3)]^(3-) `
C. `[Co(o x)_(2)(NH_(3))_(2)]Cl`
D. `[Co(en)(NH_(3))_(2)(H_(2)O)_(2)]Cl_(2)`

Answer

To determine which compound does not show optical activity, we need to understand the concept of optical isomerism and the presence of a plane of symmetry in a molecule.

### Step-by-Step Solution:

1. **Understanding Optical Activity**:
- Optical activity refers to the ability of a compound to rotate plane-polarized light. This property is exhibited by chiral molecules, which lack a plane of symmetry.

2. **Identifying Plane of Symmetry**:
- A molecule is optically inactive if it possesses a plane of symmetry (POS). This means that the molecule can be divided into two mirror-image halves.

3. **Analyzing the Given Compounds**:
- We need to analyze each option provided in the question to check for the presence of a plane of symmetry.

4. **Option 1: [Co(NH3)4Cl2]**:
- This compound has an octahedral structure. If we draw the structure, we can see that there is a plane that bisects the molecule, reflecting the two NH3 groups and the two Cl groups. Therefore, it has a plane of symmetry and does not show optical activity.

5. **Option 2: [Cr(ox)3]**:
- The oxalate ion (ox) has a structure that does not allow for a plane of symmetry when coordinated to chromium in an octahedral arrangement. Thus, this compound does not have a POS and can show optical activity.

6. **Option 3: [Co(ox)2(NH3)2]**:
- This compound can exist in both cis and trans forms. The trans form has a plane of symmetry, while the cis form does not. Therefore, it can show optical activity depending on its isomer.

7. **Option 4: Ethylenediamine (en)**:
- Ethylenediamine is a bidentate ligand that does not have a plane of symmetry when coordinated to a metal. Thus, it can show optical activity.

8. **Conclusion**:
- From the analysis, we conclude that **Option 1: [Co(NH3)4Cl2]** is the compound that does not show optical activity due to the presence of a plane of symmetry.

### Final Answer:
**The compound that does not show optical activity is [Co(NH3)4Cl2].**