Which of the following complex show maximum numbers of stereo isomers is :-

Options

A. `[PtCl_(3)(C_(2)H_(4))]^("ϴ")`
B. `[CuBr_(2)Cl_(2)]^(-2)`
C. `[Cr(NH_(3))_(2)(e n)_(2)]^(+3)`
D. `[Co(C_(2)O_(4))_(3)]^(-3)`

Answer

To determine which of the given complexes shows the maximum number of stereoisomers, we will analyze each complex one by one.

### Step-by-Step Solution:

1. **Identify the complexes**: The complexes given are:
- (i) PtCl3(C2H4)
- (ii) CuBr2Cl2
- (iii) Cr(NH3)2(en)2^3+
- (iv) Cu(C2O4)2^3-

2. **Analyze the first complex (PtCl3(C2H4))**:
- This complex has a square planar geometry.
- It can exhibit cis and trans isomerism.
- Therefore, it has **2 stereoisomers** (cis and trans).

3. **Analyze the second complex (CuBr2Cl2)**:
- This complex also has a square planar geometry.
- It can exhibit cis and trans isomerism as well.
- Thus, it also has **2 stereoisomers** (cis and trans).

4. **Analyze the third complex (Cr(NH3)2(en)2^3+)**:
- This complex has an octahedral geometry.
- It can exhibit geometric isomerism (cis and trans) as well as optical isomerism.
- The possible stereoisomers are:
- 2 cis isomers (one for each pair of en ligands)
- 1 trans isomer
- 2 optical isomers for each cis isomer.
- Therefore, it has a total of **4 stereoisomers** (2 cis, 1 trans, and 2 optical).

5. **Analyze the fourth complex (Cu(C2O4)2^3-)**:
- This complex has an octahedral geometry.
- It can exhibit cis and trans isomerism.
- The possible stereoisomers include:
- 2 cis isomers (one for each pair of oxalate ligands)
- 1 trans isomer
- 2 optical isomers for each cis isomer.
- Thus, it has a total of **3 stereoisomers** (2 cis and 1 trans).

6. **Compare the number of stereoisomers**:
- PtCl3(C2H4): 2 stereoisomers
- CuBr2Cl2: 2 stereoisomers
- Cr(NH3)2(en)2^3+: 4 stereoisomers
- Cu(C2O4)2^3-: 3 stereoisomers

7. **Conclusion**:
- The complex with the maximum number of stereoisomers is **Cr(NH3)2(en)2^3+**, which has **4 stereoisomers**.

### Final Answer:
The complex that shows the maximum number of stereoisomers is **Cr(NH3)2(en)2^3+**.