How many geometrical isomers and stereoisomers are possible for `[Pt(NO_(2))(NH_(3))(NH_(2)OH)(Py)]^(+) and [Pt(Br)(Cl)(I)(NO_(2))(NH_(3))(Py)]` respectively?

Options

A. 3 and 15
B. 3 and 30
C. 4 and 15
D. 4 and 30

Explanation

To determine the number of geometrical isomers and stereoisomers for the given coordination complexes, we will analyze each complex step by step.

### Step 1: Analyze the first complex `[Pt(NO2)(NH3)(NH2OH)(Py)]^+`

1. **Identify the coordination number and geometry**:
- The platinum (Pt) complex has a coordination number of 4 (due to 4 different ligands: NO2, NH3, NH2OH, and Py).
- The geometry of this complex is square planar.

2. **Determine the type of isomerism**:
- Square planar complexes can exhibit geometrical isomerism.
- For square planar complexes with the general formula MA2B2 (where A and B are different ligands), we can have cis and trans isomers.

3. **Identify the ligands**:
- In this complex, we have 4 different ligands: NO2, NH3, NH2OH, and Py. This corresponds to the MABCD type of complex.

4. **Determine the number of geometrical isomers**:
- For a square planar complex with 4 different ligands (MABCD), the number of geometrical isomers can be calculated based on the pairs of ligands that can be arranged in a trans configuration.
- The possible trans pairs are:
- A-B (NO2-NH3)
- C-D (NH2OH-Py)
- A-C (NO2-NH2OH)
- B-D (NH3-Py)
- In total, there are 3 geometrical isomers possible for this complex.

### Step 2: Analyze the second complex `[Pt(Br)(Cl)(I)(NO2)(NH3)(Py)]`

1. **Identify the coordination number and geometry**:
- The platinum complex has a coordination number of 6 (due to 6 different ligands: Br, Cl, I, NO2, NH3, and Py).
- The geometry of this complex is octahedral.

2. **Determine the type of isomerism**:
- Octahedral complexes can exhibit both geometrical and optical isomerism.

3. **Identify the ligands**:
- In this complex, we have 6 different ligands: Br, Cl, I, NO2, NH3, and Py. This corresponds to the MABCDEF type of complex.

4. **Determine the number of geometrical isomers**:
- For an octahedral complex with 6 different ligands, the number of geometrical isomers can be determined by the number of trans pairs.
- The number of trans pairs is given by the formula for octahedral complexes with 6 different ligands, which is known to yield 15 geometrical isomers.

5. **Determine the number of stereoisomers**:
- Since all geometrical isomers are optically active, each geometrical isomer will have a non-superimposable mirror image.
- Therefore, the total number of stereoisomers will be the sum of the geometrical isomers and their corresponding optical isomers.
- Thus, the total number of stereoisomers = 15 (geometrical) + 15 (optical) = 30.

### Final Summary:
- For the complex `[Pt(NO2)(NH3)(NH2OH)(Py)]^+`, the number of geometrical isomers is **3**.
- For the complex `[Pt(Br)(Cl)(I)(NO2)(NH3)(Py)]`, the total number of stereoisomers is **30**.

### Conclusion:
The answer to the question is:
- **Geometrical isomers for the first complex: 3**
- **Stereoisomers for the second complex: 30**