Number of stereoisomers possible for the octahedral complex `[Co(NH_3)_3 Cl_3]` and ` [Ni (en)_2 Cl_2 ]` respectively , are :
[en = 1,2 ethylenediamine ]

Options

A. 2 and 4
B. 4 and 3
C. 3 and 2
D. 2 and 3

Explanation

To determine the number of stereoisomers for the octahedral complexes \([Co(NH_3)_3Cl_3]\) and \([Ni(en)_2Cl_2]\), we will analyze each complex step by step.

### Step 1: Analyze the complex \([Co(NH_3)_3Cl_3]\)

1. **Identify the type of complex**: This complex has the formula MA3B3, where M is the metal (Co), A is the ligand (NH3), and B is the ligand (Cl).
2. **Determine the geometrical isomers**: For MA3B3 complexes, there are two possible geometrical isomers:
- **Facial (fac)**: All three identical ligands (NH3) are on one face of the octahedron.
- **Meridional (mer)**: The three identical ligands (NH3) are arranged in a plane that divides the octahedron into two equal halves.
3. **Count the stereoisomers**:
- The fac isomer is optically inactive due to its symmetry.
- The mer isomer is also optically inactive.
- Therefore, there are **2 geometrical isomers** (fac and mer) for \([Co(NH_3)_3Cl_3]\).

### Step 2: Analyze the complex \([Ni(en)_2Cl_2]\)

1. **Identify the type of complex**: This complex has the formula MA2B2, where M is the metal (Ni), A is the ligand (en, ethylenediamine), and B is the ligand (Cl).
2. **Determine the geometrical isomers**: For MA2B2 complexes, there are two possible forms:
- **Cis**: Both Cl ligands are adjacent to each other.
- **Trans**: The Cl ligands are opposite each other.
3. **Count the stereoisomers**:
- **Cis isomer**: This isomer lacks a plane of symmetry and can exist as two non-superimposable mirror images (enantiomers), making it optically active. Thus, it contributes **2 stereoisomers** (one for each enantiomer).
- **Trans isomer**: This isomer has a plane of symmetry and is optically inactive, contributing **1 stereoisomer**.
- Therefore, the total number of stereoisomers for \([Ni(en)_2Cl_2]\) is \(2 \text{ (from cis)} + 1 \text{ (from trans)} = 3\).

### Final Answer:
- The number of stereoisomers for \([Co(NH_3)_3Cl_3]\) is **2**.
- The number of stereoisomers for \([Ni(en)_2Cl_2]\) is **3**.

### Summary:
- For \([Co(NH_3)_3Cl_3]\): 2 stereoisomers (fac and mer).
- For \([Ni(en)_2Cl_2]\): 3 stereoisomers (2 from cis and 1 from trans).