For the given complex `[CoCl_(2)(en)(NH_(3))_(2)]^(+)`, the number of geometrical isomers, the number of optical isomers and total number of isomers of all type possible respectively are

Options

A. 3,2 and 4
B. 2,2 and 3
C. 2,0 and 2
D. 0,2 and 2

Explanation

To determine the number of geometrical isomers, optical isomers, and the total number of isomers for the complex \([CoCl_2(en)(NH_3)_2]^+\), we will follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The complex \([CoCl_2(en)(NH_3)_2]^+\) has a cobalt (Co) center coordinated to two chloride ions (Cl), one ethylene diamine (en), and two ammonia (NH₃) ligands. The coordination number of cobalt in this complex is 6, which typically leads to an octahedral geometry.

**Hint:** The coordination number is the total number of ligand donor atoms bonded to the central metal atom.

### Step 2: Determine the Types of Ligands
In this complex:
- Chloride (Cl) is a monodentate ligand.
- Ethylene diamine (en) is a bidentate ligand, meaning it can attach through two donor atoms (both nitrogen atoms).
- Ammonia (NH₃) is also a monodentate ligand.

**Hint:** Identify the nature of each ligand (monodentate vs. bidentate) to understand how they can arrange around the central atom.

### Step 3: Identify Geometrical Isomers
For octahedral complexes with two identical ligands (Cl) and two different types of ligands (en and NH₃), we can have geometrical isomers. The possible arrangements are:
- **Cis Isomer:** The two Cl ligands are adjacent to each other.
- **Trans Isomer:** The two Cl ligands are opposite each other.

Thus, we can have:
1. **Cis Isomer**: Cl, Cl adjacent to each other.
2. **Trans Isomer**: Cl, Cl opposite each other.

**Total Geometrical Isomers = 2**

**Hint:** Consider the positions of identical ligands in relation to each other to determine cis and trans forms.

### Step 4: Identify Optical Isomers
Optical isomers (enantiomers) occur when a molecule lacks a plane of symmetry. In this case, both the cis and trans forms can be analyzed for optical activity:
- The **Cis Isomer** can have optical isomers because it lacks a plane of symmetry.
- The **Trans Isomer** has a plane of symmetry and does not have optical isomers.

Thus, for the cis isomer, we have 2 optical isomers (enantiomers), and for the trans isomer, we have none.

**Total Optical Isomers = 2**

**Hint:** Check for the presence of a plane of symmetry to determine if optical isomers exist.

### Step 5: Calculate Total Isomers
Now, we can calculate the total number of isomers:
- Geometrical Isomers = 2
- Optical Isomers = 2 (only from the cis form)

Total Isomers = Geometrical Isomers + Optical Isomers = 2 + 2 = 4.

**Total Isomers = 4**

### Final Answer
The number of geometrical isomers, the number of optical isomers, and the total number of isomers of all types possible for the complex \([CoCl_2(en)(NH_3)_2]^+\) are:
- Geometrical Isomers: 2
- Optical Isomers: 2
- Total Isomers: 4