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

Options

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

Answer

To solve the problem regarding the complex \([CoCl_2(en)(N_3)_2]^+\), we will determine the number of geometrical isomers, optical isomers, and the total number of isomers step by step.

### Step 1: Identify the Coordination Number
The cobalt complex has:
- 2 chloride ions (\(Cl^-\)) which are monodentate ligands.
- 1 ethylenediamine (\(en\)) which is a bidentate ligand.
- 2 azide ions (\(N_3^-\)) which are also monodentate ligands.

Calculating the total coordination number:
- Chloride contributes 2 (2 monodentate ligands).
- Ethylenediamine contributes 2 (1 bidentate ligand).
- Azide contributes 2 (2 monodentate ligands).

Thus, the total coordination number is \(2 + 2 + 2 = 6\).

### Step 2: Determine Geometrical Isomers
For coordination complexes with a coordination number of 6, we can have geometrical isomers in cis and trans configurations.

1. **Cis Isomer**: Both \(Cl\) ligands are adjacent to each other.
2. **Trans Isomer**: The \(Cl\) ligands are opposite each other.

Thus, we have:
- 1 cis isomer
- 1 trans isomer

Total geometrical isomers = 2.

### Step 3: Determine Optical Isomers
Optical isomers are non-superimposable mirror images.

1. **Cis Isomer**: The cis isomer can exist in two forms (D and L) due to its asymmetric arrangement.
2. **Trans Isomer**: The trans isomer can also exist in two forms (D and L) due to its asymmetric arrangement.

Thus, for each geometrical isomer:
- Cis has 2 optical isomers (D and L).
- Trans has 2 optical isomers (D and L).

Total optical isomers = 2 (from cis) + 2 (from trans) = 4.

### Step 4: Calculate Total Isomers
Now, we can calculate the total number of isomers:
- Geometrical isomers = 2
- Optical isomers = 4

Total isomers = Geometrical isomers + Optical isomers = 2 + 4 = 6.

### Final Answer
The number of geometrical isomers is 2, the number of optical isomers is 2, and the total number of isomers is 4.

### Summary
- Number of geometrical isomers: 2
- Number of optical isomers: 2
- Total number of isomers: 4