The existence of two different coloured comlexes with the composition `|Co(NH_(3))_(2)Cl_(2)|^(+)` is due to

Options

A. linkage isomerism
B. geometrical isomerism
C. coordination isomerism
D. ionisation isomerism

Explanation

To solve the question regarding the existence of two different colored complexes with the composition \[ \text{[Co(NH}_3)_2\text{Cl}_2]^+ \], we will analyze the reasons behind this phenomenon step by step.

### Step-by-Step Solution:

1. **Understanding the Complex**:
The complex \[ \text{[Co(NH}_3)_2\text{Cl}_2]^+ \] consists of cobalt (Co) as the central metal ion, coordinated with two ammonia (NH₃) ligands and two chloride (Cl) ligands. The overall charge of the complex is +1.

**Hint**: Identify the components of the coordination complex and their roles.

2. **Identifying Possible Isomerism**:
Coordination compounds can exhibit various types of isomerism, including:
- Linkage isomerism
- Geometrical (cis-trans) isomerism
- Coordination isomerism
- Ionization isomerism

**Hint**: Recall the different types of isomerism that can occur in coordination compounds.

3. **Geometrical Isomerism**:
In this case, the complex can exhibit geometrical isomerism due to the arrangement of the ligands around the central metal ion. Specifically, \[ \text{[Co(NH}_3)_2\text{Cl}_2]^+ \] can exist in two forms:
- **Cis form**: Both NH₃ ligands are adjacent to each other.
- **Trans form**: The NH₃ ligands are opposite each other.

**Hint**: Consider how the spatial arrangement of ligands affects the properties of the complex.

4. **Color Differences**:
The different spatial arrangements (cis and trans) lead to variations in the electronic environment around the cobalt ion. This can result in different absorption of light, leading to the appearance of different colors for the two isomers.

**Hint**: Think about how the arrangement of ligands can influence the d-orbital splitting and thus the color observed.

5. **Conclusion**:
Therefore, the existence of two different colored complexes of \[ \text{[Co(NH}_3)_2\text{Cl}_2]^+ \] is due to **geometrical isomerism** (cis-trans isomerism).

The correct answer is that the two different colors arise from the geometrical isomerism of the complex.

### Final Answer:
The existence of two different colored complexes with the composition \[ \text{[Co(NH}_3)_2\text{Cl}_2]^+ \] is due to geometrical isomerism (cis-trans isomerism).