Which of the following statement is true for the complex `[Co(NH_(3))_(4)Br_(2)]NO_(2)` ?

Options

A. It shows ionisation, linkage and geometrical isomerims
B. It does not show optical isomerism because it cis and trans forms each have at least one plane of symmetry.
C. Its ionisation isomers cannot be differentiated by silver nitrate solution.
D. (A) and (B) both

Explanation

To determine which statements are true for the complex \([Co(NH_{3})_{4}Br_{2}]NO_{2}\), we need to analyze its structure and properties. Here’s a step-by-step solution:

### Step 1: Identify the Coordination Number and Geometry
The complex \([Co(NH_{3})_{4}Br_{2}]NO_{2}\) contains cobalt (Co) as the central metal ion surrounded by four ammonia (NH₃) ligands and two bromide (Br) ligands. The coordination number of cobalt in this complex is 6 (4 from NH₃ and 2 from Br).

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

### Step 2: Determine the Geometry
With a coordination number of 6, the most common geometry for such complexes is octahedral.

**Hint:** Remember that octahedral complexes can exhibit geometrical isomerism due to the different arrangements of ligands around the central metal ion.

### Step 3: Analyze Geometrical Isomerism
In an octahedral complex with the formula \([Co(NH_{3})_{4}Br_{2}]\), the two bromide ligands can be arranged in different ways:
- **Cis Isomer:** Both bromide ligands are adjacent to each other.
- **Trans Isomer:** The bromide ligands are opposite each other.

This indicates that the complex can exhibit geometrical isomerism.

**Hint:** Geometrical isomers differ in the spatial arrangement of ligands but have the same connectivity.

### Step 4: Check for Optical Isomerism
Optical isomerism occurs when a molecule can exist in two forms that are mirror images of each other (enantiomers). For a complex to exhibit optical isomerism, it must lack any planes of symmetry.

In the case of \([Co(NH_{3})_{4}Br_{2}]\), due to the presence of two identical bromide ligands and four identical ammonia ligands, the complex has a plane of symmetry. Therefore, it does not exhibit optical isomerism.

**Hint:** A complex with a plane of symmetry cannot have optical isomers.

### Conclusion
Based on the analysis:
- The complex \([Co(NH_{3})_{4}Br_{2}]NO_{2}\) shows geometrical isomerism (due to the arrangement of Br ligands) but does not show optical isomerism (due to the presence of a plane of symmetry).

### Final Answer
The true statements regarding the complex \([Co(NH_{3})_{4}Br_{2}]NO_{2}\) are:
1. It shows geometrical isomerism.
2. It does not show optical isomerism.