Complex compounds that have the same molecular formula but have different structural/space arrangements of ligands around central metal atom/ion are called isomers, these are of two types namely structural and stereoisomers.
Q. Type of isomerism exhibited by `[CrCl_(2)(NO)_(2))_(2)(NH_(3))_(2)]^(-)` complex ion are:

Options

A. ionisation, optical
B. hydrate, optical
C. geometrical, opticl
D. co-ordinate, geometrical

Answer

To determine the type of isomerism exhibited by the complex ion \([CrCl_2(NO)_2(NH_3)_2]^-\), we will analyze the structure and the possible arrangements of the ligands around the central metal atom, which is chromium (Cr).

### Step-by-Step Solution:

1. **Identify the Coordination Number and Geometry**:
- The central metal ion in the complex is chromium (Cr), which is surrounded by 6 ligands (2 Cl, 2 NO, and 2 NH3).
- With a coordination number of 6, the geometry of the complex is octahedral.

**Hint**: Coordination number refers to the number of ligand donor atoms bonded to the central metal atom.

2. **Determine the Types of Isomerism**:
- Isomerism in coordination compounds can be classified into structural isomerism and stereoisomerism.
- Structural isomerism includes ionization isomerism, hydrate isomerism, and coordination isomerism.
- Stereoisomerism includes geometrical isomerism and optical isomerism.

3. **Evaluate Structural Isomerism**:
- **Ionization Isomerism**: This occurs when different ions can be formed in solution. Since there are no counter ions in this complex, ionization isomerism is not applicable.
- **Hydrate Isomerism**: This involves the presence of water as a ligand. Since there are no water molecules in this complex, hydrate isomerism is not applicable.
- **Coordination Isomerism**: This occurs in complexes with both cationic and anionic parts. Since this complex is a single entity with no separate cation and anion, coordination isomerism is not applicable.

**Hint**: Structural isomerism can be ruled out if the complex does not have the necessary components.

4. **Evaluate Stereoisomerism**:
- **Geometrical Isomerism**: In an octahedral complex, different arrangements of ligands can lead to different geometrical isomers. For example, the ligands can be arranged in cis or trans positions.
- **Optical Isomerism**: This occurs when a complex can exist in two non-superimposable mirror images (enantiomers). If the arrangement of ligands lacks symmetry, optical isomerism can occur.

**Hint**: Look for symmetry in the arrangement of ligands to determine if optical isomers can exist.

5. **Conclusion**:
- The complex \([CrCl_2(NO)_2(NH_3)_2]^-\) can exhibit both geometrical and optical isomerism due to its octahedral geometry and the arrangement of the ligands.
- Therefore, the type of isomerism exhibited by this complex is **geometrical and optical isomerism**.

### Final Answer:
The type of isomerism exhibited by the complex ion \([CrCl_2(NO)_2(NH_3)_2]^-\) is **geometrical and optical isomerism**.