How many geometrical isomers are possible for complex `[Mab(AB)_(2)]^(n+-)`?

Options

A. 5
B. 4
C. 3
D. 6

Explanation

To determine the number of geometrical isomers for the complex \([Mab(AB)_{2}]^{n+-}\), we need to analyze the coordination environment of the metal center (M) and the types of ligands involved.

### Step-by-Step Solution:

1. **Identify the Ligands**:
- The complex contains one unidentate ligand (denoted as "a" and "b") and two bidentate ligands (denoted as "AB").
- The unidentate ligands can coordinate to the metal center at one site each, while the bidentate ligands can coordinate at two sites.

2. **Determine the Coordination Geometry**:
- Since there are two bidentate ligands and one unidentate ligand, the coordination number of the metal is 6.
- This typically leads to an octahedral geometry.

3. **Analyze Possible Geometrical Isomers**:
- In an octahedral complex, the arrangement of ligands can lead to different geometrical isomers, specifically cis and trans configurations.
- For the given complex \([Mab(AB)_{2}]^{n+-}\), we can have the following configurations:
- **Cis Isomers**: Where similar ligands are adjacent to each other.
- **Trans Isomers**: Where similar ligands are opposite to each other.

4. **Draw Possible Isomers**:
- **Cis Isomers**:
- Isomer 1: Ligands "a" and "b" are adjacent, and both "AB" ligands are adjacent.
- Isomer 2: Ligands "a" and "b" are adjacent, but the "AB" ligands are on opposite sides.
- **Trans Isomers**:
- Isomer 3: Ligands "a" and "b" are opposite, and both "AB" ligands are adjacent.
- Isomer 4: Ligands "a" and "b" are opposite, and the "AB" ligands are also opposite.

5. **Count All Possible Isomers**:
- After drawing and analyzing the configurations, we find that there are a total of 6 distinct geometrical isomers for the complex \([Mab(AB)_{2}]^{n+-}\).

### Final Answer:
The total number of geometrical isomers possible for the complex \([Mab(AB)_{2}]^{n+-}\) is **6**.