The diamagnetic complex which has two geometrical and 4 optically active isomers is :

Options

A. `[Co(gly)_(3)]`
B. `[Pt(en)_(2)Cl_(2)]^(2+)`
C. `[Co(en)_(3)]^(3+)`
D. `[Fe(Ox)_(3)]^(3-)`

Answer

To solve the question regarding the diamagnetic complex that has two geometrical and four optically active isomers, we will analyze the given complexes step by step.

### Step 1: Identify the Complex
We need to identify a complex that is diamagnetic, has two geometrical isomers, and four optically active isomers. The complex mentioned in the video is [Co(Gly)3] where Glycine acts as a bidentate ligand.

### Step 2: Understanding Bidentate Ligands
Glycine (Gly) is a bidentate ligand, meaning it can coordinate to the metal center through two different donor atoms. In this case, Glycine coordinates through its nitrogen and oxygen atoms.

### Step 3: Determine the Geometry
The complex [Co(Gly)3] has an octahedral geometry because it is a coordination complex with a central metal ion surrounded by six donor atoms (three Glycine ligands).

### Step 4: Identify Geometrical Isomers
In an octahedral complex with bidentate ligands, we can have two types of geometrical isomers:
- **Facial (fac)**: All three bidentate ligands occupy adjacent positions.
- **Meridional (mer)**: The bidentate ligands occupy positions that are opposite each other.

Thus, [Co(Gly)3] can exhibit two geometrical isomers: fac-[Co(Gly)3] and mer-[Co(Gly)3].

### Step 5: Determine Optical Activity
Optical isomers (enantiomers) are those that do not have a plane of symmetry. Since both the fac and mer isomers do not have a plane of symmetry, they can exist as optical isomers.

- For the fac isomer, it can exist in two forms (D and L).
- For the mer isomer, it can also exist in two forms (D and L).

Thus, we have a total of four optical isomers: two from the fac isomer and two from the mer isomer.

### Step 6: Conclusion
The complex [Co(Gly)3] is diamagnetic (as cobalt in this oxidation state is Co(III) with no unpaired electrons), has two geometrical isomers (fac and mer), and four optical isomers (D and L forms of both geometrical isomers).

### Final Answer
The diamagnetic complex which has two geometrical and four optically active isomers is **[Co(Gly)3]**.

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