The possible number of the optical isomers in `[Cr(en)_(2)CI_(2)]^(o+)` is .

Options

A. `6`
B. `3`
C. `4`
D. `2`

Answer

To determine the possible number of optical isomers for the complex \([Cr(en)_2Cl_2]^+\), we will follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The complex \([Cr(en)_2Cl_2]^+\) has a chromium (Cr) central metal ion coordinated to two ethylenediamine (en) ligands and two chloride (Cl) ligands. Ethylenediamine is a bidentate ligand, meaning it can form two bonds with the metal center. Therefore, the coordination number of chromium in this complex is 6. The geometry of a coordination complex with a coordination number of 6 is typically octahedral.

**Hint:** Look for the coordination number and geometry of the metal complex to understand the possible isomerism.

### Step 2: Determine the Types of Isomers
In octahedral complexes, we can have different arrangements of ligands. The two types of isomers we will consider are:
- **Cis Isomers:** where similar ligands are adjacent to each other.
- **Trans Isomers:** where similar ligands are opposite each other.

For the complex \([Cr(en)_2Cl_2]^+\), the arrangement can be either cis or trans.

**Hint:** Identify the arrangements of the ligands to classify the isomers.

### Step 3: Analyze Optical Isomerism
Optical isomers (or enantiomers) are non-superimposable mirror images of each other. In this case:
- The **cis** isomer can have optical isomers because it can form two non-superimposable mirror images.
- The **trans** isomer does not have optical isomers because it is superimposable on its mirror image.

**Hint:** Remember that only non-superimposable structures can be considered optical isomers.

### Step 4: Count the Optical Isomers
Since the cis form can produce two optical isomers (enantiomers), and the trans form does not contribute any optical isomers, we conclude:
- Total optical isomers = 2 (from the cis form).

**Hint:** Count the number of optical isomers from the arrangements you have identified.

### Final Answer
The possible number of optical isomers in \([Cr(en)_2Cl_2]^+\) is **2**.