How many isomeric halogen derivatives including stereoisomers are possible for `C_(2)H_(2)Br_(2)` ?

Options

A. 2
B. 3
C. 4
D. 5

Answer

To determine the number of isomeric halogen derivatives, including stereoisomers, for the compound \( C_2H_2Br_2 \), we can follow these steps:

### Step 1: Identify the Structure
The molecular formula \( C_2H_2Br_2 \) suggests that the compound has two carbon atoms, two hydrogen atoms, and two bromine atoms. Given that there are two carbon atoms, we can assume that there is a double bond between them, similar to ethene (\( C_2H_4 \)).

**Hint:** Consider the general structure of alkenes when dealing with \( C_2H_2Br_2 \).

### Step 2: Draw the Basic Structure
The basic structure can be represented as follows:
\[ C=C \]
With two bromine atoms and two hydrogen atoms to be arranged around the double bond.

**Hint:** Visualize the double bond and how substituents can be arranged around it.

### Step 3: Identify Possible Isomers
1. **Identify the first isomer**: Both bromine atoms can be on one carbon atom, and both hydrogen atoms on the other carbon atom:
- Structure: \( Br-Br \) on one carbon and \( H-H \) on the other carbon.

2. **Identify the second isomer (Cis)**: Both bromine atoms can be on the same side of the double bond:
- Structure: \( C=C \) with \( Br \) and \( Br \) on one side and \( H \) and \( H \) on the other side (cis configuration).

3. **Identify the third isomer (Trans)**: The bromine atoms can be on opposite sides of the double bond:
- Structure: \( C=C \) with \( Br \) on one carbon and \( H \) on the other carbon, and vice versa (trans configuration).

**Hint:** Remember that the presence of a double bond allows for cis and trans isomerism.

### Step 4: Count the Isomers
- The first isomer is the one with both bromines on one carbon and both hydrogens on the other.
- The second isomer is the cis isomer.
- The third isomer is the trans isomer.

Thus, we have three distinct isomers:
1. \( Br-Br \) on one carbon, \( H-H \) on the other.
2. Cis isomer.
3. Trans isomer.

**Hint:** Ensure that you do not double count any isomers that are identical in structure.

### Conclusion
In total, there are **3 isomeric halogen derivatives**, including stereoisomers, for \( C_2H_2Br_2 \).

**Final Answer:** The correct option is **B (3)**.