The number of optical isomers of the compound `CH_(3)CHBrCHBrCOOH` is

Options

A. 2
B. 4
C. 3
D. 1

Explanation

To determine the number of optical isomers of the compound \( CH_3CHBrCHBrCOOH \), we will follow these steps:

### Step 1: Identify the Structure
First, we need to draw the structure of the compound \( CH_3CHBrCHBrCOOH \). This compound consists of a four-carbon chain with two bromine atoms and a carboxylic acid group.

### Step 2: Identify Chiral Centers
Next, we need to identify the chiral centers in the molecule. A chiral center is a carbon atom that is attached to four different groups.

In the structure of \( CH_3CHBrCHBrCOOH \):
- The second carbon (attached to \( CH_3 \), \( Br \), \( CHBr \), and \( COOH \)) is a chiral center.
- The third carbon (attached to \( Br \), \( CH_3 \), \( COOH \), and the adjacent carbon) is also a chiral center.

### Step 3: Count the Chiral Centers
We have identified **2 chiral centers** in the compound.

### Step 4: Calculate the Number of Optical Isomers
The number of optical isomers can be calculated using the formula:
\[ \text{Number of optical isomers} = 2^n \]
where \( n \) is the number of chiral centers.

Substituting \( n = 2 \):
\[ \text{Number of optical isomers} = 2^2 = 4 \]

### Step 5: Identify the Isomers
The four optical isomers consist of two pairs of enantiomers:
1. The first pair of enantiomers (let's call them Isomer 1 and Isomer 2).
2. The second pair of enantiomers (let's call them Isomer 3 and Isomer 4).

Each pair consists of structures that are mirror images of each other and are not superimposable.

### Conclusion
Thus, the total number of optical isomers for the compound \( CH_3CHBrCHBrCOOH \) is **4**.

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