The number of isomers for the compounds with molecular formula `C_(2)BrClFI` is:

Options

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

Explanation

To determine the number of isomers for the compound with the molecular formula C₂BrClFI, we can follow these steps:

### Step 1: Identify the structure
The molecular formula C₂BrClFI indicates that we have a two-carbon compound (ethylene) where both hydrogen atoms are replaced by halogens (bromine, chlorine, fluorine, and iodine).

### Step 2: Consider the types of isomers
Isomers can be classified into two main categories: structural isomers and stereoisomers. In this case, we are primarily interested in stereoisomers, which arise from the different spatial arrangements of the halogen atoms around the carbon-carbon double bond.

### Step 3: Analyze the halogen arrangements
Since we have four different halogens (Br, Cl, F, I), we can arrange them in different ways around the double bond.

1. **Cis and Trans Isomers**: For each pair of halogens, we can have cis (same side) and trans (opposite side) configurations.

### Step 4: Generate the isomers
1. **First Isomer**: Place Br and Cl on one carbon and F and I on the other carbon (Cis).
2. **Second Isomer**: Place Br and Cl on one carbon and F and I on the other carbon (Trans).
3. **Third Isomer**: Swap F and I with Br and Cl (Cis).
4. **Fourth Isomer**: Swap F and I with Br and Cl (Trans).
5. **Fifth Isomer**: Consider F and I on one carbon and Br and Cl on the other carbon (Cis).
6. **Sixth Isomer**: Consider F and I on one carbon and Br and Cl on the other carbon (Trans).

### Step 5: Count the total isomers
After considering all possible arrangements, we find that there are a total of **6 distinct isomers** for the compound C₂BrClFI.

### Conclusion
Thus, the number of isomers for the compound with the molecular formula C₂BrClFI is **6**.