The total number of optically active alkynes having molecular formula `C_(3)FClBrI` is

Options

A. 2
B. 4
C. 6
D. 8

Explanation

To determine the total number of optically active alkynes with the molecular formula \(C_3FClBrI\), we need to analyze the structure and identify the chiral centers in the alkynes.

### Step 1: Identify the structure of the alkyne
The general structure of an alkyne is represented as \(C \equiv C\) (a triple bond between two carbon atoms) followed by another carbon atom. Thus, we can represent the alkynes as follows:
- \(C \equiv C - C\)

### Step 2: Identify possible arrangements of substituents
The molecular formula \(C_3FClBrI\) indicates that we have three carbon atoms and four different halogen substituents (F, Cl, Br, I). In order to have optically active compounds, we need to have at least one chiral carbon atom.

### Step 3: Determine chiral centers
A carbon atom is chiral if it is bonded to four different substituents. In our case, we can have the following arrangements:

1. **Chiral center on the terminal carbon**:
- Structure: \(F, Cl, Br, C\) (where C is the carbon of the alkyne)
- This configuration gives rise to 2 optically active isomers.

2. **Chiral center on the middle carbon**:
- Structure: \(C, F, Cl, Br\) (where C is the carbon of the alkyne)
- This configuration also gives rise to 2 optically active isomers.

### Step 4: Consider different combinations
We can also consider different combinations of the halogens on the terminal carbon and the middle carbon:

- **Combination 1**: \(C \equiv C - C(F, Cl, Br)\)
- **Combination 2**: \(C \equiv C - C(F, Cl, I)\)
- **Combination 3**: \(C \equiv C - C(Cl, Br, I)\)
- **Combination 4**: \(C \equiv C - C(F, Br, I)\)

Each of these combinations can yield 2 optically active isomers.

### Step 5: Calculate total optically active isomers
Since we can have 2 optically active isomers for each of the 4 combinations, the total number of optically active alkynes is:
\[ 2 + 2 + 2 + 2 = 8 \]

### Conclusion
The total number of optically active alkynes with the molecular formula \(C_3FClBrI\) is **8**.

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