statement I: Addition of `Br_(2)` to `1`-butene gives two optical isomers.
statement II: The product contains one asymmetric carbon atoms.

Options

A. Statement `I` is true, Statement `II` is true, Statement `II` is the correct explanation of Statement `I`.
B. Statement`I` is true, Statement`II` is true, Statement `II` is not the correct explanation of Statement `I`.
C. Statement `I` is true, Statement `II` is false.
D. Statement `I` is false, Statement `II` is true.

Explanation

To solve the question, we need to analyze both statements regarding the addition of \( \text{Br}_2 \) to 1-butene.

### Step 1: Understand the Reaction
1-butene is an alkene with the structure \( \text{CH}_2=\text{CH}-\text{CH}_2-\text{CH}_3 \). When \( \text{Br}_2 \) is added to 1-butene, the double bond reacts with bromine.

### Step 2: Draw the Reaction Mechanism
1. The \( \text{Br}_2 \) molecule approaches the double bond in 1-butene.
2. The pi electrons from the double bond attack one of the bromine atoms, leading to the formation of a cyclic bromonium ion intermediate.
3. The other bromine atom (now a bromide ion, \( \text{Br}^- \)) attacks the more substituted carbon of the bromonium ion.

### Step 3: Identify the Product
After the attack of \( \text{Br}^- \), we get a dibromide product:
- The product can be represented as \( \text{CH}_3-\text{CH}_2-\text{C}(\text{Br})-\text{CH}_2(\text{Br}) \).

### Step 4: Determine Chirality
In the product, the carbon atom that has the bromine attached becomes a chiral center because it is bonded to four different groups:
1. \( \text{Br} \)
2. \( \text{H} \)
3. \( \text{CH}_2\text{Br} \)
4. \( \text{CH}_3\text{CH}_2 \)

Since this carbon is attached to four different substituents, it is asymmetric (chiral).

### Step 5: Optical Isomers
A molecule with one chiral center can exist in two enantiomeric forms (optical isomers). Therefore, the addition of \( \text{Br}_2 \) to 1-butene will yield two optical isomers.

### Conclusion
- **Statement I**: True, because the addition of \( \text{Br}_2 \) to 1-butene results in two optical isomers.
- **Statement II**: True, because the product contains one asymmetric carbon atom.

Thus, both statements are true, and statement II correctly explains statement I.

### Final Answer
Both statements are true, and statement II is the correct explanation of statement I.

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