Addition of `Br_(2)` to cis-2-butene would give a product which is:

Options

A. achiral
B. racemic
C. meso
D. Optically active

Explanation

To determine the product of the addition of Br₂ to cis-2-butene, we can follow these steps:

### Step 1: Understand the Structure of cis-2-butene
Cis-2-butene has the following structure:
- It consists of four carbon atoms (C) and has a double bond between the second and third carbon atoms.
- The two methyl (CH₃) groups are on the same side of the double bond, which is characteristic of the cis isomer.

### Step 2: Draw the Structure
The structure can be represented as:
```
CH3
|
CH3-C=C-H
|
H
```

### Step 3: Addition of Br₂
When Br₂ is added to alkenes, the reaction proceeds via an anti-addition mechanism. This means that the bromine atoms will add to opposite sides of the double bond.

### Step 4: Mechanism of Anti-Addition
1. The double bond attacks one of the bromine atoms, leading to the formation of a cyclic bromonium ion.
2. The other bromine atom will then attack from the opposite side, leading to the formation of a vicinal dibromide.

### Step 5: Determine the Product
For cis-2-butene, the anti-addition will lead to the formation of two different stereoisomers:
- One product will have bromine atoms added to the opposite sides of the double bond.

The resulting products will be:
- One product will have the configuration (2R,3S) and the other will have (2S,3R), which are enantiomers.

### Step 6: Identify the Nature of the Product
Since the product consists of two enantiomers, it is classified as a racemic mixture (a 1:1 mixture of two enantiomers), which is not optically active.

### Conclusion
The addition of Br₂ to cis-2-butene results in a racemic mixture of brominated products.

### Final Answer
The product is a **racemic mixture**.

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