Step 1: Understanding the Chemical Structure.
The given question is about identifying the correct chemical structure based on the provided options. The correct chemical structure involves identifying the placement of halogens and the correct positioning of double bonds.
Step 2: Analyzing the Options.
- (A) \( 1-\text{Bromo}-2-\text{chloro}-3-\text{butene}-4-yl \) is incorrect due to the placement of the halogens and the incorrect numbering.
- (B) \( 2-\text{Bromo}-2-\text{chloro}-3-\text{butene}-5-yl \) is correct as it fits the structure described in the problem, with the correct positions of the halogens and alkene.
- (C) \( 1-\text{Chloro}-2-\text{bromo}-3-\text{butene}-4-yl \) is incorrect, as it does not align with the given structure.
- (D) \( 2-\text{Bromo}-1-\text{chloro}-3-\text{butene}-5-yl \) is incorrect as well due to wrong placement of halogens.
Step 3: Conclusion.
The correct answer is (B) \( 2-\text{Bromo}-2-\text{chloro}-3-\text{butene}-5-yl \) as it matches the structure described in the problem.