Step 1: Examine the Structure of the Compound.
The structure of the compound shows a 4-carbon chain with a double bond at position 3, and several substituents attached to it. The substituents are a bromo group at position 4, an ethyl group at position 4, and a methyl group at position 3.
Step 2: Determine the Longest Carbon Chain.
The longest carbon chain contains 4 carbon atoms with a double bond at the 3rd position, which gives the base name as "but-3-ene." The number 3 indicates that the double bond starts at the 3rd carbon.
Step 3: Analyze the Substituents.
- The bromo group is attached to the 4th carbon.
- The ethyl group is also attached to the 4th carbon.
- The methyl group is attached to the 3rd carbon.
Step 4: Apply IUPAC Nomenclature Rules.
According to IUPAC rules, the substituents are listed in alphabetical order. The number indicating the position of the substituents is chosen to give the lowest possible number to the substituent closest to the beginning of the chain.
Step 5: Final Answer.
The correct IUPAC name for this compound is "4-Bromo-4-ethyl-3-methylbut-3-ene" which corresponds to option \((4)\).
Step 6: Verification.
After evaluating the structure and considering the IUPAC nomenclature, it is clear that the correct name is option \((4)\).