Step 1: Identifying the given alkene
The molecular formula of the alkene is \( C_4H_8 \). Since it does not exhibit cis-trans isomerism, it must be a symmetrical alkene where free rotation is possible. The most likely candidate is 2-methylpropene (isobutene):
\[
CH_2 = C(CH_3)CH_3
\]
Step 2: Reaction with Bromine in UV light
- When an alkene reacts with \( Br_2 \) in the presence of UV light, a radical substitution reaction occurs instead of the usual electrophilic addition.
- The allylic hydrogen (hydrogen on the carbon next to the double bond) is replaced by bromine due to radical stability.
- In isobutene, the most stable radical forms at the allylic position, leading to the formation of 3-Bromo-2-methylpropene as the major product.
Step 3: Examining the given options
- Option 1: Incorrect, as it shows a different bromo-derivative that is unlikely in radical bromination.
- Option 2: Incorrect, as it shows an extended conjugated system that does not form under these conditions.
- Option 3: Correct, as it represents 3-Bromo-2-methylpropene, the expected product.
- Option 4: Incorrect, as it depicts an incorrect bromination position.
Step 4: Conclusion
Since 3-Bromo-2-methylpropene is the correct major product, the answer is Option (3).