Step 1: Markovnikov's Rule
Markovnikov's rule states that in the electrophilic addition of HX to an unsymmetrical alkene, the hydrogen attaches to the carbon with more hydrogens, and the halogen to the carbon with fewer hydrogens, forming the more stable carbocation.
Step 2: Evaluate Options
Option (a): HBr to propene
Propene (\(CH_3-CH=CH_2\)) reacts with HBr:
\[ CH_3-CH=CH_2 + \text{HBr} \rightarrow CH_3-CHBr-CH_3 \]
H\(^+\) adds to the \(CH_2\) carbon (more hydrogens), and Br\(^-\) to the \(CH\) carbon, following Markovnikov's rule.
Result: Applicable.
Option (b): HBr to propene with peroxides
With peroxides, HBr addition to propene (\(CH_3-CH=CH_2\)) is free radical, yielding anti-Markovnikov product:
\[ CH_3-CH=CH_2 \rightarrow CH_3-CH_2-CH_2Br \]
Br adds to the \(CH_2\) carbon, opposite to Markovnikov's rule.
Result: Not applicable.
Option (c): Br\(_2\) to ethene
Ethene (\(CH_2=CH_2\)) is symmetrical, and Br\(_2\) addition forms:
\[ CH_2=CH_2 + \text{Br}_2 \rightarrow CH_2Br-CH_2Br \]
No regioselectivity is needed, so Markovnikov's rule does not apply.
Result: Not applicable.
Option (d): Hydroboration-oxidation
Hydroboration-oxidation of propene (\(CH_3-CH=CH_2\)) gives:
\[ CH_3-CH=CH_2 \xrightarrow{\text{BH}_3, \text{H}_2\text{O}_2, \text{OH}^-} CH_3-CH_2-CH_2OH \]
Boron adds to the less substituted carbon, yielding anti-Markovnikov addition.
Result: Not applicable.
Step 3: Final Answer
Only option (a) follows Markovnikov's rule.
\[ \boxed{\text{(a)}} \]