- Baeyer's test uses dilute alkaline potassium permanganate (KMnO\(_4\)), which is purple in color.
- Alkenes react with Baeyer's reagent causing the purple color to disappear (decolorize) due to oxidation of the double bond.
- Alkanes do not react with Baeyer's reagent, so the purple color remains.
- Fehling's and Benedict's solutions are used for detecting aldehydes, not alkenes or alkanes.
- Sodium metal reacts with water and alcohols but cannot distinguish between alkenes and alkanes.
Answer: \(\boxed{\text{B}}\)
