Final answer:
The correct structure of the free-radical intermediate in the peroxide-initiated reaction of H-Br likely involves a primary or secondary alkyl radical depending on the substrate; however, without specific context, it is difficult to determine which of the provided options is correct.
Step-by-step explanation:
The structure of the free-radical intermediates in the peroxide-initiated reaction of H-Br typically includes an alkyl radical that forms when a hydrogen atom is abstracted from an alkane molecule by a free radical species. If we look at the options given, structure (a) (CH3)2CH represents a secondary free radical intermediate that would form from isopropane. Structure (b) CH3CH2 represents a primary free radical that would form by abstraction of a hydrogen atom from ethane. Structure (c) (CH3)2CBr does not represent a free radical but rather a halogenated compound, as indicated by the Br atom. Lastly, structure (d) H2C=CH-Br represents a brominated alkenyl compound rather than a free-radical intermediate.
The most likely free-radical intermediate in the peroxide-initiated reaction would be structure (b) CH3CH2, as this is a typical primary radical formed during the propagation steps of a free radical mechanism. However, without more information about the substrate involved in the reaction, it's difficult to definitively specify which option is the correct free-radical intermediate in the actual reaction taking place.