Step 1: Understanding the Reaction.
Methoxy ethane (C\(_2\)H\(_5\)OCH\(_3\)) reacts with hot concentrated HI (hydriodic acid) to give iodides. In this reaction, the ether bond is cleaved to form iodomethane (CH\(_3\)I) and iodoethane (C\(_2\)H\(_5\)I).
Step 2: Analyzing the options.
(A) iodomethane and ethanol: Incorrect. Ethanol is not formed in this reaction.
(B) iodomethane and iodoethane: Correct. The reaction produces iodomethane and iodoethane.
(C) methanol and ethanol: Incorrect. Methanol and ethanol are not formed in this reaction.
(D) methanol and iodoethane: Incorrect. Methanol is not part of the product.
Step 3: Conclusion.
The correct products of the reaction are iodomethane and iodoethane, which corresponds to option (B).