Step 1: Understanding the reaction.
The reaction of alkyl halides with sodium metal in dry ether is a Wurtz reaction. This reaction leads to the formation of alkanes by the coupling of two alkyl radicals. For 2,5-dimethylhexane to form, the reactant must have the correct structure. Isobutyl bromide (\(C_4H_9Br\)) leads to the formation of 2,5-dimethylhexane upon undergoing the Wurtz reaction.
Step 2: Analyzing the options.
(A) tert-butyl bromide: Incorrect. The reaction of tert-butyl bromide would produce a highly branched alkane, not 2,5-dimethylhexane.
(B) sec-butyl bromide: Incorrect. sec-Butyl bromide would lead to a different alkane, not 2,5-dimethylhexane.
(C) n-butyl bromide: Incorrect. n-Butyl bromide would not give the desired dimethyl-substituted product.
(D) isobutyl bromide: Correct — Isobutyl bromide produces 2,5-dimethylhexane via the Wurtz reaction.
Step 3: Conclusion.
The correct answer is (D) isobutyl bromide, which gives 2,5-dimethylhexane on reaction with sodium in dry ether.