Step 1: Understanding the Question:
Methyl bromide (CH\(_3\)Br) and n-propyl bromide (CH\(_3\)CH\(_2\)CH\(_2\)Br) react with sodium metal in dry ether via the Wurtz reaction. We need the alkane that is not formed among the options.
Step 2: Key Formula or Approach:
Wurtz reaction: \(2R-X + 2Na \rightarrow R-R + 2NaX\). With a mixture of two different alkyl halides, three products are possible: the two symmetric coupling products and one cross-coupled product.
Step 3: Detailed Explanation:
- Coupling of two methyl radicals gives ethane (C\(_2\)H\(_6\)).
- Coupling of two n-propyl radicals gives hexane (C\(_6\)H\(_{14}\)).
- Cross-coupling of methyl and n-propyl gives butane (C\(_4\)H\(_{10}\)).
Propane (C\(_3\)H\(_8\)) would require coupling of methyl and ethyl radicals, but ethyl bromide is not present in the reaction mixture. Hence, propane is not formed.
Step 4: Final Answer:
The alkane NOT formed is propane, which corresponds to option (B).