Step 1: Understanding the Concept:
Gabriel phthalimide synthesis converts an alkyl halide into a primary amine through N-alkylphthalimide, followed by hydrolysis.
Step 2: Limits of the Method:
Aryl halides do not undergo nucleophilic substitution by phthalimide anion, so aromatic primary amines like aniline cannot be made this way. Also, only primary aliphatic amines can result, not secondary or tertiary.
Step 3: Check the Options:
(A) Aniline: aromatic amine, not possible.
(B) Ethylamine: primary aliphatic amine, possible from ethyl halide.
(C) Dimethylamine: secondary amine, not possible.
(D) \(\text{C}_2\text{H}_5\text{N}(\text{CH}_3)_2\): tertiary amine, not possible.
Step 4: Conclusion:
Only ethylamine can be prepared, so (B) is correct.
Final Answer:
Gabriel synthesis gives ethylamine, option (B).
\[ \boxed{\text{(B) } \text{C}_2\text{H}_5\text{NH}_2} \]