Step 1: Understanding the Concept:
Williamson synthesis forms an ether by an \(\text{SN2}\) reaction of an alkoxide with a primary alkyl halide: \(\text{R-ONa} + \text{R'-X} \rightarrow \text{R-O-R'} + \text{NaX}\).
Step 2: Check the options:
(A) \(\text{C}_2\text{H}_5\text{Br}\) is a primary alkyl halide, so it works.
(B) The structure shown is \((\text{CH}_3)_2\text{CH-CH}_2\text{Br}\), isobutyl bromide, a primary halide, so it works.
(C) \(\text{C}_6\text{H}_5\text{-Br}\) is bromobenzene. The C-Br bond has partial double bond character from resonance, and backside attack at an sp2 carbon is blocked by the ring, so SN2 cannot occur.
(D) \(\text{C}_6\text{H}_5\text{CH}_2\text{Br}\) is benzylic and reacts readily.
Final Answer:
Bromobenzene does not undergo Williamson's synthesis, option (C).
\[ \boxed{\text{C}_6\text{H}_5\text{Br}} \]