Williamson's synthesis for preparing dimethyl ether involves

$S_N2$ mechanism

The correct answer is Option (3) → $S_N2$ mechanism

Core Concept

Williamson ether synthesis proceeds through a nucleophilic substitution reaction involving backside attack, characteristic of the SN2 mechanism.

$CH_3ONa+ CH_3I → CH_3OCH_3 + NaI$

Detailed Explanation

Option 1: SN1 mechanism

SN1 involves formation of a carbocation intermediate, which is not favored in the case of methyl halides used for dimethyl ether formation. Williamson synthesis does not proceed via carbocation formation.

Option 2: Elimination reaction

Elimination leads to formation of alkenes, not ethers. Williamson synthesis forms ethers through substitution rather than removal of atoms to form double bonds.

Option 3: SN2 mechanism

In Williamson synthesis, methoxide ion attacks methyl halide via backside attack in a single step. This bimolecular nucleophilic substitution results in formation of dimethyl ether.

Option 4: Nucleophilic addition reaction

Nucleophilic addition occurs typically in carbonyl compounds, not in alkyl halides. Williamson ether synthesis is not an addition reaction.