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$ C{H_3}C{H_2}C{H_2}Br\xrightarrow[{C{H_3}OH}]{{C{H_3}ONa}} $

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Hint: Alexander Williamson prepared diethyl by a simple method now known as Williamson’s ether synthesis. is an important method for the synthesis of symmetrical and unsymmetrical ethers. In this method alkyl halide is allowed to react with sodium alkoxide.

Complete answer:
This is an example of Nucleophilic substitution reaction as the reaction involves SN2 attack of an alkoxide ion on primary alkyl halide. The halide used should preferably be primary because secondary and tertiary alkyl halide may form alkenes as major products due to the elimination process.
 We take alkyl halide and react with the $ N{a^ + }{O^ - }C{H_3} $ . We get this in ionic form.
Now this group goes and reacts with bromopropane. The bromine is less nucleophilic than the $ {O^ - }C{H_3} $ group. Hence it replaces the bromine.
 $ C{H_3}C{H_2}C{H_2}Br\xrightarrow[{C{H_3}OH}]{{NaOC{H_3}}}C{H_3}C{H_2}C{H_2}OC{H_3} $
This is Nucleophilic substitution reaction as the reaction involves SN2 attack of an alkoxide ion on primary alkyl halide.
Aryl ethers or phenolic ethers can be prepared by using sodium phenoxides and alkyl halides. However, aryl halides and sodium alkoxide cannot be used for preparing phenolic ethers because aryl halides are less reactive towards nucleophilic substitution reaction.

Note:
The nucleophile attacks the alkyl forming an ether from back. This response takes plane in one single step. It occurs both, the cleavage and bond formation. Its halides are sterically impeded then alkoxide acts as a basis and protons in place are accessible. The products derived from a response to elimination.