In Williamson's synthesis, ethoxy ethane is prepared by,
A.Heating sodium ethoxide with ethyl bromide
B.Passing ethanol over heated alumina
C.Treating ethyl alcohol with excess of conc. ${{H}_{2}}S{{O}_{4}}$ at 430 – 440 K
D.Heating ethanol with dry $A{{g}_{2}}O$

Hint: We know that Williamson's synthesis is one of the best methods for the preparation of both simple and mixed ethers. It’s a coupling reaction. The reaction was developed by Alexander William Williamson.

Complete answer:
We know that Williamson's synthesis is the reaction of alkyl halides with sodium alkoxide or sodium phenoxide to form ethers.
Let’s now see the chemical reaction in Williamson’s synthesis .
For example, For example, $R-X+R'-ONa\xrightarrow{\vartriangle }R-O-R'+NaX$
The Alkyl halide reacts with the sodium alkoxide in presence of heat to produce Ether and sodium halide as a byproduct.

$C{{H}_{3}}C{{H}_{2}}Br+C{{H}_{3}}C{{H}_{2}}ONa\xrightarrow{\vartriangle }C{{H}_{3}}C{{H}_{2}}-O-C{{H}_{2}}C{{H}_{3}}+NaBr$

At first, we get Sodium ethoxide ( $C{{H}_{3}}C{{H}_{2}}{{O}^{-}}N{{a}^{+}}$) by passing metallic $Na$ through Ethanol $(C{{H}_{3}}C{{H}_{2}}OH)$ . Then, Ethyl Bromide reacts with Sodium ethoxide to form Ethoxy ethane (IUPAC Name: Diethyl ether) via${{S}_{N}}^{2}$ reaction.

The correct option is A. Heating Sodium ethoxide with Ethyl bromide.

Note: Williamson’s synthesis is only possible in case of primary alkyl halide used in the chemical Williamson’s synthesis is only possible in case of primary alkyl halide used in the chemical reaction. If higher degree of alkyl halide is used i.e. Secondary alkyl halide and Tertiary alkyl halide then, the reaction will go through $E2$ type of reaction instead of ${{S}_{N}}^{2}$ Reaction and result in the formation of a Alkene in the product section.