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Assertion: Reaction between $(M{e_3}CONa)$(sodium tert-butoxide) and ethyl iodide $({C_2}{H_5}I)$ does not produce an ether.
Reason: Sodium tert-butoxide is a very strong base but is a poor nucleophile.
A.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B.) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C.) Assertion is correct but Reason is incorrect.
D.) Assertion is incorrect but Reasons are correct.

Answer
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Hint: To solve this question we need to know that when sodium alkoxide reacts with alkyl halide then generally ether is formed according to Williamson ether synthesis but when the alkyl group attached alkyl halide is more steric hindered then elimination takes place.

Complete step by step answer:
We know that general Williamson synthesis reaction can be shown as below:
$R - X + NaO - R' \to R - O - R'$
Here, when alkyl halide reacts with sodium alkoxide then ether is formed. As in question, when sodium tert-butoxide reacts with ethyl iodide then sodium of the alkoxide group reacts with iodide of alkyl halide and ether is formed. This reaction can be shown as :
${C_2}{H_5}I + Na - OC{(C{H_3})_3} \to {C_2}{H_5} - O - {(C{H_3})_3} + NaI$
As we can see that in this reaction ether is formed in the product.
Hence, the assertion is incorrect.
Also, Sodium tert-butoxide is a strong base because there is an inductive effect of three electron donating groups due to which the more negative charge accumulates at oxygen and thus it can easily attract any ${H^ + }$ ion. Thus, it is a strong base.
Also, it is a weak nucleophile. A nucleophile is that species which can easily donate an electron pair to form a chemical bond but due to steric hindrance in sodium tert-butoxide which is due to three methyl groups , sodium tert-butoxide does not donate an electron pair easily to any species. Hence, Sodium tert-butoxide is a weak nucleophile and a strong base.

Note:
We need to remember that in Williamson ether synthesis reaction, ether is only formed when the alkyl group of alkyl halide is less hindered otherwise elimination takes place but the alkyl group of sodium alkoxide does not affect the reaction.