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Given reaction $NaOH\, + \,{D_2}O\, \to \,NaOD\, + \,HDO\,$ is a;
(A) exchange reaction
(B) deuterolysis reaction
(C) hydrolysis reaction
(D) softening reaction

Answer
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Hint:Heavy water is known as deuterium oxide. Its chemical formula is ${D_2}O$. When $NaOH$ also known as Sodium Hydroxide reacts with ${D_2}O$ it gives sodium deuteroxide and semi-heavy water or $HDO$. This reaction is exergonic.

Complete step by step answer:
The molar mass of ${D_2}O$ is much greater than regular water \[{{ }}{H_2}O\] because the atomic mass of deuterium is greater than protium. This results in heavy water ${D_2}O$ to have slightly different chemical and physical properties than \[{{ }}{H_2}O\] .
At STP ${D_2}O$ is colourless in appearance and an odourless liquid at room temperature. As the density of ${D_2}O$ is \[11\% \] more than\[{{ }}{H_2}O\].An ice cube made of ${D_2}O$ will sink in normal water. When ${D_2}O$ is mixed with \[{{ }}{H_2}O\] it forms a homogeneous mixture.
The reaction of sodium hydroxide with heavy water is an example of an exchange reaction. In an Exchange reaction, decomposition and product formation both occur simultaneously. An exchange reaction will occur when ions in solution form insoluble products, weak electrolytes, or nonelectrolytes.
In Exchange reactions, both cations and anions that were present in the reactants are interchanged in the products. In these reactions, the electrically neutral of the product should be maintained. By this, the products can easily be predicted
Sodium hydroxide breaks into $N{a^ + }$ and $O{H^ - }$ ions and react bond with the cation and anion of ${D_2}O$ that are $O{D^ - }$ and ${D^ + }$ to form $NaOD$ and $HDO$.

Hence, Option (A) is correct.

Note:
Heavy water is used in the preparation of Deuterium, in NMR (nuclear magnetic resonance) spectroscopy, which is used to observe the magnetic fields around the nuclei of atoms. It is also used as a moderator in nuclear reactors.