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The reaction is an example of:
\[C{{H}_{4}}+C{{l}_{2}}\xrightarrow{hv}C{{H}_{3}}Cl+HCl\]
A. a free radical substitution reaction
B. an electrophilic substitution reaction
C. a nucleophilic substitution reaction
D. a nucleophilic addition reaction

Answer
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Hint: Substitution reaction is a chemical reaction in which a functional group is replaced by another functional group. This reaction is also called a displacement reaction. The example of substitution of substitution reaction is the halogenation process which we are going to study in this question. In addition to reaction, two or more molecules are combined together to form a larger molecule.

Complete step by step answer:
Let us first understand all the four types of reactions which are given in the options:
In free radical substitution reaction, free radical acts as a reactive intermediate in a substitution reaction. Free radical substitution reaction involves three steps that are as follows:
1.Initiation
2.Propagation
3.Termination
An electrophilic substitution reaction is defined as a chemical reaction in which a functional group is displaced by an electrophile. Electrophile is defined as a species that has the ability to accept electron pairs when it forms a bond with a nucleophile.
A nucleophilic substitution reaction is defined as a chemical reaction in which an electron rich compound replaces a leaving group. Hydrolysis is a common example of nucleophilic substitution reaction.
In nucleophilic addition reaction, an electrophilic double or triple bond reacts with a nucleophile in such a way that the double bond or triple bond is broken.

Here, the reaction is given as follows:
$C{{H}_{4}}+C{{l}_{2}}\xrightarrow{hv}C{{H}_{3}}Cl+HCl$
The above reaction is a chlorination reaction in which hydrogen is substituted by a chlorine atom. This reaction is an example of free radical substitution reaction. In free radical substitution reaction, free radical acts as a reactive intermediate in a substitution reaction. Free radical substitution reaction involves three steps that are as follows:
1.Initiation: In this step, homolytic cleavage of chlorine molecule takes place that results in the formation of two chlorine atoms in the presence of ultraviolet radiation. These chlorine atoms act as a free radical and they have one unpaired electron.
2.Propagation: In a methane molecule, hydrogen atom is removed leaving a primary methyl radical. This primary radical then pulls a chlorine radical.
3.Termination: After that, a combination of two free radicals takes place.
Hence, we get the net reaction as follows:
\[C{{H}_{4}}+C{{l}_{2}}\xrightarrow{hv}C{{H}_{3}}Cl+HCl\]

So, the correct answer is Option A .

Note: In methane, there are equivalent hydrogen atoms, and therefore have an equal chance of being replaced.
The reactivity of alkane with halogen: the reactivity of alkane with fluorine is very difficult to control. The reactivity of alkane with chlorine is moderate to fast and the reactivity of alkane with bromine is very slow.