In the reaction, $\mathrm{R}-\mathrm{Br}+\mathrm{Cl}\to \mathrm{R}-\mathrm{Cl}+\mathrm{Br}$, the rates of ${\mathrm{SN}}_2$, 

reaction of ethyl bromide (I),  n-propyl bromide (II),   isobutyl bromide (III) and neopentyl bromide (IV)  follow the order:

In organic chemistry, the ${\mathrm{SN}}_2$ reaction is an example of a typical reaction mechanism. This mechanism involves the simultaneous, or sequential, formation of one bond and the breaking of another. The name of the mechanism, which refers to its Hughes-Ingold symbol, is ${\mathrm{SN}}_2$, a type of nucleophilic substitution reaction mechanism.

Hence,the correct option  (B). I > II > III > IV