Answer:
In \[{{S}_{N}}2\] reactions, reactivity depends upon the steric hindrance. (a) In 2-bromopentane, the \[\alpha \]-carbon atom attached to Br atom is further linked to two alkyl groups, i.e., methyl and n-propyl but in 1-bromopentane, it is attached to only one alkyl group, i.e., n-butyl group. Therefore, 2-bromopentane suffers greater steric hindrance to nucleophilic attack than 1-bromopentane and hence 1-bromopentane is more reactive than 2-bromopentane in \[{{S}_{N}}2\] reactions.
\[\begin{align} & \,\,\,\,C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}-\overset{\alpha }{\mathop{C}}\,\,\,{{H}_{2}}-Br \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{1-Bromopentane} \\ & \text{( }\!\!\alpha\!\!\text{ -carbon}\,\text{attached}\,\text{to}\,\text{one}\,\text{alkyl}\,\text{group,} \\ & \text{less}\,\text{steric}\,\text{hindrance}\,\text{to}\,\text{nucleophilic} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\text{attack,}\,\text{more}\,\text{reactive)} \\ \end{align}\] \[\begin{align} & \,\,\,\,C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{\overset{\alpha }{\mathop{C}}\,}}\,H-C{{H}_{3}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\text{-Bromopentane} \\ & \text{( }\!\!\alpha\!\!\text{ -carbon}\,\text{attached}\,\text{to}\,\text{two}\,\text{alkyl}\,\text{groups,} \\ & \text{more}\,\text{steric}\,\text{hindrance}\,\text{to}\,\text{nucleophilic} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\text{attack,}\,\text{less}\,\text{reactive)} \\ \end{align}\]
(b) In 1-bromo-2-methylbutane, \[\alpha \]-carbon is attached to one bulky sec. -butyl group while in 2-bromo-2-methylbutane, \[\alpha \]-carbon is attached to three alkyl groups, i.e., two methyl and one ethyl. Therefore, 2-bromo-2-methylbutane suffers greater steric hindrance to nucleophilic attack than 1-bromo-2-methylbutane, and hence 1-bromo-2-methylbutane is more reactive than-2-bromo-2-methylbutane.
\[\underset{\begin{smallmatrix} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{1-Bromo-2-methylbutane} \\ \text{( }\!\!\alpha\!\!\text{ -carbon}\,\text{attached}\,\text{to}\,\text{one}\,\text{alkyl}\,\text{group,}\,\text{less}\,\text{steric} \\ \text{hindrance}\,\text{to}\,\text{nucleophilic}\,\text{attack,}\,\text{more}\,\text{reactive)} \end{smallmatrix}}{\mathop{C{{H}_{3}}C{{H}_{2}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,H-\overset{\alpha }{\mathop{C}}\,{{H}_{2}}Br}}\,\] \[\underset{\begin{align} & \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\text{-Bromo-2-methylbutane} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{( }\!\!\alpha\!\!\text{ -carbon}\,\text{attached}\,\text{to}\,\text{three}\,\text{alkyl}\,\text{groups,}\,\text{more}\,\text{steric} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{hindrance}\,\text{to}\,\text{nucleophilic}\,\text{attack,}\,\text{less}\,\text{reactive)} \\ \end{align}}{\mathop{C{{H}_{3}}C{{H}_{2}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ \alpha | \end{smallmatrix}}{\mathop{\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{C}}\,}}\,-\overset{{}}{\mathop{C}}\,{{H}_{3}}}}\,\]
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