Arrange the compounds of each set in order of reactivity towards $S_N2$ displacement: $2-$Bromo$-2-$methylbutane, $1-$Bromopentane, $2-$Bromopentane.
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$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{Br}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{Br}\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\\\text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_2\text{CH}_2-\text{Br}\ \ \ \ \ \ \ \text{CH}_3\text{CH}_2\text{CH}_2\text{CH}\text{CH}_3\ \ \ \ \ \ \ \text{CH}_3\text{CH}_2\text{C}\text{CH}_3\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{CH}_3\\ 1-\text{Bromopentane}(1^\circ)\ \ \ \ \ \ \ \ \ \ \ \ \ \ 2-\text{Bromopentane}(2^\circ)\ \ \ \ \ \ \ 2-\text{Bromo}-2-\text{methylbutan}(3^\circ)$
An $S_N2$ reaction involves the approaching of the nucleophile to the carbon atom to which the leaving group is attached. When the nucleophile is sterically hindered, then the reactivity towards $S_N2$ displacement decreases.
Due to the presence of substituents, hindrance to the approaching nucleophile increases in the following order.
$1-$Bromopentane $< 2-$bromopentane $< 2-$Bromo$-2-$methylbutane
Hence, the increasing order of reactivity towards $S_N2$ displacement is:
$2-$Bromo$-2-$methylbutane $< 2-$Bromopentane $< 1-$Bromopentane.
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