Arrange the compounds of each set in order of reactivity towards `S_(N)2` displacement:
(i) 2-Bromo-2-methylbutane, 1-Bromopentane, 2-Bromopentane
(ii) 1-Bromo-3-methylbutane, 2-Bromo-2-methylbutane, 2-Bromo-3-methylbutane
(iii) 1-Bromobutane, 1-Bromo-2,2-dimethylpropane, 1-Bromo-2-methylbutane, 1-Bromo-3-methylbutane.

Explanation

The reactivity in `S_(N)2` reaction depends upon sterie hindrance. Lesser the sterie hindranice more the reactivity. Therefore, the reactivity of different alkyl halides towards `S_(N)2` reactions is `1^(@) gt 2^(@) gt 3^(@)`.
(a) `underset(underset((1^(@)))("1-Bromopentane"))(CH_(3)CH_(2)CH_(2)CH_(2)CH_(2)Br) gt underset(underset((2^(@)))("2-Bromopentane"))(CH_(3)CH_(2)CH_(2)underset(Br)underset(|)CHCH_(3)) gt underset(underset((3^(@)))("2-Bromo-2-methylbutane"))(CH_(3)-underset(Br)underset(|)overset(CH_(3))overset(|)C-CH_(2)CH_(3))`
(b) `underset(underset((1^(@)))("1-Bromo-3-methylbutane"))(overset(4)CH_(3)-underset(CH_(3))underset(|)overset(3)CH-overset(2)CH_(2)overset(1)CH_(2)Br)` `underset(underset((3^(@)))("2-Bromo-2-methylbutane"))(overset(1)CH_(3)-underset(Br)underset(|)overset(CH_(3))overset(2|)C-overset(3)CH_(2)overset(4)CH_(3))` `underset(underset((2^(@)))("2-Bromo-3-methylbutane"))(CH_(3)-overset(Br)overset(|)CH-overset(CH_(3))overset(|)CH-CH_(3))`
So, the order of reactivity is
`"1-Bromo-3-methylbutane"egt "2-Bromo-3-methylbutane" gt "2-Bromo-2-methylbutane"`
(c) `underset(underset((1^(@)"with no branching"))("1-Bromobutane"))(CH_(3)CH_(2)CH_(2)CH_(2)Br)` `underset(underset((1^(@)" with two branching at" beta "positions"))("1-Bromo-2,2-dimethyl propane"))(overset(3)CH_(3)-underset(CH_(3))underset(|) overset(CH_(3))overset(2|)C-overset(1)CH_(2)Br)` `underset(underset((1^(@)" with one branch at" beta "positions"))("1-Bromo-2-methyl butane"))(overset(4)CH_(3)overset(3)CH_(2)underset(CH_(3))underset(|)overset(2)CH overset(1)CH_(2)Br)`
`underset(underset((1^(@)" with one branching at" gamma "positions"))("1-Bromo-3-methyl butane"))(overset(4)CH_(2)-underset(CH_(3))underset(|)overset(3)CH-overset(2)CH_(2)-overset(1)CH_(2)-Br)`
Thus, reactivity decreases with stenie hindrance as :
`"1-Bromobutane" gt "1-Bromo-3-methylbutane" gt "1-Bromo-2-methylbutane" gt "1-Bromo-2,2-dimethylpropane"`