Correct decreasing order of reactivity of the above halogen compounds towards ${\mathrm{S}}_{\mathrm{N}}2$ reactions is

Rate of reactivity towards ${\mathrm{SN}}_2\propto \frac{1}{\mathrm{steric} \mathrm{hindrance}}$

$\therefore 1^{\mathrm{o}}\mathrm{RX}>2^{\mathrm{o}}\mathrm{RX}>3^{\mathrm{o}}\mathrm{RX}$;

Steric hindrance in n-butyl bromide < isobutyl bromide < sec.butyl bromide < tert.butyl bromide

$\therefore$ reactivity towards ${\mathrm{SN}}_2$ will be.. I > II > III > IV.