Use collision theory to estimate the Arrhenius pre$-$exponential factor in $d{m}^{3}mo{l}^{-1}{s}^{-1}$ for the reaction $,H_2(g)+C_2{H}_4(g)C_2{H}_6(g),$ at $620K,$ given that ${}_A=0\mathrm{.}28n\frac{m^2}{m}$olecule and of $H=1\mathrm{.}01\frac{g}{m}ol$;$MM$ of $C=12\mathrm{.}01\frac{g}{m}ol$ and $\frac{1}{4}(\sqrt[\phantom{2}]{{}_A}+\sqrt[\phantom{2}]{}B{)}^2.$ Show all steps of calculations and unit cancellations done in reaching the final answer with unit.

$[10$ marks$]$