A high vacuum apparatus is to be designed so that electrons accelerated at one end of chamber cross through the chamber unimpeded before being collected at the other side. Make an estimate of the maximum allowable pressure in a $31\mathrm{.}7-$cm$-$long chamber if $97\mathrm{.}2$ percent of all electrons must cross the chamber without first striking an air molecule. The temperature in the chamber is $300$ K$,$ and you should take the diameter of air molecules to be $3\backslash$times $10^-10$ m$.$