(a) Determine the number of impacts made by gas molecules on a unit area of the wall in a unit time for which the angle of incidence lies between \(\theta\) and \(\theta+d \theta\).

(b) Determine the number of impacts made by gas molecules on a unit area of the wall in a unit time for which the speed of the molecules lies between \(u\) and \(u+d u\).

(c) A molecule \(A B\) dissociates if it hits the surface of a solid catalyst with a normal translational energy greater than \(10^{-19} \mathrm{~J}\). Show that the rate of the dissociative reaction \(A B ightarrow A+B\) is more than doubled by raising the temperature of the gas from \(300 \mathrm{~K}\) to \(310 \mathrm{~K}\).