Past exam of the physics B course of the University of Cambridge / 2016 / Paper 2 / Section C / C12 / a / Solution

The collision flux contains an extra normal velocity $v\cos \theta$: a faster atom sweeps out a longer approach cylinder per unit time. Integrating the Maxwell-Boltzmann distribution over the incoming hemisphere givesThereforeHere $J$ is the number striking unit area per unit time and $\overline{v}=\sqrt{8k_{B}T/(\pi m)}$ is the bulk mean speed. A simple factor of one half would count the incoming hemisphere but miss the projection factor and velocity weighting.