Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 41

A hydrogen molecule (diameter \(1.0 \times 10^{-8} \text{ cm}\)), traveling at the rms speed, escapes from a \(4000 \text{ K}\) furnace into a chamber containing cold argon atoms (diameter \(3.0 \times 10^{-8} \text{ cm}\)) at a density of \(4.0 \times 10^{19} \text{ atoms/cm}^3\). (a) What is the speed of the hydrogen molecule? (b) If it collides with an argon atom, what is the closest their centers can be, considering each as spherical? (c) What is the initial number of collisions per second experienced by the hydrogen molecule? (Hint: Assume that the argon atoms are stationary. Then the mean free path of the hydrogen molecule is given by Eq. 19.5.2 and not Eq. 19.5.1.)