Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 85

Uranium diffusion. To enhance the effectiveness of the nuclear fission of uranium, the highly fissionable U-235 isotope must be separated from the less readily fissionable U-238 isotope. One way to do this is to form the uranium into a gas ($\text{UF}_6$) and allow it to diffuse repeatedly through a porous barrier (up 4000 times). The lighter molecule will diffuse faster, the effectiveness of the barrier being determined by a separation factor $\alpha$, defined as the ratio of the two rms speeds. What is the separation factor for the two kinds of uranium hexafluoride gas molecules?