Randall D. Knight — The Micro/Macro Connection: Problem Problem_53

Uranium has two naturally occurring isotopes. $^{238}\text{U}$ has a natural abundance of $99.3\%$ and $^{235}\text{U}$ has an abundance of $0.7\%$. It is the rarer $^{235}\text{U}$ that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, $\text{UF}_6$, which is a gas, then allowing it to diffuse through a series of porous membranes. $^{235}\text{UF}_6$ has a slightly larger rms speed than $^{238}\text{UF}_6$ and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of $^{235}\text{UF}_6$ to that of $^{238}\text{UF}_6$?