2.2 Exercise 25

In the problems in this section, assume all gases are ideal.

There are two important isotopes of uranium, $^{235} \text{U}$ and $^{238} \text{U}$; these isotopes are nearly identical chemically but have different atomic masses. Only $^{235} \text{U}$ is very useful in nuclear reactors. Separating the isotopes is called uranium enrichment (and is often in the news as of this writing, because of concerns that some countries are enriching uranium with the goal of making nuclear weapons.) One of the techniques for enrichment, gas diffusion, is based on the different molecular speeds of uranium hexafluoride gas, $\text{UF}_{6}$. (a) The molar masses of $^{235} \text{U}$ and $^{238} \text{UF}_{6}$ are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their typical speeds $v_{\text{rms}}$? (b) At what temperature would their typical speeds differ by 1.00 m/s? (c) Do your answers in this problem imply that this technique may be difficult?