59. IE ••• During the race to develop the atomic bomb in World War II, it was necessary to separate the lighter

“fissionable” isotope of uranium (U-235) from the more massive “non-fissionable” isotope (U-238). The uranium was first converted into a gas, uranium hexafluoride

(UF6), and the two uranium isotopes were separated by a process called gaseous diffusion which relied on the difference in their rms speeds.

(a) As a two-component molecular mixture at room temperature, which of the two types of molecules would be moving faster, on average: (1) 235UF6 or (2) 238UF6. Or (3) would they move equally fast? Explain.

(b) Determine the ratio of their rms speeds, light molecule to heavy molecule. Treat the molecules as ideal gases and neglect rotations and/

or vibrations of the molecules. The masses of the three atoms in atomic mass units are 238 and 235 for the two uranium isotopes and 19 for fluorine.