During the race to develop the atomic bomb in World War II, it was necessary to separate a lighter isotope of uranium (U-235 was the fissionable one needed for bomb material) from a heavier variety (U-238). The uranium was converted into a gas, uranium hexafluoride (UF6), and the two uranium isotopes were separated by gaseous diffusion using 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.