College Physics with MasteringPhysics 7th Edition by Jerry Wilson,Anthony Buffa,Bo Lou

Exercise 83

During the race to develop the atomic bomb in World War IT, 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 (UF 6 ), and the two uranium isotopes were separated by gaseous diffusion using the difference in their rms speeds. As a two-component molecular mixture at room temperature, which of the two types of molecules would be moving faster, on average: (1) 235 UF6 or (2) 238 UF 6. 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.