Solved: Gaseous Diffusion of Uranium. (a) A process called

Chapter 18, Problem 18.31

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Gaseous Diffusion of Uranium. (a) A process called gaseous diffusion is often used to separate isotopes of uranium that is, atoms of the elements that have different masses, such as \({ }^{235} \mathrm{U}\) and \({ }^{238} \mathrm{U}\). The only gaseous compound of uranium at ordinary temperatures is uranium hexafluoride, \(\mathrm{UF}_{6}\). Speculate on how \({ }^{235} \mathrm{UF}_{6}\) and \({ }^{238} \mathrm{UF}_{6}\) molecules might be separated by diffusion. (b) The molar masses for \({ }^{235} \mathrm{UF}_{6}\) and \({ }^{238} \mathrm{UF}_{6}\) molecules are 0.349 kg/mol and 0.352 kg/mol, respectively. If uranium hexa- fluoride acts as an ideal gas, what is the ratio of the root-mean-square speed of \({ }^{235} \mathrm{UF}_{6}\) molecules to that of \({ }^{238} \mathrm{UF}_{6}\) molecules if the temperature is uniform?