There are two important isotopes of Uranium: U-235 and U-238. These isotopes are
ID: 1399574 • Letter: T
Question
There are two important isotopes of Uranium: U-235 and U-238. These isotopes are nearly identical chemically, but only U-235 is useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different velocities of the uranium hexafluoride gas. The molecular masses for uranium hexaflouride with the two isotopes of uranium are 349.0 g/mol and 352.0 g/mol. What is the ratio of the average velocities of these molecules in a gas? At what temperature would the velocities differ by 1.0 m/s?!
Explanation / Answer
Let v1 = rms velocity of U-235
v2 = the rms velocity of U-238
Note that
v1/v2 = sqrt(MM2/MM1)
Thus,
v1/v2 = sqrt(352/349)
v1/v2 = 1.0042888 [ANSWER, ratio of the average velocities)
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Note that
vrms = sqrt(3RT/MM)
Thus,
v1 - v2 = sqrt(3RT/MM1) - sqrt(3RT/MM2) = 1.0 m/s
Solving for T,
T = 767.2 K [ANSWER]