There are two important isotopes of uranium 235U and 238U; these isotopes are nearly identical chemically but have different atomic masses. Only 235U is very useful in nuclear reactors, One of the techniques for separating them ( ga5 diffusion) is based on the different average speeds vrms of uranium hexafluoride gas, UF . 6 (Use k=1.38

Question

There are two important isotopes of uranium

-^{235} U

and

^{238} U

; these isotopes are nearly identical chemically but have different atomic masses. Only

^{235} U

is very useful in nuclear reactors, One of the techniques for separating them (

g a 5

diffusion) is based on the different average speeds

v_{r m s}

of uranium hexafluoride gas, UF .

_{6}

(Use

k = 1.38 \times 1 0^{- 23} J / K

for this question.) (a) The molecular masses for

^{235} UF_{6}

and

^{238} UF_{6}

are

349.0 g / mol

and

352.0 g / mol

, respectively. What is the ratio of their average speeds? (Enter your answer to at least 4 decimal places.)

\frac{v _{235}}{v _{238}} =

Use the kinetic theory of gases to find the ratio of the rms velocities. (b) At what temperature would their average speeds differ by

1.75 m / s

? What is the difference in the two rms speeds in terms of the answer you got in part (a)?

K

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