I keep calculating the square root of 3RT/M, and am not worrying about the temperature. I keep using 238 and 235 as my M when I do calculate it for both isotopes. Then I end up getting 1.00 as my final answer. That can't possibly be correct, can it?

Question

The question was: The two isotopes of uranium, 238U and 235U, can be separated by effusion of the corresponding UF6 gases. What is the ratio (in the form of a decimal) of the root-mean-square speed of 238UF to that of 235UF6 at constant temperature?

Answer 1

I expect you are not carrying it out to enough decimal places. The ratio of 235/238 is almost 1.00 (but not quite).
The other thing is you need to include UF6 and not just U. Sine the 3*R*T will be the same, you can get by, I think with just sqrt(1/M) vs sqrt(1/M). I went through in a really big hurry and got something like 1.004 or so but you need to do it more precisely. I worked in Oak Ridge, TN for a while (where one of the gaseous diffusion plants is located) and they have many, many separation stages (because the ratio IS so close to 1.00 as you point out).