Ratio of rms speeds of two isotopes

[Linus Pauling]

1. Uranium has two naturally occurring isotopes. 238U has a natural abundance of 99.3% and 235U has an abundance of 0.7%. It is the rarer 235U that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, which is a gas, then allowing it to diffuse through a series of porous membranes. has a slightly larger rms speed than and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of 235UF6 to that of 238UF6?

Express answer to five significant figures.




2. v_rms = sqrt[3k_B*T/(m)]



3. Since I need a ratio, I simply ignored the 2*k_B*T as well as the hexfluoride, and computed the ratio of v_rms 235U/235U, obtaining an asnwer of 1.0064, which is incorrect.

 

[Linus Pauling]

Nevermind I got it.

 

[kerimek]

I would like to point out that the equation used in this scenario is incorrect. The correct equation for calculating the rms speed is v_rms = sqrt[(3RT)/M], where R is the gas constant and M is the molar mass of the gas. Furthermore, the assumption that the gas used in the separation process is only made up of the uranium isotopes is incorrect. Therefore, the calculated ratio of 1.0064 is not accurate and cannot be used to determine the separation of the isotopes. A more accurate approach would involve using the correct equation and considering the composition of the gas mixture in the separation process.