A quick question about U238 vs U235

  • Thread starter Thread starter Kites
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on the separation of uranium isotopes U-238 and U-235, emphasizing the significance of U-235 for nuclear reactors due to its 0.7% natural abundance. The isotopes are separated using uranium hexafluoride (UF6) gas, which diffuses through porous membranes, with U-235 diffusing slightly faster due to its lower mass. The relevant equation for calculating the root mean square speed (Vrms) is Vrms = ([3*kb*T]/m)1/2. The user seeks assistance in correctly applying this equation to find the ratio of the rms speeds of the two isotopes.

PREREQUISITES
  • Understanding of isotopes and their natural abundances
  • Familiarity with uranium hexafluoride (UF6) and its properties
  • Knowledge of the root mean square speed equation (Vrms)
  • Basic principles of gas diffusion through porous membranes
NEXT STEPS
  • Study the principles of gas diffusion and separation techniques
  • Learn about the applications of U-235 in nuclear reactors
  • Explore the derivation and implications of the Vrms equation in different contexts
  • Investigate the mass conversion between atomic mass units (amu) and kilograms
USEFUL FOR

Students in nuclear physics, chemists working with isotopes, and professionals involved in nuclear energy research will benefit from this discussion.

Kites
Messages
39
Reaction score
0

Homework Statement



Uranium has two naturally occurring isotopes. U_238 has a natural abundance of 99.3% and U_235has an abundance of 0.7%. It is the rarer U_235 that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride UF_6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235UF_6 has a slightly larger rms speed than 238UF_6 and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of 238UF_6? to that of 238UF_6 ?



Homework Equations



The relevant equation is only this.

V_rms = ([3*k_b*T]/m)^(1/2)



The Attempt at a Solution



My attempt thus far is

V_rms_1/V_rms_2 = solution ; Simple right?

Let's go further...

1u= 1.6691729*10^-27
([3*k_b*T]/(238*1u)^(1/2)/([3*k_b*T]/(235*1u)^(1/2)

This has come out wrong several times. I believe my error lies in converting the masses somehow since it's the only possible variable. Sadly I don't have a strong background in chem or working with these. Help would be very appreciated.
 
Physics news on Phys.org
Since 3*k_b*T will be the same for both of the uranium isotopes you could ignore it and leave it as a variable 'A' or just completely remove it.

Then you could get an easier formula V_rms = (A/m)^1/2

When you set the ratio of V_rms_1 / V_rms_2 just go ahead and cancel the A values out and the formula you get will look better. (And again, to form a ratio you will not need to convert amu units to kg, a ratio is unitless and as long as you have the same mass units for both isotopes the equation will yield the same results)
 

Similar threads

Ratio of rms speeds of two isotopes
  • · Replies 1 ·
Replies
1
Views
5K
Uranium238 vs U235, which are true?
  • · Replies 1 ·
Replies
1
Views
9K
How many effusion stages required to increase the 235U to 4%
  • · Replies 2 ·
Replies
2
Views
2K