A quick question about U238 vs U235

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In summary, uranium has two naturally occurring isotopes, U_238 and U_235, with abundances of 99.3% and 0.7%, respectively. The rarer U_235 is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride UF_6 and allowing it to diffuse through porous membranes. The ratio of the root-mean-square speed of 238UF_6 to that of 235UF_6 can be calculated using the equation V_rms = (A/m)^1/2, where A represents a constant value and m is the mass of the isotope. The ratio can be found by setting V_rms_1/V_rms_2 and canceling
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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.
 
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  • #2
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)
 
  • #3


I would first commend the student for their attempt at finding a solution to the problem. It is clear that they have a basic understanding of the relevant equations and are on the right track.

However, I would also point out that the correct approach to solving this problem would involve using the relative atomic masses of U-238 and U-235, rather than their individual masses. The relative atomic mass of an isotope is the average mass of that isotope compared to the mass of a carbon-12 atom, and it takes into account the natural abundance of each isotope.

In this case, the relative atomic masses of U-238 and U-235 are 238 and 235, respectively. So the correct calculation would be:

V_rms_1/V_rms_2 = ([3*k_b*T]/(238*1u))^(1/2)/([3*k_b*T]/(235*1u))^(1/2)

where 1u = 1.66054 x 10^-27 kg.

This would give the correct ratio of the rms speeds of U-238 and U-235 isotopes. It is also important to note that the temperature (T) should be in Kelvin and the gas constant (k_b) should be in units of Joules per Kelvin (J/K).

Furthermore, as a scientist, I would also emphasize the importance of understanding the underlying principles and concepts behind a problem, rather than just focusing on plugging numbers into equations. In this case, it is important to understand why U-235 is needed for nuclear reactors, and how the separation process works based on the slightly different diffusion rates of the two isotopes.

Overall, it is great to see students taking an interest in scientific problems and seeking help when needed. Keep up the good work!
 

1. What is the difference between U238 and U235?

U238 and U235 are two isotopes of the element uranium. They have the same number of protons but different numbers of neutrons, resulting in different atomic masses. U238 has 92 protons and 146 neutrons, while U235 has 92 protons and 143 neutrons.

2. Why is U235 more commonly used in nuclear reactors?

U235 is more commonly used in nuclear reactors because it is the only naturally occurring isotope of uranium that can undergo fission, which is necessary for nuclear reactions to occur. U238, on the other hand, is not capable of sustaining a chain reaction.

3. Is U238 radioactive?

Yes, U238 is radioactive, but it is not as radioactive as U235. U238 has a much longer half-life (4.5 billion years) compared to U235 (700 million years), meaning it takes longer for half of the atoms in a sample of U238 to decay.

4. How is U238 converted into U235 for nuclear fuel?

U238 can be converted into U235 through a process called enrichment. This involves separating the two isotopes based on their different masses. One method of enrichment is through gaseous diffusion, where uranium hexafluoride gas is forced through a series of membranes to separate the isotopes.

5. Can U238 and U235 be used to make nuclear weapons?

Both U238 and U235 can be used to make nuclear weapons, but U235 is the preferred isotope because it is easier to separate and has a higher probability of undergoing fission. U238 can also be used in the production of plutonium, which is another element commonly used in nuclear weapons.

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