Why is Uranium-236 less stable than Uranium-235 and Uranium-238?

[Josh0768]

Why is Uranium-236 less stable than Uranium-235 and Uranium-238?

 

[mathman]

This is a specific question about isotope stability. The answer requires a detailed many problem analysis of nucleons.

 

[snorkack]

Two simple parts of answer:
U-236 is less stable than U-238 because it has a lower mass. The half-lives of even isotopes of U are:
U-232 - 69 years
U-234 - 240 000 years
U-236 - 24 000 000 years
U-238 - 4 500 000 000 years
Now, all even isotopes of U, and their daughters, have zero spin.
Odd isotopes of U have nonzero spin. And there is no requirement that the spin of mother and daughter should be equal. In case of U-235, they are not. Which contributes to long half-life of U-235.
Can anyone expand?

 

[UppercaseQ]

I do not understand "U-236 is less stable than U-238 because it has a lower mass. " I thought lower mass usually contributes to greater stability. I think density would have a lot of influence on stability.

 

[snorkack]

I do not understand "U-236 is less stable than U-238 because it has a lower mass. " I thought lower mass usually contributes to greater stability.

Well, now I managed to look up decay energies, they were ordered as expected:
U-238 - 4270 keV
U-236 - 4494 keV
U-234 - 4870 keV
The reason U-238 has smaller decay energy than U-236 is that both have the same number of protons to repel each other, but U-238 has more neutrons binding them together by strong force.

 

[mfb]

For a given mass number (sum of protons and neutrons) there is an optimum proton to neutron ratio - the lowest energy state for that mass number. The farther away you are from that optimum the more energy nuclei have, which makes them less stable. It's not always a 1:1 relation but it's a pretty consistent pattern. U-235 and U-238 are close to that optimal ratio, while the uranium isotopes with fewer or more neutrons are a bit away from it.

U-237 with its short half life (a week) is an outlier here.

 

[UppercaseQ]

The reason U-238 has smaller decay energy than U-236 is that both have the same number of protons to repel each other, but U-238 has more neutrons binding them together by strong force.

Of course. I understand. And two more neutrons are not going to increase the diameter that much - not going to make two repelling protons that much further apart. While I am at it though, I think I heard that protons do not have strong force for each other. Personally I think they would. I would not think losing or gaining an electron would affect whether or not they have strong force.

 

[mfb]

I think I heard that protons do not have strong force for each other.

They do. The strong interaction doesn't really care about protons vs. neutrons.

 

[Vanadium 50]

It's not clear what "stable" means in the question. It may mean that U-235 has a longer half-life than its neighbors, but one cannot determine that by studying the parent nucleus in isolation: half-life is a function of both the parent and daughter.

Further, one is not going to be able to determine this by qualitative arguments like "not going to increase the diameter that much". The energy difference between parent and daughter is ~1/500 of the binding energy. You don't get 0.2% precision with qualitative arguments.

 

[Vanadium 50]

I found this at MIT:

It's hard to see, but the point of this is that a small change in energy difference (alpha particles are typically 4-5 MeV) makes a huge difference in lifetime: of order a factor of a billion per MeV. You need a very precide knowledge of energy levels, and you don't get that with hand-waving. You need serious calculation.

 

[snorkack]

For a given mass number (sum of protons and neutrons) there is an optimum proton to neutron ratio - the lowest energy state for that mass number. The farther away you are from that optimum the more energy nuclei have, which makes them less stable. It's not always a 1:1 relation but it's a pretty consistent pattern. U-235 and U-238 are close to that optimal ratio, while the uranium isotopes with fewer or more neutrons are a bit away from it.

U-237 with its short half life (a week) is an outlier here.

U is an even element. All even U isotopes from 230 to 238 are stable to beta decay or electron capture. Odd isotopes just 233 and 235.
U-237 has too many neutrons so it decays in under 7 days.
U-238 has even more neutrons but it cannot beta decay - it would form Np-238 which is odd-odd - so the neutrons stabilize the nucleus and make alpha decay slower.
U-239 is odd and has beta decay in 23 minutes - faster than U-237.
U-240 is even and has so great neutron excess that it can beta decay despite forming odd-odd isotope. But its halflife is 14 h - longer than U-239, exactly because it is even and daughter has to be odd-odd.