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We have a uranium-236 nucleus that fissions into two equal fragments, and I'm supposed to find the electrical potential energy just as the two fragments split apart. No other information is provided.

I am very confused about this problem for two reasons. First, U-236 is electrically neutral, with exactly 92 protons and 92 electrons. After it splits into two equal fragments, why would there be a charge on the resulting pieces? Secondly, electric potential energy of two point charges is inversely proportional to the distance r between the particles. But since the question asks for the potential energy immediately after fission, r=0 and potential energy goes to infinity.

I'm appreciate any guidance!

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Like dmckee says, the potential energy of electrons in an atom doesn't really compare to the energy of the nucleus. Since the nucleus is so tightly packed, and (in the case of Uranium) contains so many protons, they have a lot of potential energy—it takes a lot of work to "push" them together. The strong force holds protons and neutrons together when they're close enough together. It's sometimes compared to a glue in that sense. However, this force disappears very quickly once the nucleons become separated past a certain distance (on the order of a femtometer), so for a large nucleus like that of Uranium, the protons on one end of the nucleus aren't "stuck" to the protons on the other side, but there's still plenty of electrostatic force pushing them apart. That's why large nuclei are unstable; especially those with a higher proton-to-neutron ratio, like U-235 (or U-236). If you can destabilize that nucleus enough (you could imagine it stretching out like a football), its own electric force will tear it apart, and release a tremendous amount of energy as the fragments accelerate apart.

It seems that you've already considered that to a degree, but yes, you don't have to worry about electrons. Just think about the protons, because the nucleus is definitely not neutral. It is a bit of a problem if you don't know how close together those nuclear fragments start out, but you could probably estimate it by considering the nuclear radius of uranium, which is about 7 or 8 fm (it's hard to find an exact figure), or by using double the radius of the fragments it creates, which, it would seem, would be paladium nuclei. Obviously the protons weren't in the same place when they start out, but they were very close together.

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Thank you! I think I got it. –  half-pass May 22 '13 at 2:15
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Has your instructor (or your book) mentioned how much bigger a atom is than a atomic nucleus? On order of 10000 times.

Moreover, except for the $s$-shell electrons, most electron never come very close to the center (the $p$, $d$, etc shells all have nodes at $r=0$) so at the moment of fission the nuclei are sitting roughly at the middle of a roughly spherical shell of electrons.

You are probably meant to ignore the electrons and work it as if only the protons and neutrons mattered.

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