Electric potential energy after nuclear fission

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!

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.