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Can we uniquely determine the particles emitted in a neutron induced binary fission of a radioactive element?

For example, if we have $ \newcommand{\U}{\mathrm U} \newcommand{\Mo}{\mathrm{Mo}} \newcommand{\Xe}{\mathrm{Xe}} \newcommand{\n}{\mathrm n}$ $ ^{235}_{92}\U$, which decays into $^{98}_{42}\Mo$ and $^{136}_{54}\Xe$, then can we uniquely tell which particles would have been emitted?

The equation would be $$^{235}_{92}\U+ {^{1}_{0}\n} \rightarrow {^{98}_{42}\Mo}+ {^{136}_{54}\Xe} + {}?$$

Now, we know the unknown particles would have a mass of $235+1-98-136=2 $ units and the total charge would be $-4$.

Surely, this could mean $4$ electrons + $2$ neutrons or $5$ electrons + $1$ proton + $1$ neutron and similarly multiple more possibilities.

It was a subpart of a problem asked in a textbook, in which they have taken the case of $4 ~e^{-1}+2 ~^1_0 \n $ and ignored others.

Could the reason be that probability of emission of $4 ~e^{-1}+2 ~^1_0 \n $ is much more than others, but theoretically all others are also possible? If so, why?

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  • $\begingroup$ I’ve just reread your question and realized that the suggestion of balancing the charge in this unphysical reaction by emitting electrons came from your textbook. Permit me to suggest respectfully that, if that caliber of error survived the editing process, you should strongly consider putting this textbook in the garbage and finding a replacement. $\endgroup$
    – rob
    Commented Apr 17, 2021 at 20:27
  • $\begingroup$ @rob The textbook is not a standard physics textbook, it is just for practicing elementary physics problems and building a conceptual clarity. In my opinon, it doesn't care whether the reaction is possible in reality or not, it is just posing a hypothetical solution, that "if" the reaction proceeds as given, then what would happen. $\endgroup$
    – V.G
    Commented Apr 18, 2021 at 3:27

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It’s possible in principle. In general we don’t: most fission happens within the uranium medium. The fission products are heavy and strongly-interacting, so it’s hard to extract them into a detector in real-time for tagging. And neutrons are slippery at the best of times. If you’re triggering fission with some neutron source, it’s very hard to say whether a neutron you detect afterwards is from the fission or from the source. (This was the problem during the “bubble fusion” drama twenty years ago. As a colleague put it, “those guys had neutrons everywhere. They had neutrons in their pockets. They had neutrons on the floor.”)

In practice we rely on evidence from other experiments that, unless the weak interaction is involved, the numbers of protons, neutrons, and electrons in any reaction are separately conserved. Or rather, what’s conserved is the number of electrons minus the number of anti-electrons, in situations where pair production may take place. Fission reactions don’t liberate enough energy to produce anti-protons or anti-neutrons, so we don’t worry about people who forget to mention them.

Your particular reaction is impossible: your two fission products have ninety-six protons, but uranium only has ninety-two protons. You can’t balance the charge by conjuring electrons from nowhere; your problem is that you’ve conjured protons. In general, the atomic numbers ($Z$) of the fission fragments add up to the atomic number (here $Z=92$) the fissioning nucleus. A free proton in the final state is technically allowed, but that decay mode is highly suppressed.

You may be thinking of the more sophisticated conservation laws that govern weak interactions, such as the neutron decay

$$ \rm n \to p + e^- + \bar\nu $$

Here we are separately conserving “baryon number” and “lepton number.” But unless the weak charged current is involved (and in fission it’s not; fission is a strong process) then the number of neutrons and the number of protons are conserved separately.

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  • $\begingroup$ Sir, this is a question of mine that you answered, and it has been deleted by community after it was closed, but I don't want it to get deleted as it could be useful for me in future also, so can you undelete it? $\endgroup$
    – V.G
    Commented May 12, 2021 at 16:24
  • $\begingroup$ I think it’d be inappropriate for me to use my moderator powers to override the community consensus and un-delete my own answer. See this help center page to learn why that closed question was automatically deleted and how you can prevent some such deletions in the future. If you flag the other question, another moderator will look at it. It won’t get more deleted; you can hang on to your link. $\endgroup$
    – rob
    Commented May 12, 2021 at 16:54
  • $\begingroup$ Sir, probably it was because I forgot to upvote and check mark your answer, if that is the issue, I will do that if it gets un-deleted. Also I'm okay if it doesn't get deleted permanently from my deleted questions list, because I suspect that it would only show it till the 60th day after deletion and after that it would no longer be visible, so it would get lost permanently. Edit: I have flagged it as you suggested. $\endgroup$
    – V.G
    Commented May 12, 2021 at 17:50
  • $\begingroup$ I see you’ve had the flag declined twice, by two of the other diamond moderators. Leaving that question deleted is probably also the decision I would have made if I weren’t involved. Your link to the question will continue to work, if you save it as a bookmark in your browser; it’ll just disappear from the list of “recently deleted questions” on your profile. $\endgroup$
    – rob
    Commented May 13, 2021 at 13:50

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