In nuclear fission, by bombarding the heavy nucleus with smaller nuclei will result in the production of energy, nuclei. That means the number of neutrons in the heavy nucleus increases. But addition of neutrons increases the strong force. Then how does the nucleus get torn apart by repulsion of the positive charge, when the strong force will be stronger?
[Physics] In nuclear fission, how does the strong force get dominated by the electrostatic repulsive force
nuclear-physics
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First, the strong force acts on scales where our classical idea of forces as something that obeys Newton's laws breaks down anyway. The proper description of the strong force is as a quantum field theory. On the level of quarks, this is a theory of gluons, but on scales of the nucleus, only a "residual strong force", the nuclear force remains, which can be thought of as being effectively mediated by pions.
Now, a force mediated by pions is very different from one mediated by photons, for the simple reason that pions are massive. Massive forces do not, in their classical limit, follow a pure inverse square law, but yield the more general Yukawa potential, which goes as $\propto \frac{\mathrm{e}^{-mr}}{r^2}$ where $m$ is the mass of the mediating particle. That is, massive forces fall off far faster than electromagnetism.
So this makes it already difficult to tell what the "strength" of a force exactly is - it depends on the scale you are looking at, as Wikipedia's table for the strengths of the fundamental forces rightly acknowledges. However, in no sense is the strong force "infinitely stronger" than the electromagnetic force - it is simply much stronger than it, sufficient to keep nuclei together against electromagnetic repulsion.
Now, the person who said that it is "infinitely stronger" might have had something different in mind which is not actually related to the strength of the force but to its fundamentally quantum mechanical nature: Confinement, the phenomenon that particles charged under the fundamental (not the residual) strong force cannot freely exist in nature. When you try - electromagnetically or otherwise - to separate two quarks bound by the strong force, then you will never get two free quarks. The force between these two quarks stays constant with increasing distance, it does not obey an inverse square law at all, and in particular the energy to being on of the two quarks to infinity is not finite. At some point, when you have invested enough energy, there will be a spontaneous creation of a new quark-antiquark pair and you will end up with two bound quark systems, but no free quark. In this sense, one might say that the strong force is "infinitely stronger", but crucially this is not the aspect of the strong force that keeps nuclei together; the theory of pions shows no confinement.
[Physics] Why does the weak nuclear interaction have a shorter range than strong nuclear interaction
They are mixing two different things here.
The strong force does not work between protons and neutrons, it works between quarks. As a side-effect of the way it works, it also constantly creates new particles, mesons. This particle-creation process is conservative in that if you consider all of the particles that are created, their momentum, charge, spin and so on all add up to zero.
It's all those mesons interacting with each other and the quarks that give rise to a second force, the nuclear force. It is the nuclear force that "acts on protons and neutrons to keep them bound to each other inside nuclei", not the strong force. Of course, one is the result of the other, so half full sort of thing... and that's why you see it called the strong nuclear force, or the strong interaction or all sorts of other names just to confuse things.
The distance that the nuclear force operates over is simply a function of the mass of the mesons and the uncertainty principle; all virtual particles with mass have a maximum lifetime, and if you simply see how far these mesons can go in that time, presto, you get a distance.
UPDATE: I realized I missed the closure.
The weak force is also mediated by massive particles, the W's and Z's. Like the mesons in the nuclear force, they are thus subject to the same range limitations due to the uncertainty principle. However, the mass of a simple meson like a pion is about 100 MeV, while the Z is a whopping 90 GeV. That's heavier than an entire iron nucleus! Now it might sound odd that such a heavy object can be created ex nihlo inside something like a helium nucleus, which is way lighter, but that's the whole idea of the uncertainty principle, for a very short time this is allowed, and that's why it's range is so short and the reaction is so rare in comparison.
Best Answer
The U-235 nucleus is unstable with respect to fission into Barium-141 and Krypton-92. You can see this by looking at the graph of binding energy per nucleon:
(this graph is all over the Internet - I got it from the question Why only light nuclei are able to undergo nuclear fusion not heavy nuclei?)
I've marked the U-235 nucleus and it's two fission products by red circles, and it's obvious from the graph that fission increases the binding energy per nucleus so it should happen spontaneously. The reasin it doesn't happen is because there is a large energy barrier to the fission process. Splitting a U-235 nucleus in two requires a wholesale rearrangement of the nucleons and that costs energy. The final state will have a lower energy but the intermediate states have a higher energy and present a barrier.
It's important to note that the neutron doesn't produce a more fissile nucleus. In fact absorption of a nucleus produces U-236 and U-236 is not fissile. What the neutron does is provide a pathway for the U-235 nucleus to get round the energy barrier and allow the fission to occur. This isn't simply a matter of adding some energy since even low energy thermal neutrons will cause fission. Luc refers to an energy of 10MeV but neutrons with just a few eV of energy will cause fission and these can't possibly be providing enough energy to get over the barrier.
Exactly what goes on I don't know, but I would guess that the nucleus rearranges when an extra neutron is added, and in that process the nucleus passes through a configuration where the energy barrier is much reduced.