How **does** a neutron split an atom?

Factual Questions
1

I did a bit of nuclear physics in college, like the most basic of basic stuff so I understand a bit of what takes place, a neutron hits the nucleus of an atom, and it splits into two smaller nuclei of different elements, two,ti three neutrons and energy.

Th question, what exactly causes it, the targeted atom, to break into two. I am thinking of the neutron being like a rifle bullet hitting a pebble, shattering it into multitude of pieces, but from memory at the sub atomic level it doesn’t work that way, or does it? As I recall the energy if the neutron has to exceed the nucleus binding energy for it to fission? Also the “debris” after the collision isn’t uniform for every individual collision, since fission products usually are a variety of nuclei and sometimes fairly light ones. Again, why? Does it matter where the neutron, err strikes the nucleus, maybe a glancing blow makes one heavy and one light nuclei and a dead Center one making two medium sized ones?

2

I’m no new clear fizzy cyst, but: atomic nuclei are a balance between the electromagnetic force wanting to push the like-charged protons apart and the strong force wanting to hold them together. The electromagnetic force has a longer range than the strong force. There is an extremely limited number of configurations of clumps of protons and neutrons where the protons are held close enough together for the strong force to keep them together. (A few hundred stable and briefly stable isotopes out of an infinite number of plausible combinations, such as an atom with 783 protons and 3 neutrons.) Mess with that configuraton by changing the number of protons and neutrons (or even do something to chanve the shape of the same clump) can push the nucleus out of the delicate balance of forces and cause it to break apart.

3

Also if you deform the nucleus by smacking it with a neutron, parts of it can squish out far enough that the EM force wins. There are newer models that predict the outcome better, but this liquid drop model is easy to think about for the underinformed (talking about myself here.)

4

Something that is important to keep in mind is that it doesn’t always cause a fission.

The things that we think of as fissionable are just more likely to split than things that are not. If you hit PU239 with a thermal neutron, it only has a about 2/3’rds chance of splitting, the rest of the time, it absorbs it and starts moving up the transuranic actinide ladder. Something like U-238 could fission, but very rarely does, instead absorbing it, and eventually turning into Pu239. It’s less about the thermal energy of the incoming neutron, and more the instability that it creates when it is added to an already unstable nucleus. The binding energy involved in the nucleus is much more than the kinetic energy delivered by the neutron.

The electromagnetic forces trying to push the atom apart are pretty considerable. There’s about 20 pounds of force trying to push parts of it away, that’s 20 pounds on a proton, which weighs just a bit less. Disrupting the delicate balances of forces keeping it together is more what is going on, than a brute force disintegration of the nucleus.

When you get to “fast” reactors or bombs, the higher the energy of the incoming neutron, the more likely that it is to cause it to split (but also the more likely it is to miss entirely).

Faster neutrons can split U-238 just fine, if they hit. This is where a significant amount of the energy of a thermonuclear bomb comes from. The fast neutrons from the fusion shoot out and split up the u-238 in the tamper. This is more like your bullet analogy.

The reason that fast reactors are used (or mostly not used, in practice) for breeding fuel is not because the fast neutrons are more likely to cause fission, but because they are more likely to create more free neutrons in the process. Pu239 produces a little less than 2 neutrons, on average, per fission in the thermal spectrum, not enough to continue fission and breed more fuel. But it produces more in the fast spectrum, with more energy corresponding to more neutrons.

5

One thing I’ve never understood is why a U-240 wouldn’t be more stable than U-238 since the same number of protons are slightly diluted by more neutrons.

To put this in perspective, I had believed that U-235 is less stable than U-238 because the fraction of protons repelling each other was lower in the latter (because more neutrons).

6

It is a bit more stable in the nucleus not falling apart aspect.

But, it is less stable because neutrons are unstable. By itself, a neutron will decay to a proton in 10-15 minutes.

U238 usually decays by tossing off a helium nucleus. U240 almost never decays that way.

Instead, with a half life of about 14 hours, one of the neutrons beta decays, where it emits an electron and a (anti)neutrino, and turns into a proton. Then you have Np 240, which again, isn’t too happy, and will beta decay again in about an hour to Pu240. This is a bit happier, and will stick around for thousands of years until it spits out an alpha particle, making U236, which then hangs out for millions of years before alpha decaying again to Th232, which is pretty stable (for an unstable atom) with a half life a bit longer than the current age of the universe.

This isn’t wrong, but it is a bit more complicated. Neutrons do contribute to the strong force holding the nucleons together, without contributing to the electromagnetic force pushing them apart. The shell model involves pretty complex math in order to better explain things, but yeah, in general, your understanding here is more or less correct.

Basically, if there is an element that has higher binding energy, and there is a decay process that can get there, then the atom will use that process to turn into it. The difference of binding energies, and the cross section of the process determine the half life involved. for instance, if it requires double electron capture, I wouldn’t advise sitting around and waiting for it.

There is a balance, where if you have too many neutrons, they beta decay to protons, and if you have too many protons, the nucleus alpha decays to an element 2 lower on the periodic table. Sometimes that’s more stable, sometimes its not.

The sweet spot in the middle is where elements have the longest half lives, or are entirely stable.

7

There are several terms in the empirical mass formula for the liquid-drop model. Too many protons are bad, but a proton-neutron asymmetry is also bad, etc. Maximizing the binding energy gives a supposedly optimal neutron-proton ratio, one that will depend on the atomic weight.

Actual N/Z for U-238 is 1.587.

8

ETA which is close to optimum according to that simple model, even before taking into account anything more accurate

9

Also of note, heavy atoms can sometimes fission completely spontaneously, even without an extra neutron being added. It’s these occasional spontaneous fissions that provide the trigger that starts the chain reaction.

And the Strong Force would work most efficiently if the numbers of protons and neutrons were the same. This can be thought of as a consequence of the Pauli Exclusion Principle: Two protons can’t be in the same state, but a proton and a neutron can, so if there was room for a proton there, there’s also room for a neutron, and vice-versa. Of course, this has to be balanced against the electromagnetic force, which is more relevant for larger atoms (which have a nucleus too great in diameter for the Strong Force to be relevant between particles on opposite sides of it). That’s why light atoms like helium, carbon, and oxygen tend to have the same number of protons and neutrons in their most stable isotope, but heavy atoms like uranium tend to have a good deal more neutrons.

Similar Pauli considerations also cause even numbers to be favored: Because protons and neutrons are both spin-1/2 particles, they each have two spin states available, and so if you have one in one spin state, you might as well have one in the other.

10

And why plutonium bombs can’t be the simple gun type like U-235 can be.

A pure Pu-239 bomb could be made that way, but, that’s just not practical to do, and you will inevitably have at least some Pu-240 contamination. And Pu-240 undergoes spontaneous fission just often enough that there was a decent chance that it would start the chain reaction before the bomb was fully “assembled*”, leading to a fizzle. Still a nuclear reaction, just far less than what was desired (by the one dropping, not the one being dropped on). Which is why they had to use a more complicated implosion design.

Also, in a reactor, this is often the case that the reaction is allowed to start up on its own, through either spontaneous fission or stray neutrons in the environment. In a bomb, this is usually not left to chance, and a neutron source is employed to start it off.

*assembled meaning all the fissionables moved into a critical configuration for fractions of a second using explosives, not meaning the building or construction of it.

As a general rule, but not always. For instance, U236 and U234 have much shorter half lives than U235.

11

Withdrawn.