I’m currently studying for a test to become a Radiological Control Technician.
I understand why a proton rich nucleus is unstable. The electromagnetic forces from the protons in the nucleus are too strong and overcome the nuclear forces. This is why the line of stability curves down under the 1:1 radio in the Chart of the Nuclides. You need more neutrons to hold the nucleus together.
But I don’t understand why a neutron rich nucleus is unstable. It seems to me that if the neutrons hold a proton rich nucleus together, more neutrons would be better. But I haven’t been able to find exactly why this isn’t the case.
It’s probably significant that protons are more stable than neutrons: a sole proton (hydrogen) is the most common element in the universe with a half-life that requires exponents (10^32 years or so). There aren’t any stable neutron-only configurations. A neutron left to itself has a half-life of only 10.3 minutes.
Maybe the real questions are “Why are there stable neutrons at all? How do protons stabilize neutrons in an atomic nucleus?”
There’s talk that neutrons and protons also fill “shells” that are like the electron shells. Electron shells are necessitated by the Pauli Exclusion Principle - two electrons cannot be exactly the same (i.e. cannot have exactly the same quantum numbers) so you can get one shell of co-existing electrons where everything is the same except for different spins. As shells get bigger, there are more variables and you can get more electrons into them, but the bigger shells are at higher energy levels. Electrons do whatever they can (emitting photons in this case) to move into lower-energy shells, if there is room for them to do so under the Pauli Exclusion Principle.
If the same is true in the nucleus (and I don’t think anyone is positive that it is), then mixing protons in with neutrons gets you a better packing of the energy levels, since protons have different properties from neutrons and could co-exist in a lower shell. In that case, beta decay makes sense - a neutron-rich atom is less stable because it’s got empty low-energy proton shells but high-energy neutron shells. If a neutron emits an electron, it becomes a proton and moves into the lower-energy shell.
There are also subtleties in how the strong nuclear force works. The electromagnetic force between any two given particles is either always attractive or always repulsive, depending on the charges of the particles. But the strong force appears to be attractive on short length scales, but repulsive on long length scales. So if you get too many nucleons in a nucleus, it’s not going to be stable no matter what mix of protons and neutrons it is, since there are more nucleons that are far apart than there are ones that are close together.
That’s a jolly good question! I was looking for the answer myself when I came across it.
The main reason neutron-rich nuclei are unstable (as I understand it) is that the pairing term (of the Liquid-Drop Model and the semi-empirical mass formula) ceases to exist at a ratio of about N = 2.5 Z.
This means that the potential well isn’t so deep for these “extra” neutrons (it’s missing the pairing part), and so these neutrons can tunnel out quite easily and become the halo neutron.
Neutrons and protons are not subject to the Pauli exclusion principle. They are bosons, not fermions (or do I have that backwards). However, I cannot help with the OP.
That’s also why equal numbers of protons and neutrons tends to be most stable: There are a set of states at different energy levels for them, and two protons can’t be in the same state, but a proton and a neutron can be.
While we’re at it, helium is particularly stable in nuclear reactions for basically the same reason it’s stable in chemical reactions: All of its constituent particles are each in their ground state. You can fit two of each kind of particle in each respective ground state because they’re opposite spin: A spin-up and spin-down electron, around a spin-up and spin-down proton, and a spin-up and spin-down neutron.
