Why are lighter nuclei dominated by $\beta$-decay and heavier ones by $\alpha$-decay?

While I'm trying to understand the nature of radioactive decay, I found that the lighter nuclei mostly have $$\beta$$-decay while heavier nuclei have $$\alpha$$-decay.

From what I know is that the $$\beta$$-decay happens to stabelize an atom whith more neutrons than protons. This mostly happen for the lighter atoms.

For heavy nuclei, the nuclear force is related with atomic mass $$A$$ while the Coulomb force is related with the electric charge $$Z^2$$ (with $$Z$$ the numbers of protons). So the repulsive Coulomb force become much stronger than the nuclear force for heavy nuclei, even when there are far more neutrons than protons. Thereby the protons are expelled and the nuclear force cannot hold them any more, so an $$\alpha$$-particle can escape the nuclei. But why does this happen for very heavy atoms with atomic mass higher than $$200$$ and not for less heavier atoms? And why does very heavy atoms not have $$\beta$$-decay to transform protons into neutrons and stabilize the nucleus?

Thanks in advance.

• protons are expelled to the surface That doesn't sound right. See en.wikipedia.org/wiki/Nuclear_shell_model – PM 2Ring May 27 at 14:29
• I know it's formulated a bit shady, but that doesn't take a away the core of my question. – Belgium_Physics May 27 at 14:32
• Agreed. There's some useful info in the answers here, although that question is focused on why proton & neutron numbers are roughly equal for small stable nuclei. – PM 2Ring May 27 at 14:35
• Plenty of heavy nuclides do undergo beta decay, of one form or another. The Wikipedia alpha particle article is quite good. It explains why almost no light nuclides emit alphas. Also see en.wikipedia.org/wiki/Nuclear_drip_line – PM 2Ring May 27 at 15:14

1 Answer

It is all about size. The nuclear force holding the nucleus together is short ranged (actually it becomes repulsive on very short ranges, to keep the nucleons apart, but it becomes attractive at certain short ranges), but the EM force repelling the protons has unlimited range.

As the nucleus grows in size, as you add more and more neutrons and protons, the strong force will not be able to hold against the EM repulsion.

Alpha decay occurs in those bigger sized nuclei to increase stability by reducing size.

You are asking why this does not occur in smaller nuclei, the answer is size, in smaller nuclei, the strong force can more easily hold against the EM repulsion. Reducing size with these smaller nuclei would not increase stability. These nuclei rather undergo beta decay. Why? Because with smaller nuclei, this is a more efficient form of increasing stability.

Please see here: