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.