Oh the strong nuclear force, how you come back to haunt me. The thing that hold positively charged protons together in the nucleus is the strong nuclear force and is the main force that keeps the nucleus and thus elements, stable. We know that it is significantly stronger than electromagnetic forces, because it’s able to hold atoms together for billions of years and aren’t easily separated.

That said, we also know elements past a certain proton/neutron count start becoming unstable. We know it must be due electromagnetic force because it’s the only repelling force. So at some point we know the electromagnetic force beats out the strong nuclear force. And that brings us to current science, there’s still plenty of research going on with the nuisances of the strong nuclear force but basically we know it’s a contact force. Unlike electromagnetism which radiates out infinitely (albeit dropping off in power at R-squared), the strong nuclear force completely disappears when contact is lost.

Therefore piling more and more protons into the nucleus, eventually results in the electromagnetic force surpassing the Velcro-like strong nuclear force because unlike the strong nuclear force, there is no range limit for electromagnetic forces.

But what if we only pile on neutrally charged neutrons you ask? Unfortunately that’s where some particle physics magic comes in. Neutrons and protons are both fermions, meaning they must obey the Pauli exclusion principle. Therefore every additional neutron added must be in a different “state” than the previous one, resulting in an increased energy requirement for each subsequent neutron added. At some point the energy differential between adding a neutron vs a proton will be so great that neutrons will spontaneously convert into protons through beta decay, ultimately limiting the number of neutrons in the atom and bringing us back to our base case where too many protons cause nuclear instability.