I have no idea, I think not. I know if you happen to have a spare hadron collider in your shed you can break them apart, but I’m pretty sure we wouldn’t exist if they weren’t stable.
Apparently they are quite stable! Do you know where you can find protons – not in an atom together with neutrons and electrons, but just a proton by itself? In water! Water is H2O, and some of it dissociates into a H+ ion and a OH- ion. The H+ ion is really just a proton – a hydrogen atom that’s lost its electron. So while it is positively charged, and would much rather be together with something else that’s negatively charged, it’s quite alright sitting on its own for a bit.
Protons by themselves are not really stable, and prefer to be in the company of negatively charged particles (electrons) and neutrons, which have no charge on them. This makes everything a bit more stable. The bigger they are as well, the less stable they are.
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