My (extremely limited) understanding of what causes an element to be either stable or reactive is due to a mismatch in energy in the nucleus due to either extra protons or extra neutrons. So why wouldn’t something like Plutonium-188 be stable, since it would have 94 protons and 94 neutrons?
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As mentioned, the basic parts of atomic nuclei are protons (p) and neutrons (n). There is something called the _(strong) nuclear force_ which is, as the name implies, rather strong, and it is also pretty weird. The important part is that it makes p and n behave similar to electric or magnetic poles: different ones attract, same ones repel each other.
So just a bunch of protons will not stick together, not even just two of them, unless there is at least one neutron “between” them. Indeed 2p+1n is Helium-3, which is stable.
If you have way more p than n, then it cannot hold together, the p’s are pushed apart more than the few n’s can counteract. Similarly, too many n’s compared to the p’s is bad, too. Only the right mix works.
But now there is yet another force: electric repulsion. The protons are positively charged as well, so they repel each other even more. Meanwhile, neutrons don’t care about this charge at all. That in the end means that you need often a bit more neutrons than protons for optimal stability. Especially of there are many protons.
But even if you have the right ratio of both, a nucleus with too many p’s and n’s won’t keep. Try to get a bunch of marbles in two colors, you want to arrange them in 3D in such a way that same–colored ones are as far apart as possible, while each marble touches as many different-colored ones as possible. There is no good way to do this perfectly, there will always be same-colored ones close. And the larger the number, the worse this gets for the center balls. At some size, it simply won’t hold together anymore.
Even more, if you “shake” a barely stable atom too hard, e.g. by hitting it with very intense light (_photons_) or a collision, it can become temporarily unstable. Effectively because the arrangement got disturbed away from the state where it was already barely able to stay together.
Lastly, lets quickly take a look what happens if the current arrangement is unstable:
If there are too many protons for the neutrons to counteract their repulsion, the nucleus does what we call _alpha decay_: it shoots out 2p+2n as a bundle (the nucleus of Helium-4). This usually improves the ratio, and also reduces the number of protons. In more extreme cases, especially if it was previously “shaken”, it can just explode into multiple globs; this is what happens in nuclear reactors/bombs after Uranium-235 got hit with a neutron. This is also what happens if you just stick 2 protons without a neutron together: it flies apart almost instantly.
If on the other hand there are too many neutrons, another force of nature, the _weak force_, allows a neutron to turn into a proton (plus electron and a _anti-neutrino_ both of which are shot away and don’t matter here), called _beta decay_. This again improves the ratio towards something more stable. This also happens if you only have a neutron without any proton around: after a dozen minutes or so, it turns into a proton.
Much rarer it could also happen in an almost-reverse: a proton turning into a neutron (sending away an anti-electron and a neutrino). This is rather rare, but happens in a few elements (potassium-40 for example). Commonly those elements mainly decay by one of the first two options, and only rarely by this third one. But it could even happen with the 2p stuck together, creating 1p+1n (_deuterium_); which is how the fusion in the sun works, and why it is actually extremely slow.
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