system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5 why certain isotopes of chemical elements become radioactive, and why they have varying half-lives

I know the number of protons makes a spot in the periodic table, but I don't understand how neutrons work or why. I was going to name this "ELI5 Radioactivity" but it'd probably be too vague for what I ask.
gpt
So inside the nucleus of atoms there are protons and neutrons.

There is a certain ratio of neutrons:protons which is stable. It's close to 1:1, though as elements get heavier the ratio shifts in favor of neutrons.

This stable configuration minimizes potential energy of the nucleus.

Anything outside this stable configuration has higher potential energy than the minimum necessary to hold the atom together.

Whenever something has higher potential energy than the minimum, it's unstable. This is simply a fact of our universe.

So this means that the unstable nuclei "want" to reconfigure themselves to be more stable.

This process of reconfiguring nuclei means that they have to get rid of excess potential energy, and the way that happens is through radiation.

There are a number of ways this can happen; alpha, beta and gamma decay are the most common.

Beta decay is the big driving factor for decay. Protons can turn into neutrons, and neutrons can turn into protons through the two forms of beta decay.

This means that an unstable element can either decrease its atomic number by turning a proton into a neutron, or increases its atomic number by turning a neutron into a proton.

In addition to changing the nucleon (neutrons and protons are collectively called nucleons), it results in the release of either electrons and electron anti-neutrinos, or positrons and electron neutrinos depending on which form of beta decay happened. These highly energetic electrons are the beta radiation.

Alpha decay is the release of 2 protons and 2 neutrons - which is basically a helium nucleus. These helium nuclei emerge with a lot of energy and are the alpha radiation.

Gamma radiation is a bit different than the other two. If you've taken high school chemistry you should be familiar with the idea that electrons have energy levels, and can be excited into higher energy levels and decay into lower ones in a structured form.

Well inside the atomic nucleus, nucleons *also* have energy levels in much the same way (although the precise form of it is a little different.)

Things happening inside a nucleus can excite nucleons into higher energy levels, then they decay down to the ground state by emitting photons - the same way that electrons do. However, the much higher energy inside a nucleus means those photons have much higher frequency, and come out as x-rays and gamma rays.

The half-life of an element is simply a measurement of how radioactive it is - how frequently decay events are going to happen. This depends largely on how far away from "stable" it is and how much energy it has. So heavier elements tend to be more unstable.