Simple classification of radioactive decay

In how many different ways can an isolated neutral non-exotic atom decay?

When an atom decays, it spontaneously changes into something else. That “something else” is inevitably two or more particles, none of which is the same kind of atom as the original.

I also need to also explain what a “kind of atom” is. Note that I’m only concerned about the atomic nucleus, not the state of its electrons. An atom can be characterized by a triplet of integers: the number of protons, the number of neutrons, and the “nuclear energy state”. Virtually all familiar atoms are in their lowest possible nuclear energy state (state 0), but this parameter cannot be ignored. Atoms with different nuclear energy states (“nuclear isomers”) have different properties, and different half lives.

When describing different kinds of atoms, the terms isotope and nuclide are used. These words are essentially synonyms, but isotope implies you are discussing different kinds of the same element (e.g. carbon-12 vs. carbon-14), while nuclide has no such implication (e.g. carbon-12 vs. nitrogen-14).

Back to the original question. While there are lots of kinds of radioactive decay, there are really only three or four general classes of decay possible for an isolated atom:

  1. Beta decay
  2. Fission
  3. Isomeric transition
  4. Proton decay

Notes:

  • After a decay, the most massive remaining particle inevitably has a lower mass than the original atom. This enforces a “direction” to the decay processes. Two atoms cannot decay back and forth into each other.
  • Any decay that is not forbidden by the laws of physics (conservation of energy, etc.) will eventually occur, if you wait long enough. But it may take an insanely long time.
  • I’m sure I’m oversimplifying all this. For one thing, after a decay, the nucleus is often in an excited energy state. So it immediately decays again, usually by isomeric transition. Is that one decay or two? And I’m not sure, but I think that in extreme cases it’s possible for the resulting “nucleus” to not even be a bound particle. I won’t attempt to classify this.

1. Beta decay

Generalized beta decay is when a neutron turns into a proton, or a proton turns into a neutron.

Beta minus decay is when a neutron turns into a proton (and other particles).

Beta plus decay is when a proton turns into a neutron. One way this can happen is for one of the atom’s electrons to be absorbed by the nucleus, in a process called electron capture. If the decay would liberate a sufficient amount of energy, then instead of an electron being eliminated, a positron can be created, in a process called positron emission.

In some nuclides for which a single beta decay is impossible, double beta decay, in which two beta decays happen simultaneously, is still possible.

For a given atomic mass number, there is one and only one nuclide that is immune to all forms of beta decay: the one with the lowest mass (the lowest “isotopic mass”). [Edit: This is not quite correct; see this post.] So, for example, even if you know nothing about carbon-14 and nitrogen-14, you can be sure that at least one of them can decay by some form of beta decay.

2. Fission

Fission is when the nucleus splits into two or more pieces, each containing at least one nucleon.

The most common type of fission is alpha decay, in which one of the pieces is an alpha particle (two protons and two neutrons), and the other piece has all the other nucleons.

Other types of fission are cluster decay, positron emission, neutron emission, and spontaneous fission.

Fission is rare for nuclides with fewer than around 145 nucleons, unless they have an extreme abundance of protons or neutrons.

All nuclides with at least 100 or so nucleons can theoretically decay by fission, but for some it’s so rare that it effectively doesn’t happen.

3. Isomeric transition

Isomeric transition is when the nucleus moves to a lower energy state, typically emitting a photon in the process. Think of it as the protons and neutrons being rearranged into a more compact structure. The number of protons and the number of neutrons remain the same.

Instead of emitting a photon, the atom may eject one of its own electrons, in a process called internal conversion.

Most atoms are in their lowest possible nuclear energy state, so they cannot decay by isomeric transition.

4. Proton decay

Proton decay is a hypothetical process in which a proton decays into less massive particles. It might not exist. If it does, then all atoms have a finite half life.

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