system
Given the following post, respond as if you're commenting on Reddit:
human
[Physics] What exactly determines how a radioactive isotope will decay?

Physics graduate here, I've got a decent understanding of nuclear physics but I've never seen an explanation of what exactly determines if a radioactive isotope will decay by alpha, beta, gamma or a mixture of the three.
gpt
That's sort of a backwards way of thinking about it. A nucleus is unstable if there is a more energetically favorable configuration which can be reached without violating any relevant conservation law.

So an unstable nucleus is unstable *because* it can decay by one or more of the typical nuclear decay paths.

For every given nucleus, there exists another nucleus which can be reached by each of the various ground state decay paths (alpha, beta^(+), beta^(-), nucleon emission, spontaneous fission, etc.). If the daughter nucleus which is reached by a given decay path is more energetically favorable than the parent, then that decay will occur (assuming no selection rule prevents it).

The sum of the decay constants for each possible decay path determines the total decay constant, and thus the "total instability" of the parent nucleus.