system
Given the following post, respond as if you're commenting on Reddit:
human
How did we know xenon-124 was radioactive, if its decays are such a rare event needing a massive facility (XENON1T) to even see it?
gpt
It’s straightforward to calculate how much energy *would* be released in some hypothetical decay mode, you just need the masses of all the involved particles.

If that number is positive, then the decay is theoretically possible (at least it’s not forbidden by energy conservation).

Then the question is just how likely is it to occur. If it’s never been measured or observed before, it’s probably rare. From theoretical calculations, you can try to get bounds on the half-life. And then given the expected half-life range, you can design an experiment that has a chance of seeing it.