eli5 / How do we know the half life of (or even that it is radioactive) Bismuth-209 when it is literally longer than the age of the universe by several orders of magnitude
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The half-life is how long it takes for half of a sample to decay. In half the half-life, one-quarter will have decayed. This can be extended to where an experiment of say a dozen years length will have some really tiny fraction of the sample has decayed. You might think that there comes a limit to where the sample size at the beginning is too small for the decay to be measured, Avogadro’s Number is a really, really, REALLY big lever, though, and bismuth is not rare. So it isn’t that difficult actually to get enough bismuth together such that over a chemistry department’s lifespan you’d be able to measure some decays.
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