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 just the way we like to record the number. It isn’t some fundemental trait, but just a way of *measuring* a fundemantal trait.
i.e. Half-life is just one convenient way to write down the decay rate, but we can scale it however we like.
We could instead record the ‘99%-life’, which would be the time taken for 99% of the material to remain. Or we could record the ‘99.999%’ life.
Half-life is just a more useful way to think about it. Perhaps if everything took eons to decay (or everything decayed very fast), we’d have measured it differently, but we have to deal with a wide array of ways things change, and conceptually ‘half’ is very easy, and I think that is why we went with ‘half-life’.
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So, in a way, your question is kind of like “How can we measure the size of germs in meters, when they are so much smaller than a meter?”
or “How can we measure the size of a planet in meters, when the are so much larger than a meter?”
It is just a difference in measurement.
Something can be millions of a meter (or millions of meters) in size.
Similarly, we can measure a millionth of a half-life, or millions of half-lives (ok well millions of half-lives may be a bit too much in practical terms because it scales so fast, but in principle that isn’t a problem.).
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(It is a little bit more than a difference in measurement, since half-life is on a log-scale, and meters are on a linear scale, but fundementally I think that isn’t a big deal.)
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