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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WeDriftEternal’s answer is fantastic. To put it back into atomic halflife terms:
You don’t need to measure or observe a whole half-life to figure out what the half-life is. We just measure how long it takes for a small fraction of a sample to decay, and then use that to work out how long it would take for 50% to decay (which is what half-life means).
So like: “In one week of observation, 1% of the sample decayed, so it would take 50 weeks for 50% to decay. The half life is 50 weeks.”***
Or in the case of bismuth, it’s more like: “In one week of observation, 0.000000000000000001% of the sample decayed, so it would take 50000000000000000 weeks for 50% to decay.”
The key is that we have very sensitive detectors that can measure even a few atoms decaying. Even a very small sample of material has trillions of atoms. So even for something with a very slow decay rate like bismuth-209, you can watch it and see how long it takes for like 10 atoms out of 100 trillion atoms to decay, and then just extrapolate to how long it would take for 50 trillion of those 100 trillion to decay, and that’s the half-life.
***This is not how the actual math goes – it’s not actually linear like this. That was an ELI5 simplification. The point is from a small fraction decaying you can work out how long it would take any larger portion to decay. Thanks to Way2Foxy for calling this out!
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