It’s been little over 100 years since we discovered radioactivity. How then do we know the half life of elements that have half lives in hundreds plus years?
In: 21
By measuring how quickly it decays
You don’t need to wait for it to get to half to know what the half life is, once you have a few data points you can do the calculation
If you’ve got a hunk of an element and a special sensor set up to capture and count each time it decays(measure the gamma/beta/alpha particles) then you just need a couple data points far enough apart to get a reliable answer
If our chunk creates 1 trillion decay events in the first hour we’re measuring it, then the next day at the same time its down to 999,999,998 decay events, then the next day we’re down to 999,999,996 decay events, you can run the numbers and determine it has a half life of around 950,000 years. More measurements and more time will let you get a more precise answer, but in 48 hours you determined an answer of 950,000 years
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