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?
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Half-life is how long it would take for half of a sample to decay, but you can measure how long it takes for much less than half to decay and then just scale/multiply that out to how long it will take for half to be gone.
The other big thing is samples have a LOT of atoms. Even very-rare decay events are happening frequently, because there’s just so many atoms.
EXAMPLE: Uranium-238 has a half life of 4.5 billion years. But **1 pound of Uranium-238 has 273,126,530,000,000,000,000,000,000 atoms.** **There has to be millions of atoms decaying every day for half of them to be gone in “*****only*****” 4.5B years**. Much more than millions actually, so you’d use a much smaller sample than a pound of U-238. You can easily measure the decays for a few minutes or an hour or a day, and then you know the rate and can calculate how long it will take for half to be gone.
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