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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It’s easily calculated if we know how many atoms we have and can count how many of those disintegrate every second.
In some cases it’s not that easy. Bismuth-209 was found th have the longest half life ever discovered, and it took a detector cooled to near absolute zero to count out 128 alpha particles over 5 days: https://physicsworld.com/a/bismuth-breaks-half-life-record-for-alpha-decay/
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