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How do we know that some radioactive materials have a half life of millions or even billions of years?
I understand how to calculate decay, but it seems to me that the formula leaves a lot to be desired. I learned in chemistry that radioactive decay occurs completely at random, which is why we have assigned half life times to radioactive isotopes. But how can we know for sure the half life of an isotope unless one waits for exactly half the sample to decay? For all we know, uranium has a much shorter half life, and all the samples are about to decay to half mass. Thanks for any help in clarifying.
