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Only Hydrogen/Helium/Lithium existed after the bigbang. Uranium is created in small quantities in Super Nova. The Uranium on planet earth was very likely formed about 5 billion years ago after a SN helped spawn our solar system. There's 3 types of radiation also; Alpha, Bata, gamma rays which play a part in the decay calculations. That's It..it all I know..Well, point being, if the uranium existed shortly after the universe happened, wouldn't that be the beginning of its life?
As opposed to when someone stumbled on a deposit within human existence?
I reckon "half life" is indeed an arbitrary time frame term...