So half lives are different based on the stability of the atom in question. The stability is determined by size and ratio of protons to neutrons. Obviously for every atom and isotope these numbers are different. This causes the difference in stability and thus different half lives.
As for how half lives are found we take a sample and measure the radiation coming off a known amount. Knowing how much a single decomposition of the atom releases we can then calculate half life.
Or if you are cool just hold a lump of metal and count how long till half of it is gone/s
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