Half-life of things

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I’ve been reading about HL, but I still don’t get why would you use it. So, if half life of coffee is 5h, how that info is relevant when we know that full life is 10 (roughly)? On top of that, how do you get the half-life of a material other than waiting to be completely ‘dead’ and say, ok full life is X, the half life is X/2.
Also, let’s take uranium which in Earth’s crust has a half-life of almost 4.5 billion years.. how did we get this number?

Thank you!

In: Chemistry

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> Also, let’s take uranium which in Earth’s crust has a half-life of almost 4.5 billion years.. how did we get this number?

The decay of each individual atom is random, but if you have enough then you get predictable patterns. You can e.g. get a sample of 10^20 = 100000000000000000000 uranium atoms. You measure that around 500 of them decay each second. You might have 520 decays in a specific second, or 490, or whatever, but the average will be 500. That means 0.00…5% of them decay each second and 99.99…5% stay. You can use that information to extrapolate how much uranium will be left at any point in the future. Half of it will be left after 4.5 billion years, a quarter will be left after 9 billion years, 1/8 after 13.5 billion years and so on.

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