Since naturally occurring uranium (U-238) has a half life of 4.5 billion years, then it means half of the uranium on earth has decayed into lead by now. But why only half, and why that specific half? What was special about the particles that did decay? Were they different in some way?
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It’s statistics – pure and simple. Let’s start with coins. We’re going to toss a LOT of coins. Every time a coin comes up tails, we’ll throw it away. So – take a REALLY BIG bag full of a LOT of identical coins. Toss every one of them once. On average, (very close to) half of them will be tails, so we’ll throw away (very close to) half. But it was a REALLY BIG bag of coins, so we still have a BIG bag left.
Take the ones that are left, and toss all of them again once. On average, (very close to) half of them will be tails, so we throw away (very close to) half. But it was a BIG bag of coins, so we still have quite a few left. And we can pretty much keep going until we run out of coins, and statistics will mean that, every time, (very close to) half of what we have left will come up tails.
The half-life of our coins in this experiment is, literally, “one toss”. After each toss, half the remaining coins have gone. We have absolutely no way of knowing ahead of times which coins will go and which will stay, because all the coins are the same, the coins don’t care; every single toss could come down either way, with equal probability. And the probabilities don’t change with more tosses – the chance for any individual coin, at any individual toss, is always 50%.
Radioactivity is just like that. Whatever may be ACTUALLY happening under the covers of reality, atomic decay happens just like our coin tosses, except that, rather than single tosses, we’re talking about periods of time. if you toss a single atom of U-238 – i.e. watch it for 4.5 billion years – there is a 50% chance that it will decay at some point during that period, and throw itself away. If it doesn’t, and you toss it again – watch it for another 4.5 billion years – there is still (only) a 50% chance that it will decay during that time. So if we have a LOT of U-238 atoms, and we watch them for any given period of 4.5 billion years, at the end of it half of them will have decayed and half of them won’t. Which is precisely the definition of radioactive half-life. But – there’s absolutely nothing special about individual atoms, and we have no way of knowing which ones will decay and which won’t.
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