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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its a natural behavior of random systems.
you flip 100 coins, you expect 50 of them to be tails. you flip the other 50, you expect 25 to be tails. you flip the remaining 25…
> What was special about the particles that did decay?
it’s actually an important fact that the answer is “nothing.” radioactive decay is *genuinely* random.
Nothing, its just the law of large numbers. Even if you have random unrelated events, try a bunch of times and the probabilities turn into fraction.
Or rather thats how probabilities are introduced. If you want to know the probability of an event try more and more and see what fraction of the results end in your event. What that fraction is approaching is the probability.
So flip a coin, once. H or T? Hard to say. Flip a coin 1 000 000 times. About 500 000 H and 500 000 T. Once you have enough attempts statistics allow for probabilistic thinga to be predictable. Since everything that can happen does happen and the question is how much something has happened.
If you throw a die 10 times its hard to predict how many sixes you got. But throw it 6 million times and saying its 1 million sixes is extremely accurate. With large numbers we are not asking if something has happened, we are asking how much the event happened.
Imagine I have a huge bag full of dice. Every 5 minutes I throw the dice on the floor. Any one that comes up a 6, I and put it to one side. All the dice that don’t come up a 6, I put back into the bag, and 5 minutes later, I throw the dice in the bag on the floor again.
On the first throw, about 1/6 of the total will come up with a 6, and 5/6 will go back in the bag. On the second throw, about 1/6 of the remaining (so 5/36 of the original total) will come up a 6, so I have 25/36 of the original left never having had a 6. Then 125/216, then 625/1296 etc. As decimals, these will be 1, 0.83333, 0.694444, 0.5787, 0.482253 … After the 4th round, so 20 minutes, you can see that the number left that have never had a 6 goes from 0.57 to 0.48, so half the dice are gone.
If I put all the dice back in the bag, and start again, I will get the same basic result. The individual dice that come up a 6, and the number of throws they take to come up a 6 will be different, but the basic fact that 1/6 of the total will come up a 6 on each throw will still be the case.
Obviously this depends on there being a lot of dice. If I start with 10, random chance will mean the results are different. If I start with 1000, though, I will get predictable results. If I start with a billion (1000000000), the results will be very even. If I start with a billion, do 4 throws so I have 4822530000 or so left, I will still see the same pattern for the next 4 throws. And so on.
In 250g of Uranium, there are over 600000000000000000000000 atoms of Uranium present. That is a very big number indeed.
Radioactive decay is like rolling a dice. Any one atom could decay at any one time, and there is no way to predict which one will, or in which order. There is nothing special about any one of them. What matters is that there is a truly huge number of them, and then the statistical probability wins.
Each individual atom as a certain probability of decaying. Take a very large group of atoms and it becomes very predicable.
We made up the idea of a half life because its a simple way of classifying activity. Easier to say half will be gone in x years instead of each atom has a .00000…1% chance of decaying today.
Statistics. It’s not a ‘specific half’ that decays. It’s just that you statistically expect 50% of the uranium to decay after 4.5 billion years, based on the chance of any given uranium atom to decay within a year. You don’t know which half will decay, just that it’s likely to be very very close to half.
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