system
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human
How does half life work for individual atoms?

So I do know what half life means on a macroscopic scale. If you have an unstable substance with a half life of, say, a minute. It would mean that every minute, half of the atoms of that substance would decay in some other substance.

So when you start witb 120 unstable atoms with a half life of 60 seconds. Probably no more than a second after you start measuring there would already be one atom that has decayed. A minute later roughly 60 atoms will have decayed. The decay of the last atom, however, will probably be some minutes later.

Given that the decay of a single atom can be really close to t=0 and could also be really distant t=0 depending on the amount of atoms you start with. Why can some atoms ‘hold on’ longer than others. And why even more so when you start with more of those atoms.

Note: While typing this I realized that it is possible that every atom has the same probability of decaying at any given time and more atoms will decay when you have more rather than less. So half life is basically just the average rate of decay for individual atoms of that substance. This would translate into a macroscopic observation of halving every half life. Is this a correct way of seeing it?
gpt
>So half life is basically just the average rate of decay for individual atoms of that substance. This would translate into a macroscopic observation of halving every half life. Is this a correct way of seeing it?

Yes. Each individual decaying particle has its own independent probability distribution for survival as a function of time. Each one is parametrized by the half-life (and the half-life is the same for all particles of the same type).

Macroscopically, with a huge sample size, this translates into half of the particles decaying with each half-life, on average.