Because radiation is in a way unpredictable, we can not say when decay happens, we can only measure a probability for it.
Half life is basically the point where there is 50% chance for the atom to have decayed. After that point, no matter how many atoms you have, it is more likely that half of them have decayed than not.
Now there is nothing that says that there must be. They could all decay at once or last for an eternity.
And since probabilities get really hard to work with after a while. It is easier to consider half life steps. Each step is half of the last. So half, fourth, eight.
The fundamental problem is that an individual atom is unpredictable. But law of large numbers, make a mass more predictable. So half life is just the point, where it is 50% chance for decay to have happened. Therefor it is the point where in a mass 50% probably have decayed.
From this we can predict the by products and energy release, and be fairly confident about it. There is nothing saying that it must have happened. It could all decay at once or not at all, it is just very improbable.
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