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 doesn’t, it decays with random chance. After 4.5 billion years a single uranium-238 atom has a 50% chance to have decayed.
There are so many atoms in a sample of uranium, that after 4.5 billion years, almost exactly half of them have decayed. It’s just a matter of statistics.
For any given sample, if you could count every atom, it may vary from sample to sample how many have decayed, but there’s so many that it’s just a rounding error.
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