I’m sure there is an easy answer to this, but for some reason I can’t wrap my head around how a sample of an element can ever decay all the way to zero, when measured in half lives. It seems like you could always split a number in half, it would just be infinitesimally small.
In: Chemistry
The half-life is a friendly rewording of “the time in which a single atom has a 50% chance of decaying”. And this time exists for a single atom, and this time exists for every atom in a heaping pile, and in theory it’s the same time unless you make a critical mass or something.
And if you divide the half-life by ln(2), you get the [average lifetime](https://en.wikipedia.org/wiki/Exponential_decay#Mean_lifetime) of an atom. (The average lifetime can be more statistically useful than the 50% time.)
But remember you can be 100% sure that your coin is 50/50 fair, yet you can never be 100% sure that 8 coinflips will return 4 heads. In the same way, you can never be sure that all atoms in your sample will decay away. There is a probability that some will remain, and in a million billion zillion years, it will decay infinitesimally close to zero, but it will never be certain.
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