[eli5] If a half-life is the amount of time it takes for a radioactive substance to lose half its radioactivity, and this number is constant no matter how much radiation remains, will there come a time when the substance loses all radioactivity?
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Sort of. First, when we say a “substance loses its radioactivity” remember that we are talking about some radioactive element becoming a different element. That “different element” (the decay product) can also be radioactive and have a completely different half-life.
Speaking strictly in terms of one specific radioactive element, then yes, there will come a time when all atoms of that element have decayed into something else and, if its decay products are also radioactive, a time when it arrives a stable, non-radioactive element.
We just can’t ever say when that will be, which is why we have to use half-lives.
Yes, the substance is made of a finite, albeit large, number of atoms. When you’re down to only one atom, there is a 50% chance it will decay over the next half-life of time. Eventually, however, it decays and you are left with nothing radioactive.
Halflife works on a large scale because of the law of large numbers in probabilities.
If you have a 1 kg mass of Uranium, you have roughly 2.5 * 10^(24) atoms. All of those atoms independently have a chance to decompose, but there are just so many of them that any variance is such a small amount that it’s kind of irrelevant.
When you get down to very small amounts, then you don’t have the law of large numbers helping out. Each atom can individually decay. However, when you’re at that kind of low amount, then the effects of single atoms are very hard to even notice.
Yes, the half-life is a stochastic number. It’s an expression of a probability. Simplified one can say that for 1 atom there’s a 50/50 chance (like a coin flip) that it will have decayed within 1 half-life.
If you have a lot of atoms that means that around half of them will have decayed after 1 half-life and the others will remain. If we have 1 000 000 000 atoms the chance is extremely high that around 500 000 000 atoms will be left over. Roughly the same amount of heads and tails you got from flipping your coin 1 000 000 000 times.
That all of the atoms or none at all have decayed after that time is in theory a possibility, but it’s absurdly small, especially considering that my numbers are peanuts compared to the actual amount of atoms in just a few grams. Imagine flipping a coin 1 000 000 000 times and every single time it shows heads.
As you have less and less atoms left over, this changes though. With just 5 atoms the chance that no or all atoms decay (5 coin flips show heads) is still pretty small, but not unimaginable. Then as they become less and less it becomes increasingly more expected that all of the atoms left over fall apart with the next set of coin flips.
With that wall of text written down, there is still the matter of decay products. The fragments that the original atoms have fallen apart into can also be radioactive and the whole numbers game will begin from the start, only with different half-lives.
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