Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?
In: 910
Because the “full life” never arrives. It just gets closer and closer to it without ever quite reaching it.
Imagine the equation y = 1/x.
It has values like this:
x y
—— ——-
1 1
10 0.1
100 0.01
1000 0.001
10000 0.0001
No matter how big you make x, y never quite reaches zero. It gets closer and closer to it because the fraction 1/x gets smaller and smaller, but it never quite reaches zero.
There is no such thing as “how big does X have to get in order for Y to fall all the way to zero?” if Y won’t *ever* quite become zero all the way.
If you don’t already know what the graph 1/x looks like, click this link and you’ll see a graph of it: https://www.wolframalpha.com/input?i=y+%3D+1+%2F+x
A phenomenon like this is what radioactive decay is trying to describe. You can’t say “after X years all the radioactive isotopes will be gone and it will be all be done decaying”.
So instead what you can do to describe the “shape” of the decay is to just pick the point where about half of it will be gone. THAT is a point that can actually be reached. In the formula y = 1/x, y will be 1/2 when x gets up to 2.
Now, actual radioactive decay isn’t exactly a 1/x kind of phenomenon, but for ELI5 purposes it gets you the idea.
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Interesting footnote: because matter is made of countable quantum stuff, and not infinitely continuous, technically there *will* eventually be a point where literally all the decay is actually finished, as you cannot have less than one atom of an isotope left. But because there’s an *enormous* number of atoms, we may as well model it as if it’s infinitely divisible because it would be eons before any little chunk of material actually could reach that point.
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