Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?
In: 910
Zeno’s paradox is easy enough for a 5year old.
Go halfway to the wall. Go half of what remains. Go half of what remains. Go half of what remains…. Do it forever. Never reach the wall.
Radioactive materials are radioactive forever. In one half life’s time, activity diminishes by half. It never gets to the wall.
So there’s your answer. With this mathematical model for radiation, the full life for any substance is *forever*.
Now, all you 7 year olds might be smart enough to realize that if you keep halfing you eventually just get down to a single atom. One mole of a substance can be halved 80 times before this point is reached. So, a mole of radium225 ( about a spoonful) with halflife 14.9 days, will be utterly free of ra225 after 1192 days.
The fun don’t stop, though, because many radioactive substances decay into things that are themselves radioactive. On the way to turning into Pb (the stable last link of most heavy radioactive chains) you get a spectrum of decay products, many of which last much longer than ra225.
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