Steve Butts said:
Half-Life does not represent the time it takes for a given quantity of radioactive material to decay. It represents the amount of time it takes for half of the quantity to decay. Hence half-life. At the point you reach an isotope's half-life, half of it has become inert. Half of the remaining half decays over the same period, and then half of the half of that half that's left. Then half of that half, etc. (To really break your brain, bring Zeno's Paradox into this.)
Zeno's paradox (The dichotomy paradox to be exact) doesn't apply here because we're not talking about infinately divisable amounts here. We're dealing with atoms. (atom = greek for indivisible). After 79 halflives, for every mol of matter you started out with you are most likely to only have one atom left. After that, for every half-life that passes, the likelyhood that this atom will remain in existance, and not decay, halves.
That can lead to some mind-boggling numbers. Let's say for instance that we assume there is
one atom of Iodine-131 (one of major worries in a nuclear incident/accident) left from the Chernobyl accident. Now I-131 has a half-live of 8.1 days, and the accident happened on april 26, 1986. How much I-131 would have had to be released from Chernobyl in order to have one atom remaining?
24 ½ years * 365.25 days per year = 8900 days. Hm, let's say 8100 days for nice numbers.
8100 days = 1000 half-lives of I-131. 2 ^ 1000 = 10 ^ 301.
Ten to the threehundred and first power... a one followed by 301 zeroes. That is how many atoms we would have had to start out with. That is a truly mindboggling number, which is next to impossible to wrap your head around.
For comparison: the total amount of matter in the obeservable universe is expected to be at approximately 10^80 atoms... ten to the 80:th power. So if our entire universe was just one atom in another universe with as much matter as ours, and every atom in that universe was a universe like ours, full of the same amount of matter, we'd reach 10^160. And again... 10^240... and again... 10^320.
If your brain just exploded, don't worry... it's a normal reaction.
Anyway... conclusion is this: there isn't any left, at all. The last atom of I-131 from Chernobyl vanished even before the Soviet Union crumbled.
/S