Radioactive elements have half-lives. That is, over a period of time specific to the radioactive isotope, half of the original sample will have decayed. Repeat that period and half of the remaining half will have decayed and so on.
Now, I know I have to be wrong about this but nevertheless it remains a thought I've had because I don't know how to go about finding the answer to my question nor do I know if the answer would require knowledge of the kinds of mathematics that go WAY beyond my capacity to understand.
The thing is, take a sample of the standard element for dating old organics: Carbon-14. 14C is radioactive and decays into stable nitrogen-14 via beta decay (that is, a neutron emits an electron and antineutrino, becoming a proton and upping the element by one). The half life of this isotope is approximately 5,730 years.
Now here's the thing...
After 5,730 years a sample of carbon-14, say ten pounds worth, will have gone through the first of its half-lives leaving five pounds of carbon-14 and five pounds of nitrogen-14. Now I'm guessing this might violate the Heisenberg Uncertainty Principle but if you could (somehow) isolate the half of the carbon-14 from the original ten pound sample that did not decay, would you now be in possession of a five pound sample of carbon-14 that is not radioactive? Or at least not radioactive for 5,730 years?
I know the answer has to be no...but why is it no? I can't help but feel that if one could somehow be intuitive enough to separate such a sample that it could be done. I also think about stuff like Uranium-238 which has a half-life of almost 4½ billion years. I don't know when the first atoms of uranium were forged but I would have to assume with a half-life of that long, that atoms of uranium-238 from the first supernova that produced them way back when still exist.
What makes certain radioactive atoms more stable than others? What about extremely radioactive elements like astatine which has no stable isotopes and the longest lived one is measured in hours? Are some of astatine-210's atoms (and I am probably using the wrong word) meta-stable and could conceivably last the lifetime of the universe?
The nature of the basic math behind half-lives suggests that it is impossible to get rid of all the original sample. Atoms are small so if you have a mole of astatine-210 (which has never been witnessed by the way...I hear such a sample if it could somehow be synthesized would explode from the heat of its radioactivity), with a mole being some 6 x 1023 atoms (a HUGE number), how many times could you divide such a sample in half and still be left with a number greater than 1? Maybe not as many times as I suspect (I don't feel like doing the algebra right now), but it would still be quite a number of divisions meaning some of those atoms will last a lot longer than 8.1 hours. Some potentially for years.
I wonder why that is so? Why are some radioactive atoms more (temporarily) stable than others?
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