Radioactive isotope used for radiometric dating
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Just like your popcorn, radioactive particles have half-lives. But how do we know when the cobalt-60 atoms are going to decay? Initially it may seem like atoms decay randomly, but their probability of decaying can be predicted using an atom's half-life.
Again, after 30 seconds have passed, dump your coins on a table and remove all the 'heads.' Write down how many remain, and continue this process until all your coins have 'decayed.' Notice at the end how you can never have half of a coin, so when you're down to just one or two coins, you can see the probabilistic nature of them decaying.
You may end up shaking one coin for many 30-second half-lives because it just won't decay!
Scientists measure how much carbon-14 is left in a sample, and they are able to estimate how many half-lives it went through.
This will allow them to get an approximate idea of how old the material is. However, many don't pose much of a threat because they have such long half-lives.