# Radioactive isotopes in carbon dating

When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.The carbon-14 isotope would vanish from Earth's atmosphere in less than a million years were it not for the constant influx of cosmic rays interacting with molecules of nitrogen (N) into organic compounds during photosynthesis, the resulting fraction of the isotope 14C in the plant tissue will match the fraction of the isotope in the atmosphere.After plants die or are consumed by other organisms, the incorporation of all carbon isotopes, including 14C, stops. So with that said, let's go back to the question of how do we know if one of these guys are going to decay in some way. That, you know, maybe this guy will decay this second. Remember, isotopes, if there's carbon, can come in 12, with an atomic mass number of 12, or with 14, or I mean, there's different isotopes of different elements. So the carbon-14 version, or this isotope of carbon, let's say we start with 10 grams. Well we said that during a half-life, 5,740 years in the case of carbon-14-- all different elements have a different half-life, if they're radioactive-- over 5,740 years there's a 50%-- and if I just look at any one atom-- there's a 50% chance it'll decay. Now after another half-life-- you can ignore all my little, actually let me erase some of this up here. So we'll have even more conversion into nitrogen-14. So now we're only left with 2.5 grams of c-14. Well we have another two and a half went to nitrogen. So after one half-life, if you're just looking at one atom after 5,740 years, you don't know whether this turned into a nitrogen or not. At any given moment, for a certain type of element or a certain type of isotope of an element, there's some probability that one of them will decay. If I wait carbon-14's half-life-- this is a specific isotope of carbon. So when you have the same element with varying number of neutrons, that's an isotope. Let's think about what happens after another half-life. And by the law of large numbers, half of them will have converted into nitrogen-14. This might be the one ultra-stable nucleus that just happened to, kind of, go against the odds and stay carbon-14. Radiocarbon dating can be used on samples of bone, cloth, wood and plant fibers.

What's going to happen after one billion years? And then you didn't build your time machine well. So, the fossil is 8,680 years old, meaning the living organism died 8,680 years ago.SAL: In the last video we saw all sorts of different types of isotopes of atoms experiencing radioactive decay and turning into other atoms or releasing different types of particles. So you might get a question like, I start with, oh I don't know, let's say I start with 80 grams of something with, let's just call it x, and it has a half-life of two years. So what we do is we come up with terms that help us get our head around this. So I wrote a decay reaction right here, where you have carbon-14. So now you have, after one half-life-- So let's ignore this. I don't know which half, but half of them will turn into it. And then let's say we go into a time machine and we look back at our sample, and let's say we only have 10 grams of our sample left.

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