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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.
Now you could say, OK, what's the probability of any given molecule reacting in one second? But we're used to dealing with things on the macro level, on dealing with, you know, huge amounts of atoms. So I have a description, and we're going to hopefully get an intuition of what half-life means. And how does this half know that it must stay as carbon? So if you go back after a half-life, half of the atoms will now be nitrogen. Then all of a sudden you can use the law of large numbers and say, OK, on average, if each of those atoms must have had a 50% chance, and if I have gazillions of them, half of them will have turned into nitrogen. How much time, you know, x is decaying the whole time, how much time has passed?
Free 5-day trial Radiometric dating is used to estimate the age of rocks and other objects based on the fixed decay rate of radioactive isotopes.
Learn about half-life and how it is used in different dating methods, such as uranium-lead dating and radiocarbon dating, in this video lesson. As we age, our hair turns gray, our skin wrinkles and our gait slows.
These two uranium isotopes decay at different rates. The half-life of the uranium-238 to lead-206 is 4.47 billion years.
It works because we know the fixed radioactive decay rates of uranium-238, which decays to lead-206, and for uranium-235, which decays to lead-207. And maybe not carbon-12, maybe we're talking about carbon-14 or something. And then nothing happens for a long time, a long time, and all of a sudden two more guys decay. And the atomic number defines the carbon, because it has six protons. If they say that it's half-life is 5,740 years, that means that if on day one we start off with 10 grams of pure carbon-14, after 5,740 years, half of this will have turned into nitrogen-14, by beta decay. What happens over that 5,740 years is that, probabilistically, some of these guys just start turning into nitrogen randomly, at random points. So if we go to another half-life, if we go another half-life from there, I had five grams of carbon-14. So now we have seven and a half grams of nitrogen-14. This exact atom, you just know that it had a 50% chance of turning into a nitrogen. 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. Radiometric dating, or radioactive dating as it is sometimes called, is a method used to date rocks and other objects based on the known decay rate of radioactive isotopes.Different methods of radiometric dating can be used to estimate the age of a variety of natural and even man-made materials.