# Carbon dating half life worksheet

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. Scientists call that time its "*half*-*life*."Living things constantly replenish the *carbon* in their bodies, animals from food, plants from the atmosphere, but after death, that process stops.The amount of **carbon**-12 stays the same, but the **carbon**-14 decays away, at a constant rate, making **carbon**-14 a ticking atomic clock.Meet paleoclimatologist Scott Stine, who uses radiocarbon *dating* to study changes in climate. What we think of as normal *carbon* is called *carbon*-12: six protons plus six neutrons. Several times a year, scientist Scott Stine travels to the shores of Mono Lake, near Yosemite National Park. He's studying the long history of droughts in California, trying to determine how frequently they occur and how long they last.Find out what it means for an isotope to be radioactive and how the *half*-*life* of *carbon*-14 allows scientists to date organic materials. But about one percent of *carbon* atoms have an extra neutron, giving them seven. Over the millennia, the water level has risen and fallen, as the area has cycled between wet periods and dry times. During times when the climate was dry, Mono Lake dropped down, exposed the shore lands, and allowed trees and shrubs to grow. 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?

If a fossil contains 60% of its original **carbon**, how old is the fossil? That means this is how long it takes for **half** the nuclei to decay.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. But the question is, when does an atom or nucleus decide to decay? So it could either be beta decay, which would release electrons from the neutrons and turn them into protons. And normally when we have any small amount of any element, we really have huge amounts of atoms of that element. That's 6.02 times 10 to the 23rd **carbon**-12 atoms. This is more than we can, than my head can really grasp around how large of a number this is. Unlike the other natural isotopes of *carbon*, *carbon*-14 is unstable. One of its neutrons turns into a proton and spits out an electron.Now, with seven protons instead of six, it's turned into nitrogen. And scientists know exactly how long it will take for **half** of any amount of **carbon**-14 to decay away.