# Carbon dating and half life

### Carbon - Wikipedia

There are several reasons why, but the main reasons is that Carbon is a naturally occurring isotope in all forms of life and its half-life is. Theoretically, if one could detect the amount of carbon in an object, one could establish that object's age using the half-life, or rate of decay, of the isotope. Even though it decays into nitrogen, new carbon is always being formed in the wood decreases with time as it decays into nitrogen with a half-life of about.

And let me erase this stuff down here. So I have a description, and we're going to hopefully get an intuition of what half-life means. So I wrote a decay reaction right here, where you have carbon It decays into nitrogen And we could just do a little bit of review.

You go from six protons to seven protons. Your mass changes the same. So one of the neutrons must have turned into a proton and that is what happened. And it does that by releasing an electron, which is also call a beta particle. We could have written this as minus 1 charge.

It does have some mass, but they write zero.

This is kind of notation. So this is beta decay. Beta decay, this is just a review. But the way we think about half-life is, people have studied carbon and they said, look, if I start off with 10 grams-- if I have just a block of carbon that's 10 grams. If I wait carbon's half-life-- this is a specific isotope of carbon. 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.

And the atomic number defines the carbon, because it has six protons. Carbon has six protons. But they have a different number of neutrons.

### Radiocarbon dating - Wikipedia

So when you have the same element with varying number of neutrons, that's an isotope. So the carbon version, or this isotope of carbon, let's say we start with 10 grams. If they say that it's half-life is 5, years, that means that if on day one we start off with 10 grams of pure carbon, after 5, years, half of this will have turned into nitrogen, by beta decay. And you might say, oh OK, so maybe-- let's see, let me make nitrogen magenta, right there-- so you might say, OK, maybe that half turns into nitrogen.

**How Carbon Dating Works**

And I've actually seen this drawn this way in some chemistry classes or physics classes, and my immediate question is how does this half know that it must turn into nitrogen? And how does this half know that it must stay as carbon? And the answer is they don't know. And it really shouldn't be drawn this way. So let me redraw it. So this is our original block of our carbon What happens over that 5, years is that, probabilistically, some of these guys just start turning into nitrogen randomly, at random points.

So if you go back after a half-life, half of the atoms will now be nitrogen. So now you have, after one half-life-- So let's ignore this. So we started with this. All 10 grams were carbon. This is after one half-life. And now we have five grams of c And we have five grams of nitrogen Let's think about what happens after another half-life.

So if we go to another half-life, if we go another half-life from there, I had five grams of carbon So let me actually copy and paste this one.

This is what I started with. Now after another half-life-- you can ignore all my little, actually let me erase some of this up here. Let me clean it up a little bit. After one one half-life, what happens? Well I now am left with five grams of carbon And by the law of large numbers, half of them will have converted into nitrogen So we'll have even more conversion into nitrogen So now half of that five grams.

### BBC - GCSE Bitesize: Uses of half life

So now we're only left with 2. And how much nitrogen? Well we have another two and a half went to nitrogen. So now we have seven and a half grams of nitrogen And we could keep going further into the future, and after every half-life, 5, years, we will have half of the carbon that we started.

## Half-life and carbon dating

But we'll always have an infinitesimal amount of carbon. But let me ask you a question. Let's say I'm just staring at one carbon atom. Let's say I just have this one carbon atom. You know, I've got its nucleus, with its c So it's got its six protons. It's got its eight neutrons.

It's got its six electrons. What's going to happen? What's going to happen after one second? Well, I don't know. It'll probably still be carbon, but there's some probability that after one second it will have already turned into nitrogen What's going to happen after one billion years? Well, after one billion years I'll say, well you know, it'll probably have turned into nitrogen at that point, but I'm not sure.

This might be the one ultra-stable nucleus that just happened to, kind of, go against the odds and stay carbon So after one half-life, if you're just looking at one atom after 5, years, you don't know whether this turned into a nitrogen or not. Now, if you look at it over a huge number of atoms.

I mean, if you start approaching, you know, Avogadro's number or anything larger-- I erased that. I don't know which half, but half of them will turn into it. C ratio in the remains decreases. Comparing this ratio to the C C ratio in living organisms allows us to determine how long ago the organism lived and died.

Image used with permission CC-BY 4. C dating does have limitations. For example, a sample can be C dating if it is approximately to 50, years old. Before or after this range, there is too little of the isotope to be detected. Substances must have obtained C from the atmosphere. For this reason, aquatic samples cannot be effectively C dated.

Lastly, accuracy of C dating has been affected by atmosphere nuclear weapons testing. Fission bombs ignite to produce more C artificially. Samples tested during and after this period must be checked against another method of dating isotopic or tree rings. To calculate the age of a substance using isotopic dating, use the equation below: Ra has a half-life of years. Radioactive Dating Using Nuclides Other than Carbon Radioactive dating can also use other radioactive nuclides with longer half-lives to date older events.

For example, uranium which decays in a series of steps into lead can be used for establishing the age of rocks and the approximate age of the oldest rocks on earth.

- Uses of half life
- 5.7: Calculating Half-Life
- Radiocarbon dating

Since U has a half-life of 4. In a sample of rock that does not contain appreciable amounts of Pb, the most abundant isotope of lead, we can assume that lead was not present when the rock was formed.

Therefore, by measuring and analyzing the ratio of U Pb, we can determine the age of the rock. This assumes that all of the lead present came from the decay of uranium If there is additional lead present, which is indicated by the presence of other lead isotopes in the sample, it is necessary to make an adjustment.

Potassium-argon dating uses a similar method. K decays by positron emission and electron capture to form Ar with a half-life of 1. If a rock sample is crushed and the amount of Ar gas that escapes is measured, determination of the Ar K ratio yields the age of the rock.

Other methods, such as rubidium-strontium dating Rb decays into Sr with a half-life of As ofthe oldest known rocks on earth are the Jack Hills zircons from Australia, found by uranium-lead dating to be almost 4.