How does half life work in carbon dating
Chemically, carbon is no different from non-radioactive carbon atoms, so it ends up in all the usual carbon places — one trillionth of the carbon atoms in air, plants, animals and us are radioactive. All radioactive atoms eventually decay into something more stable, and carbon decays into nitrogen.
For a rare event it happens pretty damn often — one million carbon atoms in your body decay into nitrogen every minute! But don't panic — of the ,,,,,,,, carbon atoms in every one of us, about ,,,, are carbon, so we've got a few to spare. Not only that, we top up our carbon levels every time we eat. And plants top up their radioactive carbon every time they turn carbon dioxide to food during photosynthesis.
It's not that the radioactive carbon in air or food doesn't decay, it does. But something else is going on that keeps producing new carbon — otherwise it would have all turned to nitrogen millions of years ago. Earth's upper atmosphere is constantly being bombarded by cosmic rays usually protons travelling at nearly the speed of light.
When those speedy protons hit atoms you end up with a few stray neutrons zipping around the place. And when one of those energetic neutrons hits a nitrogen atom, the nitrogen spits out a proton.
With an extra neutron and one less proton, that's no longer a nitrogen atom — six protons plus eight neutrons spells carbon The newly formed carbon atoms end up in carbon dioxide, which ends up in plants, which end up on our dinner plates as fruit, veg or a highly processed version of plants known as meat. So the proportion of carbon inside living things is the same as the proportion of carbon in the atmosphere at that time.
How do geologists use carbon dating to find the age of rocks?
But when we stop eating, or when plants stop photosynthesising, our carbon levels no longer get topped up. From the moment we die the proportion of carbon compared to non-radioactive carbon in what's left of our bodies starts to drop as it gradually turns to nitrogen. And the longer dead things lie around, the lower the carbon levels get. If you know the rate that carbon decays at, and how much of the carbon in a shroud, iceman or piece of old wood or bone is radioactive, you can work out how long ago they stopped breathing or photosynthesising.
It just involves a bit of maths. We know that on average it takes an atom of carbon a little over 8, years to decay to nitrogen although you never know when an individual atom is going to decay — it's completely random. We even know that in a gram of carbon, 14 carbon atoms turn into nitrogen every minute. The 14 is a coincidence! But the value that's used to calculate the age of an object isn't an absolute figure, it's a statistical term called half-life.
The half-life of a radioactive isotope is the amount of time it takes for half of the atoms in a sample to decay. Carbon has a half-life of 5, years. That means that no matter how many carbon atoms were present when something died, after 5, years only half of them are left — the rest have decayed to nitrogen.
And after 11, years two half-lives , only a quarter of the original carbon atoms are left. That's why radiocarbon dating is only reliable for samples up to 50, years old. But old age isn't the only thing that affects the accuracy of carbon dating. The level of radiocarbon in the atmosphere has varied over time — it was about two per cent higher 3, years ago, possibly due to factors affecting cosmic rays like changes in solar cycles or the Earth's magnetic field.
And nuclear reactions have seen a leap in carbon activity since Luckily for us we have a record of atmospheric carbon levels for every one of the last 12, years. 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.
How Does Carbon Dating Work
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. 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.
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.
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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.
Half-life and carbon dating (video) | Nuclei | Khan Academy
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.
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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. So now we're only left with 2. And how much nitrogen?