###### By Don Lincoln, Ph.D., Fermi National Accelerator Laboratory (Fermilab)

## Take a closer look at the process of carbon 14 dating and find the answers to some of the foundational questions such as, what are the existing ratios of different isotopes of carbon? How does carbon 14 come into existence and propagate across the food chain? And, why can carbon 14 dating equations only be used to age organic materials?

### The Carbon 14 Dating Equation

If a sample has some quantity of carbon 14, five half-lives later, just shy of 29,000 years, only about 3% of the original carbon 14 will remain. Thus, if one knows how much carbon 14 an object once had and then how much left is measured, then just how old it is can be figured out.

It can simply be written that the percent remaining equals 100% times 1/2 raised to the n power. N is simply the number of half-lives.

And, for a percentage of remaining carbon 14, the number of half-lives can be figured out by the equation: That means take the log of the remaining percentage, subtract the log of 100 and then divide the entire thing by the log of a half. And, if you want to turn that into years, you simply multiply the number of half-lives by the number of years per half-life and, voila! Instant years!

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### The Limitation of the Equation

This equation, while correct, is not super useful. It would require that somehow all of the nitrogen that came from carbon 14 decays would be able to be collected. And since old objects, for example, a mummy, a mammoth, or a mermaid, are not found in sealed containers, one cannot know how much carbon 14 has decayed just by looking at the carbon 14. Hence, a broader study is needed.

### Delving Deeper into the Ratios of Different Carbon Isotopes for Carbon 14 Dating

Among the three known carbon isotopes, carbon 12 and 13 are stable. That means that when they are made, they do not change. Carbon 14, on the other hand, is radioactive and it decays.

So, this can be pursued by covering the ratios of the three different kinds of carbon. What fraction is carbon 12? What fraction is carbon 13? And what fraction is carbon 14? It turns out that carbon 14 is very, very, very rare. Carbon 12 is about 99% of the carbon in the atmosphere, while carbon 13 is about 1%. So, how much is carbon 14?

It is super tiny, just one carbon 14 atom per every one to one-and-a-half trillion carbon 12 atoms. So, what it means is that if a walnut that just fell from a tree were to be picked up and tested for carbon 14, it starts out with a carbon 14 content of about one in a trillion. Then, after 5,730 years, it would have one carbon 14 atom out of 2 trillion carbon atoms.

Wait 11,460 years and the nut would have one carbon 14 atom out of 4 trillion carbon atoms, and so on.

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### Why Does Carbon 14 Not Decay Completely?

The world of measuring carbon 14 concentrations is a very precise one. That actually might be an understatement. However, if carbon 14 is radioactive and decays, then that means that after a long time, there should be no carbon 14 in the atmosphere. It would all have decayed away. The fact that it is still to be found in the atmosphere means that there must be some sort of way to make it. How does that work?

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### The Creation of Carbon 14

Carbon 14 originates in the air above us. Cosmic rays from space slam into the Earth’s atmosphere. Cosmic rays are just high energy protons generated in supernovae and other complicated astronomical phenomena. These cosmic rays constantly bombard the atmosphere.

It is not so easy to explain in detail what happens when the protons slam into the Earth. It is pretty complicated. But one of the outcomes is that these collisions make neutrons that are more or less stationary, just floating around in the air maybe five or 10 miles away. Now the Earth’s atmosphere is a mixture of gases, mostly nitrogen and oxygen, with nitrogen being about three times more common than oxygen. And what happens is the neutron eventually bumps into a nitrogen atom and turns into carbon 14.

So, that is where carbon 14 comes from. Every second of every day, carbon 14 is created by these collisions. And the rate can even be calculated. It turns out to be about, on average, 17,000 atoms per every square meter of the Earth’s surface per second. The Earth is big and the year is long, but if all that is combined together, it works out to be a measly 11 pounds of carbon 14 made in the atmosphere every year.

Carbon 14 is not created uniformly over the Earth’s surface. It is preferentially made near the Earth’s poles for the same reason that the auroras are found there. That reason is because the Earth’s magnetic field guides cosmic rays to the poles. But the carbon 14 gets mixed in due to the winds.

### The Dispersion of Carbon 14

It does not take all that long to mix either. Carbon 14 that is made today will be dispersed pretty well on a time scale of a handful of weeks. The total amount of carbon 14 on Earth is not all that large. Most of it is in the Earth’s oceans, but something like 1800 pounds of carbon 14 is found in the atmosphere. It really is a trace substance in the world’s ecosystem.

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### Why Is Carbon 14 Used to Date Only Living Things?

To explain how carbon 14 can be used to date living things and not other things, like rocks or swords, and so forth. Basically, carbon gets into living things because of food. It is not that it is breathed in and it somehow gets stuck inside the body. It is because things that have carbon 14 in them are eaten.

For instance, plants bring in carbon dioxide from the air around them. They toss in some sunlight, a splash of water, a dollop of phosphorus, nitrogen, and some trace elements and they make plant tissue. The carbon in the grass in someone’s yard or the park they visit has come from carbon dioxide in the air. And that carbon is carbon 14 about one or two times for every trillion carbon atoms.

So, if grass contains carbon 14 and cows eat grass, the cows are made of carbon 14. And, of course, if people eat cows then they are made of carbon 14, in small doses of course. And, other things that contain carbon 14 are wood, leather, fur coats, discarded bones, shells, woolen and cotton textiles, etc. Basically, any plant that grew or any animal that ate a plant, or even one that ate an animal that ate a plant, all of these contain carbon 14 in the ratio of one or two parts per trillion.

Now think about what happens when a tree is cut down. A once-living plant is killed and its metabolism is stopped. That means it does not bring in any new carbon 14. And what does carbon 14 do? It starts decaying. And this is how carbon 14 works. Cosmic rays from the atmosphere make carbon 14 that is eaten by grass, then cows, then us, and then it decays away.

### Common Questions about Using Carbon 14 Dating

**Q: Can a living human be carbon dated?**

No, carbon 14 works on the basis of carbon 14 depletion ratio to other carbon isotopes, which starts only after the death of the organic matter.

**Q: How is carbon 14 used to date fossils?**

Carbon 14, a radioactive isotope of carbon, is used to measure the age of an ancient fossil. Since the depleting carbon 14 content is present in all the living things, it can be reliably used to measure the age of a fossil.

**Q: How far back is it possible to carbon date?**

The halving period for carbon 14 is 5,730 years. And after nine halving periods or 50,000 years, the carbon 14 content becomes too little to ascertain the age of a specimen.

**Q: How is carbon dating calculated?**

The exponential decay equation, N (t) = N_{0}e ^{kt}, can be used to calculate the decay of carbon 14.