Carbon dating is one of science's most elegant applications of nuclear physics to archaeology. By measuring the fraction of radioactive carbon-14 remaining in a once-living sample and using its known half-life of 5,730 years, scientists can calculate when that organism died — reliably dating materials up to about 50,000 years old.
What is carbon-14?
Carbon exists in three isotopes: the two stable isotopes carbon-12 (¹²C, 98.9%) and carbon-13 (¹³C, 1.1%), and the radioactive isotope carbon-14 (¹⁴C), which is present in trace amounts in the atmosphere.
Carbon-14 has 6 protons and 8 neutrons (mass number = 14). It is unstable because the extra neutrons make the nucleus radioactive. It decays by beta-minus decay:
¹⁴₆C → ¹⁴₇N + e⁻ + antineutrino
A neutron converts to a proton, emitting a beta particle and a nitrogen-14 nucleus is formed. The half-life of carbon-14 is 5,730 years — in any sample of C-14, half the atoms will have decayed after 5,730 years.
How is carbon-14 produced in the atmosphere?
Carbon-14 is continuously created in the upper atmosphere through the interaction of cosmic ray neutrons with nitrogen-14:
¹⁴₇N + n → ¹⁴₆C + p
Cosmic rays are high-energy particles arriving from space, mainly protons. When they collide with atoms in the upper atmosphere they produce cascades of secondary particles, including neutrons. These neutrons strike nitrogen nuclei (the most common gas), converting them into carbon-14 and releasing a proton.
The carbon-14 quickly oxidises to carbon dioxide (¹⁴CO₂) and mixes throughout the atmosphere. The rate of production is roughly balanced by the rate of decay, so the fraction of carbon-14 in atmospheric CO₂ has been broadly stable for hundreds of thousands of years — approximately 1.2 × 10⁻¹² (one in a trillion carbon atoms).
How do living organisms absorb carbon-14?
All living organisms absorb carbon-14 during their lifetime:
- Plants fix CO₂ from the atmosphere during photosynthesis, incorporating ¹⁴CO₂ alongside ¹²CO₂. The ratio of C-14 to C-12 in plant tissue matches the atmospheric ratio.
- Animals eat plants (or eat animals that ate plants), so the C-14/C-12 ratio in their tissues also mirrors the atmospheric ratio.
While an organism is alive, it continuously takes in and expels carbon (through eating, breathing, and metabolism), so the C-14/C-12 ratio remains constant — equal to the atmospheric ratio.
What happens when an organism dies?
At death, carbon exchange stops. The organism no longer takes in carbon, so:
- The amount of stable C-12 in the sample stays constant
- The amount of C-14 decreases through radioactive decay
Over time the C-14/C-12 ratio falls. By measuring how much the ratio has dropped compared with the known atmospheric ratio, scientists can calculate how long ago the organism died.
How do you calculate the age of a sample?
Using the half-life formula:
N = N₀ × (½)^(t / t½)
where:
- N = current amount of C-14
- N₀ = original amount of C-14 (assumed equal to the atmospheric ratio)
- t = time since death (what we want to find)
- t½ = half-life of C-14 = 5,730 years
Worked example:
A piece of ancient wood has 25% of the C-14 activity of a living sample. How old is it?
After 1 half-life (5,730 years): 50% remains After 2 half-lives (11,460 years): 25% remains
The wood died approximately 11,460 years ago.
Summary of C-14 remaining versus time:
| Half-lives elapsed | Time (years) | C-14 remaining (%) |
|---|---|---|
| 0 | 0 | 100 |
| 1 | 5,730 | 50 |
| 2 | 11,460 | 25 |
| 3 | 17,190 | 12.5 |
| 4 | 22,920 | 6.25 |
| 5 | 28,650 | 3.125 |
After about 8–9 half-lives (45,000–50,000 years), C-14 levels become too low to measure accurately with current instruments.
What are the limitations of carbon dating?
Carbon dating is highly accurate for materials within its range but has important limitations:
- Range limitation — reliable only up to about 50,000 years. For older samples, virtually no C-14 remains, making measurement impossible.
- Assumes constant atmospheric C-14 — this is broadly true but not perfectly constant. Changes in cosmic ray flux, Earth's magnetic field, and recent burning of fossil fuels (which dilute atmospheric C-14 with non-radioactive carbon) cause small errors. Scientists use calibration curves based on tree rings and other records to correct for these variations.
- Contamination — modern carbon can contaminate an old sample (e.g. through fungal growth, handling, or conservation treatments), making it appear younger than it is.
- Only works for organic materials — pottery, metal, stone, and inorganic materials cannot be dated by C-14. Other radioactive dating methods (potassium-argon, uranium-lead) are used for these.
Frequently asked questions
Why is carbon-14 useful for dating but carbon-12 is not?
Carbon-12 is stable — it does not decay. Without a decrease over time, it cannot act as a clock. Carbon-14 decays at a known, constant rate (half-life 5,730 years), so measuring how much has decayed tells you elapsed time. The key is that C-14 is replenished during an organism's life but not after death, making the moment of death the starting point of the clock.
Why can't carbon dating be used for dinosaur fossils?
Dinosaurs died approximately 66 million years ago. After about 10 half-lives (~57,300 years), less than 0.1% of the original C-14 would remain; after 100 half-lives, the amount is vanishingly small — far below detection limits. Any C-14 detected in a supposed dinosaur fossil would indicate modern contamination, not surviving original carbon. Palaeontologists date dinosaur fossils using different radiometric methods, such as uranium-lead dating (uranium-238 half-life: 4.47 billion years) of the rock layers surrounding the fossil.
How do scientists know what the original C-14 level was?
Scientists assume the original C-14/C-12 ratio was the same as today's atmospheric ratio — which is approximately true over the past ~50,000 years. To account for small historical variations, they use calibration curves constructed from samples of known age (tree rings dated by counting; corals; cave formations; varves — annual sediment layers). The current internationally accepted calibration curve, IntCal20, is based on measurements from thousands of tree rings going back 55,000 years and corrects for known fluctuations in atmospheric C-14.
Is carbon dating ever used in forensics?
Yes — carbon dating has forensic applications. The atmospheric C-14/C-12 ratio changed dramatically after 1950 due to above-ground nuclear weapons testing, which roughly doubled atmospheric C-14 between 1955 and 1963 (the "bomb spike"). Living tissue incorporates this elevated C-14. By measuring C-14 levels in human tissues (such as tooth enamel or eye lens), forensic scientists can estimate when someone was born and even when specific tissues formed, helping identify unknown victims and detect fraudulent claims of age.
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