+ **Radiocarbon dating** works out how long ago something living died, by measuring how much [[carbon-14]] is left in it. It reaches back about 50 000 years and it is the reason we can put dates on the human past at all.+ Willard Libby's team developed it in the years after the Second World War, and he won the 1960 Nobel Prize in Chemistry, in the committee's words,++ > for his method to use carbon-14 for age determination in archaeology, geology, geophysics, and other branches of science++ ## The trick++ Carbon-14 is made in the upper atmosphere. [[cosmic ray]]s smash air molecules, the debris includes free [[Neutron]]s, and a neutron hitting ordinary nitrogen swaps a proton out:++ > ¹⁴N + n → ¹⁴C + p++ The ¹⁴C oxidises to CO₂ and mixes through the whole atmosphere. Plants breathe it in. Animals eat plants. Every living thing therefore runs at roughly the same ¹⁴C-to-¹²C ratio as the air — about one ¹⁴C atom in a trillion carbon atoms.++ Death closes the account. No new carbon comes in, and the ¹⁴C that is there starts running down its [[half-life]]. Measure what fraction is left, and you have the time since death.++ ++ ## The nuclide++ | property | value |+ |---|---|+ | half-life | 5700 ± 30 years |+ | mean life | 8223 years |+ | decay mode | β⁻, 100% of the time |+ | decay energy (Q) | 156.4765 ± 0.0037 keV |+ | daughter | ¹⁴N (stable) |+ | natural abundance in living carbon | ≈ 1 part in 10¹² |++ Two things about that table shape the whole method.++ The half-life sets the **range**. After ten half-lives — 57 000 years — a thousandth of the original ¹⁴C remains, and that is below what anyone can separate from contamination. In practice laboratories quote a limit near 50 000 years, about 8.8 half-lives.++ The decay energy sets the **method**. At 156 keV the beta particles are feeble, and the decays are rare: a gram of modern carbon puts out only about twelve betas a minute. Libby had to count them one by one. Modern labs skip the waiting and use **[[accelerator mass spectrometry]]**, which weighs the ¹⁴C atoms directly instead of waiting for them to decay. That cut sample sizes from grams to milligrams and made it possible to date a single seed or a thread of a tapestry.++ ## Two half-lives, one on purpose++ This is the part that trips people up. Libby measured the half-life as **5568 ± 30 years**. Later work put it at **5700 ± 30 years** — about 2.4% higher.++ The field never switched. A "conventional radiocarbon age" is still calculated with Libby's 5568-year value, on purpose, so that every measurement ever published stays comparable. The correction is folded into calibration instead. The other fixed conventions:++ - **BP means "before present", and "present" is AD 1950** — the year radiocarbon dating arrived, and the last year before atmospheric bomb testing wrecked the baseline.+ - Ages are normalised to a δ¹³C of −25‰ to remove the different appetites plants have for the heavier carbon isotope.+ - Results carry a ± because counting decays is a statistical business, not because the lab is being cautious.++ So a radiocarbon age is not a date. It is a raw measurement in a defined unit that then has to be converted.++ ## Calibration: the assumption that isn't true++ The method assumes atmospheric ¹⁴C has always been at today's level. It has not. Cosmic-ray intensity varies with the Sun's activity and the Earth's magnetic field, and ocean circulation moves old carbon around. So a radiocarbon year is not a calendar year.++ The fix is a calibration curve, built by measuring ¹⁴C in material whose true age is known independently — tree rings counted one at a time by [[dendrochronology]], plus corals and cave deposits dated by uranium series. The current standard is **IntCal20**, covering **0 to 55 000 calendar years BP**.++ The size of the correction is not small:++ | calendar age (cal BP) | measured ¹⁴C age | offset |+ |---|---|---|+ | 0 | 199 ± 11 | +199 |+ | 500 | 429 ± 10 | −71 |+ | 1 000 | 1 126 ± 13 | +126 |+ | 2 000 | 2 070 ± 14 | +70 |+ | 5 000 | 4 439 ± 15 | −561 |+ | 10 000 | 8 872 ± 21 | −1 128 |+ | 20 000 | 16 566 ± 45 | −3 434 |+ | 30 000 | 25 664 ± 92 | −4 336 |+ | 40 000 | 34 918 ± 125 | −5 082 |+ | 50 000 | 47 531 ± 354 | −2 469 |++ At the far end of the Ice Age, an uncalibrated result is wrong by more than three thousand years. Anyone quoting a raw radiocarbon age as a historical date is quoting the wrong number.++ ### Plateaus: where the method goes blind++ The curve is not just offset, it is bumpy — and where it flattens, dating stops working. The **Hallstatt plateau** is the notorious one:++ | calendar age (cal BP) | ¹⁴C age |+ |---|---|+ | 2 450 | 2 428 |+ | 2 500 | 2 482 |+ | 2 600 | 2 462 |+ | 2 700 | 2 496 |++ Two and a half centuries of real time compress into about 70 radiocarbon years — less than the measurement error. A sample from anywhere in the European Iron Age calibrates to a wide, flat range and no amount of laboratory precision fixes it. Archaeologists work around it with tree-ring sequences and stratigraphy instead.++ ## Where it breaks++ - **Marine and freshwater samples.** Ocean water carries dissolved carbon that has been out of contact with the atmosphere for centuries, so shellfish and fish-eaters date old. A separate Marine20 curve exists for this.+ - **Volcanic settings.** Vents leak ¹⁴C-free carbon dioxide, and plants growing nearby take it up.+ - **Anything not once alive.** Stone, metal, and pottery clay contain no biological carbon. What gets dated is charcoal in the temper, or soot on the surface, not the object.+ - **Contamination.** A tiny amount of modern carbon on a 40 000-year-old sample shifts it enormously, because at that age there is almost no original ¹⁴C left to be swamped.+ - **Fossil-fuel and bomb carbon.** Burning coal and oil released carbon so old it has no ¹⁴C left, diluting the atmosphere; atmospheric nuclear testing then roughly doubled it in the early 1960s. Both effects make post-1950 material a special case with its own curves — which is also why "present" was frozen at 1950.++ See also: [[half-life]], [[radioactive decay]], [[beta decay]], [[Isotope]], [[Nuclear binding energy]], [[chemical element]].
History of Radiocarbon dating
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