Radiocarbon age is just a number

Abstract

The idea of radiocarbon existing at equilibrium within Earth’s atmosphere has established radiocarbon dating. Adam Fleisher takes a look at its beginnings, achievements and limitations.

Once a living thing stops taking up carbon, what remains will act as a radioactive version of one of those beeping clocks from the most dramatic scene in an action movie and begin to tick down. Every clock ticks at its own rate. For radionuclides like ¹⁴C, this rate is inversely proportional to the half-life. As recommended by the Decay Data Evaluation Project, an international collaboration of metrologists, the radiocarbon half-life is (5700 ± 30) years¹. When the half-life and the background radiation levels are known, radiocarbon dating is achieved by either measuring the ¹⁴C activity or the number of ¹⁴C atoms from a sample.

The idea of radiocarbon dating is attributed to Willard Libby. In 1947, he and his colleagues reported² that enriched biomethane samples taken from a sewage plant did contain ¹⁴C. On the contrary, samples of methane derived from fossil fuels showed no detectable radiocarbon levels: ‘old’ carbon was essentially ¹⁴C-free, whereas ‘living’ carbon was not.

Assigning a ¹⁴C age somewhere between ‘living’ and ‘old’ required knowledge of the rate at which the radioactive clock ticks. But in the 1940s — only a decade after its discovery — estimates of the radiocarbon half-life were wide-ranging and highly uncertain³. Libby and colleagues established the first precise value of (5720 ± 47) years by comparing ¹⁴C ages against known ages of samples such as deck boards from an ancient Egyptian funerary boat⁴.

A few years later, a consensus value of (5568 ± 30) years emerged³, known as the Libby half-life. This value was used in the 1960s to date artefacts such as the Lake Nemi ships — attributed to Roman emperor Caligula — and is still in use today. But the Libby half-life differs significantly from the value recommended by the Decay Data Evaluation Project. So, is there chaos in precision dating using radiocarbon?

The answer is simple: the exact value of the ¹⁴C half-life is not needed. Instead, conventional ¹⁴C ages — those calculated from decay counting or atom counting using the Libby half-life — are calibrated with dendrochronology — tree-ring dating — used in combination with other methods including sedimentary layer counting and coral dating.

Chronologies do not only provide empirical correction functions. They also reveal breakdowns in Libby’s basic assumption of constant rates of cosmic ¹⁴C formation and reservoir exchange, which impact studies across a range of fields in physics. This is particularly true the further back in time that we look using the ¹⁴C half-life⁵. The wandering and switching of Earth’s magnetic field, reservoir effects related to ocean carbon uptake, and ebbs and increases in bombardment of Earth’s atmosphere by cosmic rays all lead to fluctuations in the background ¹⁴C amount. On top of this, the burning of fossil fuels since the Industrial Revolution introduced exclusively ‘old’ carbon depleted in ¹⁴C, and the prolific testing of nuclear weapons in the 1950s and 1960s resulted in a sizable ¹⁴C spike.

In the 1980s, the confluence of accelerator mass spectrometry and improved calibration curves led to an explosion in precision assignment of calendar ages for precious relics, such as the Shroud of Turin⁶. Although calibration solved a practical problem in dating, there is still the fundamental question of an accurate radiocarbon half-life. As an example of its impact, we already discussed that deviations between ¹⁴C ages and calendar ages are indicative of physics-based changes in Earth’s radiocarbon equilibrium. Accurate estimates of these deviations against a modern baseline are therefore valuable.

Libby himself recognized the need to use different measurement approaches to establish half-life accuracy³. Early on, these included solid, liquid and gas decay-counting methods and mass spectrometry atom-counting methods. In the last decade, highly sensitive optical spectroscopy methods have also been applied to low-level ¹⁴C detection. With the aid of quantum chemistry calculations of molecules, optical methods can directly retrieve the ratio of isotopic amounts in a sample. Therefore, accurate and traceable measurements of both activity and number of radiocarbon atoms from the same sample could ultimately provide a complementary determination of the ¹⁴C half-life.

Advanced optical radiocarbon sensing technology is under development at several laboratories around the world. Beyond questions of the radiocarbon half-life, these technologies could also address challenges in climate change mitigation, biomaterials verification, and nuclear emissions monitoring — each an application that may impact the future of radiocarbon sensing and metrology beyond precision radiometric dating.