1. The basic science of radiocarbon dating Marco Ricci
Chambéry, 05 May 2018

2. The atomic model - 1
As a first approximation, we can think atoms as made of a small central nucleus (positively charged) with one or more electrons (negatively charged) revolving around it. The nucleus is made of one or more protons which carry the positive charge and, typically, of a similar number of neutrons without any electric charge. From any practical point of view, protons and neutrons account for virtually all the atom mass.

3. The atomic model - 2
The number of protons in the nucleus univocally defines to which chemical element an atom belongs and its place in the Periodic Table of the elements. E.g.:
all atoms with 6 protons in their nucleus are carbon atoms;
all carbon atoms have 6 protons in their nucleus.
However, the atoms of any element can occur in several forms differing for different numbers of neutrons and, as a consequence, for their mass. Since these different forms have the same number of protons, they belong to the same chemical element and occupy the same place in the Periodic Table: they are referred to as isotopes (from the Greek ἴσος τόπος, same place).

4. Radioactivity
Many isotopes are perfectly stable but those with too many or too few neutrons are not, and undergo radioactive decay, a process by which they lose energy by emitting particles or radiation.
Radioactive decay is a stochastic (i.e. random) process and it is impossible to predict when any particular atom will decay. However, the decay rate of a large collection of atoms is fully described in terms of their half-life, the time required for a quantity of a radioactive isotope to reduce to half its initial value.
The radioactive decay occurs at a rate proportional to the number of radioactive nuclei and is described by the equation:
dN/dt = - λ N
N = number of the nuclei
t = time
λ = constant (decay constant)
… and its solution is:
N(t)/N0 = e-λ t
N(t) = number of residual radioactive
nuclei at time t
N0 = initial number of radioactive nuclei
e = 2.718…
Half-life = t1/2 = ln 2/λ ≈ 0.693/λ
A colourful account of the discovery of the radioactivity and isotopes is provided in chapters XXI, XXIII and XXIV of
O. Sacks, Uncle Tungsten. Memories of a Chemical Boyhood, 2001 (Italian: Zio Tungsteno, Adelphi 2002).

5. Carbon isotopes Carbon occurs in nature into three different isotopes:
12C a stable isotope with 6 protons and 6 neutrons in the nucleus. It accounts for ca % of all carbon atoms.
13C a stable isotope as well, with 6 protons and 7 neutrons in the nucleus.
It accounts for ca. 1.1% of all carbon atoms.
14C with 6 protons and 8 neutrons in the nucleus. It is an unstable isotope,
i.e. a radioactive one (‘radiocarbon’). It is also very rare: ca %
(one or two atoms out of 1012) of all carbon atoms.
stable stable radioactive

6. 14C in the atmosphere - 14C decays into nitrogen through beta decay:
146C → 147N + e- + νe
14C has a half-life of 5730 ± 40 years, so its concentration in the atmosphere should substantially decrease over few thousands of years.
so its concentration in the atmosphere might be expected to reduce substantially over thousands of years.
However, 14C is constantly produced in the upper atmosphere where incoming cosmic rays, colliding with air atoms, undergo various transformations, some of which produce neutrons (n) that, in their turn, can react with nitrogen atoms of terrestrial atmosphere resulting in 14C formation:
147N + n → 146C + p
Thus, 14C atmospheric concentration is kept at a (nearly) stationary value.
Modelling allows to estimate the rate of 14C production at 15,000 to 20,000 14C atoms*m−2*s−1. After its production, 14C quickly reacts with atmospheric oxygen to form carbon dioxide (14CO2). -

7. The principle of the datation
During their life, plants exchanges carbon with the environment, mainly by fixing CO2 through photosynthesis and by emitting it by respiration. Since they fix both 12CO2 and 14CO2, the carbon they contain has the same proportion of 14C as the atmosphere. The same holds for animals which assume 14C by feeding on plants. Once plants or animals dye, however, they stop to get 14C which, in their biological tissues, will gradually decay, so that the ratio [14C]/[12C] will continuously decrease. Since we know the rate at which 14C decays, this ratio can be used to determine how long it has been since a given sample of plant or animal origin stopped exchanging carbon: the older the sample, the less 14C and the smaller [14C]/[12C] ratio will be found. Thus we can date samples of plant or animal origin such as wood, charcoal, bones, ivory, paper, textiles, etc. (

8. Is it really that simple ?
No! It is not. Indeed, some assumptions the method relies upon are not always verified. E.g.:
14C concentration in the atmosphere is not really constant. Rather, the 14C production rate changed in the past due to variations in the solar activity (and, hence, in the neutrons formation rate) and in the intensity of the Earth’s geomagnetic field which offers some shields from cosmic rays and which changes on the k-years scale. Furthermore, huge volcanic eruptions (and burning of fossil fuels as well) release in the atmosphere, as CO2, large amounts of ancient carbon, deprived of 14C isotope. On the other hand, tests of nuclear weapons in the ‘60s greatly enhanced the 14C amount (ca. 2x in the Northern hemisphere; 1.5x in the Southern one).
14CO2 behaves (slightly) differently from 12CO2 in the photosynthetic process.
Sample contamination by modern carbon decreases its apparent age: appropriate cleaning is important.
Most of these issues are effectively dealt with by the researchers but, in few cases, some uncertainty may still survive.

9. The measure: counting electrons
14C Decay involves the production of electrons (beta rays): 146C → 147N + e- + νe There are several methods to count the electrons, including the well known Geiger counters. These methods only rely upon the small fraction of 14C atoms which decay during the experiment. In order to get meaningful results, samples weighing at least 8-10 grams and up to 2 days of measurement are typically required. -

10. The measure: AMS (Accelerator Mass Spectrometry)
AMS measures the 14C/12C ratio directly, instead of the sample radioactivity.
The sample is initially burnt to transform its carbon into CO2. Further work-up allows to get electrically charged particles (ions) to be injected into a magnetic field which deflects and separates them according to their mass*: ions of the same mass undergo the same amount of deflection and can be counted by suitable devices.
A high-energy ions accelerator provides
the high resolution needed to distinguish
14C from other atoms or molecules very
close in mass, such as 14N, 13CH and 12CH2.
A significant fraction of all the 14C atoms
is used (instead than the few decaying during
the experiment), which allows to analyse
small samples, even less than 1 mg.
Very complex and sophisticated
experimental set-up: see next slide for few
more details.
* More precisely, according to their mass-to-charge ratio.
An AMS instrumentation at the Lawrence Livermore
National Laboratory, California (

11. Key features of AMS (https://bioams. llnl
Samples are burnt to produce CO2, then catalytically reduced to graphite. Bombardment by a Cs+ beam forms negative atomic or molecular ions (14N does not form stable negative ions).
A molecular disassociation step converts the negatively charged molecular ions into positively charged atomic nuclei.
High energies (MeV) provide the necessary resolution to distinguish 14C from other atoms or molecules very close in mass, such as 14N, 13CH and 12CH2.
14C ions are counted one by one
in a particle detector; more
abundant 12CH2 and 13CH are
measured as electrical
currents.
AMS tandem accelerator at ETH, Zürich (

12. Who made this possible?
W. F. Libby ( ) (
Willard Frank Libby (USA; ) received the 1960 Nobel Prize in Chemistry "for his method to use carbon-14 for age determination in archaeology, geology, geophysics, and other branches of science”.
“Seldom has a single discovery in chemistry had such an impact on the thinking in so many fields of human endeavor”
The Nobel Committee (1960)