Radiometric dating

Radiometric dating is based on the principle of exponential decay, by which certain atoms called radionuclides undergo nuclear fission, changing their elemental identities in specific ways. The relative amounts of specific radionuclides are identified, permitting the determination of the amount of time that has passed since the formation of the particular sample.

Atoms and Isotopes

According to modern atomic theory, the structure of atoms consists of three basic particles in a specific structural arrangement. These particles are the positively charged proton, the negatively charged electron, and the electrically neutral neutron. Protons and neutrons are essentially equal mass, 1,834 and 1,835 times as massive as an electron, respectively.

According to quantum mechanics, atoms have a small, dense nucleus containing almost all the atom's mass, as protons and neutrons, surrounded by a diffuse cloud of electrons. The atom's identity is determined solely by the number of protons contained in its nucleus. Each neutral atom has an equal number of electrons and protons. The atom's identity also determines the chemical element's identity and chemical properties.

The nucleus of any atom may contain a different number of neutrons from other atoms of the same element. Such atoms are called isotopes, meaning atoms with the same elemental identity according to the number of protons but a different number of neutrons. Some isotopes are entirely stable, but others are not stable and spontaneously break down by nuclear fission to produce either the stable isotopic form of the same atom or atoms with different chemical identities.

Exponential Decay

The rate at which a radioisotope breaks down follows a specific exponential decay pattern described mathematically by the equation A = Aoe−kt. The symbol A represents the amount of a specific isotope present at the time t, whereas the symbol Ao is the amount of that material that was present originally, and k is the rate constant for the particular process. A special relationship exists for this formula when A is exactly one-half of Ao, which occurs after a specific time called the half-life has elapsed.

The relationship is constant for exponential decay in that it requires exactly the same amount of time for one-half of an amount of material to decompose, no matter how much of the material is present. The same amount of time is required for one kilogram of a material to decompose to one-half kilogram as it does for one gram of the material to decompose to one-half gram of the material. Because the breakdown begins and ends with specific materials, the exact amounts of each are also related to the elapsed time for the process. Thus, the ratio of the materials that are present is an important factor in determining age by radiometric methods.

Time Scales, Identifiability, and

Isotopic fission takes place at very different rates according to the isotopes involved. Some isotopes undergo fission quickly, while others require billions of years. Tables of isotopes and their half-lives, or lifetimes (commonly listed in reference books such as the CRC Handbook of Chemistry and Physics), show isotopic half-lives ranging from 10⁻¹⁶ seconds to more than 10⁹ years. This range provides the opportunity to employ an appropriate radiometric dating method for different ages.

Each method requires that the fission process end with the formation of stable elements so that the proportion of starting radionuclide to final element can be determined. The method also provides the best results when the final element is uniquely identifiable within the matrix in which it is contained. These conditions of time range and identifiability have greatly limited the number of useful isotopic changes.

Mass spectrometry is the most widely used and exact method of determining the ratios of radionuclides. The mass spectrometry technique relies on the ratio of the mass of an ion to the electrical charge on that ion as it determines the trajectory of the ion traveling through a magnetic field. According to precise mathematical relations, the ion moves along a circular path with a specific radius determined by the strength of the applied magnetic field and the charge/mass ratio of the ion. In typical techniques, a sample containing the nuclides to be measured is injected into the high-vacuum inlet of the mass spectrometer, where it is given an electrical charge and directed into the magnetic field. The detector section determines the relative numbers of ions of each mass present in the sample, providing the nuclide ratio. In the twenty-first century, the development of Accelerator Mass Spectrometry (AMS) has improved mass spectrometry accuracy while reducing the sample size needed. 

Nuclide Pairs

Fission of a radionuclide occurs by distinct steps governed by the law of conservation of mass. The emission of a single electron or positron termed a “β-particle” (beta particle) from a nucleus does not reduce the isotopic mass of those atoms but may alter their elemental identity. However, the emission of an α-particle (alpha particle), a helium nucleus containing two protons and two neutrons, changes the atom's mass and its elemental identity. The change is specific, and identifying corresponding nuclide pairs as starting material and product of a fission process is fundamental to radiometric dating.

Three of the most commonly used nuclide pairs for radiometric dating are carbon-14 and nitrogen-14 (C¹⁴ – N¹⁴), potassium-40 and argon-40 (K⁴⁰ – Ar⁴⁰), and uranium-238 and lead-206 (U²³⁸ – Pb²⁰⁶). In the transition from C¹⁴ to N¹⁴, it is believed that one of the extra neutrons in C¹⁴ decomposes into a proton by emitting a β- particle (an electron) to produce the more stable N¹⁴ atom. The half-life of C¹⁴ is 5,730 ± 30 years. The C¹⁴ – N¹⁴ transition is thus most useful for the radiocarbon dating of materials from organic sources and carbonaceous minerals.

The K⁴⁰ – Ar⁴⁰ transition has a half-life of 1.28 × 10⁹ years and presumably occurs by a similar but opposite process in which a proton and an electron combine to produce the extra neutron of the resulting highly stable argon atom. The U²³⁸ – Pb²⁰⁶ transition is a more complicated process, occurring by α-particle decay through rapid intermediate stages resulting in the formation of lead-206. The common key feature of these transitions is that the atoms of the elements that end the corresponding chain are entirely stable and do not decompose further.

Radiocarbon Dating

The factor that makes radiocarbon dating by the C¹⁴ – N¹⁴ transition feasible originates in the constant bombardment of cosmic ray neutrons that impinge upon Earth's atmosphere. These neutrons convert some of the normal N¹⁴ of atmospheric nitrogen (N₂) into the C¹⁴ radionuclide. This labeled carbon is then taken up along with normal CO₂ in various biological and mineralization processes. Photosynthesis is the most common process by which C¹⁴ is incorporated into organic materials, while the formation of carbonate minerals is the predominant means of incorporating C¹⁴ into inorganic materials. The rate of incorporation does fluctuate but is essentially constant in the time plants and animals are functionally alive and ceases immediately upon the organism's death. Compared with the amount in living organisms, the amount of C¹⁴ remaining in the material provides the number of half-lives that have occurred since the replenishment process ceased.

The radiocarbon dating of inorganic materials is somewhat more demanding in principle because no living system is involved in the process and because the rates of incorporation are more speculative. Stalactites taken from caves containing human and other remnants may be dated absolutely by radiocarbon methods by measurement of the ratio of C¹⁴ in specific material samples. They can be dated relatively by comparison with the dating of any accompanying organic materials.

Radiocarbon dating is most appropriate for materials between one hundred and fifty thousand years old. Before one hundred years, insufficient conversion of C¹⁴ has taken place to allow an accurate determination of age, while after fifty thousand years, insufficient C¹⁴ remains to permit comparison. In both cases, the error limits of the determination exceed the precision of the measurement.

Mineralogical Dating

The K⁴⁰ – Ar⁴⁰ transition and the U²³⁸ – Pb²⁰⁶ transition overlap extensively, and they are most useful for mineralogical dating, including the determination of Earth's age. Potassium is incorporated into biological systems, particularly animal systems, according to its natural abundance for the duration of the living process; as in C¹⁴ dating, the ratio of Ar⁴⁰ to K⁴⁰ in the remnant is used to calculate the age of a material such as a fossil. The half-life of K⁴⁰ and the ready identifiability of Ar because of its chemical nature as an inert gas allow the K⁴⁰ – Ar⁴⁰ dating of inorganic materials and minerals from 100,000 years of age to the formation of the planet some 4.6 billion years ago. This makes it useful in geological studies involving muscovite, biotite, and hornblende minerals, and intact volcanic rock.

The U²³⁸ – Pb²⁰⁶ transition has a half-life of some 4.51 billion years, with the end product atoms of lead being both common, stable, and easily recovered. The precision of analyses involving the U²³⁸ – Pb²⁰⁶ transition is adversely affected more by the scarcity of U²³⁸ and the presence of several other uranium nuclides than by any difficulties with the end product, the lead atoms. However, the extreme longevity of the half-life makes the transition suitable for radiometric dating of materials from ten million years of age to the formation of the planet. Accordingly, it is useful in geological studies involving zircon, uraninite, and pitchblende, or uranium ore.

Relative Age Versus Absolute Age

Radiometric dating provides valuable chronological data regarding the age of materials, which allows other observed phenomena and properties to be placed into a chronological context. One example of the utility of this method is in determining the ages of fossil materials and much more recent archaeological findings. An important distinction is made between a material's relative age and absolute age.

Relative age, as the name implies, is determined in relation to the occurrence of other materials. The applicable assumption in geology is that underlying strata are older than those above. Accordingly, strata having the same or similar characteristics and material content but at a different location can be assigned, at least tentatively, to be approximately the same age. Relative dating thus does not relate the age of an object or a material to the present time.

The validity of radiometric age determination is based on assumptions about the original state of the material. The half-life of a material, for example, assumes that the material was in its pure form or was otherwise not contaminated by the presence of its breakdown nuclides at the outset. Such an assumption can be validated for many materials. For example, if an ore contains a measurable amount of U²³⁸ and an appropriate amount of Pb²⁰⁶, one can conclude that the age of that ore is at least 4.51 billion years, the half-life of the original amount of U²³⁸ that was present in the ore. However, this value cannot be used to determine whether the ore is older than 4.51 billion years because there is no comparative standard for the older age.

Absolute age requires a phenomenon or characteristic that links the age of a material directly to a known point in time and is most useful when that link is made to the present day. The best example of a mechanism for absolute age is found in annual growth rings. These provide an unequivocal determination of the age of the tree, fish scales, or other structures in which they are found. In the same way, the relative proportions of nuclides in a material, according to a specific nuclide pair transmutation, provide a direct link from the present time to the date of origin of the material within the practical error limits to which such a determination can be made.

As the twenty-first century progressed, radiometric dating techniques continued to provide vital answers for scientists. For example, radiometric dating techniques have allowed insights into human evolution, including when scientists used volcano ash and such techniques to estimate that the Australopithecus fossil "Lucy" lived about 3.18 million years ago.

Principal Terms

beta (β) particle: a subnuclear particle emitted during nuclear fission as an electron (β–) from the decomposition of a neutron

exponential decay: a process of decomposition, particularly nuclear fission, that obeys the time-related function A = Aoe−kt

fissible: capable of undergoing nuclear fission

fission: the splitting of a nucleus through the emission of nuclear particles to form atoms of a different element

fusion: the combination of two atomic nuclei to produce a single nucleus of a higher element; the opposite of fission

half-life: the length of time required for one-half of an amount of material to decompose or be consumed through an exponential decay process

isotope: an atom of a specific element that contains different numbers of neutrons in its respective nucleus

labeling: the incorporation of atoms of a detectable radionuclide into the normal molecular structure of a material

radionuclide: a specific radioactive isotope of an element

transmutation: the conversion of one element into another by natural or artificial fission or fusion processes

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