Isotope geochemistry

The presence of an excessive or deficient number of neutrons in an atomic nucleus renders that nucleus unstable. The nucleus may then transmute into atoms of other elements through a number of nuclear fission processes. The transmutation is accompanied by the release of subatomic particles and energy, or radioactivity. The relative quantities of atomic isotopes, normally measured by mass spectrometry, can be used to determine the age of a sample or to identify the location and formation of a mineral source through forensic examination.

Modern Theory of Atomic Structure

To understand the principles of isotope geochemistry, it is necessary to have a sound comprehension of the modern theory of atomic structure, realizing that it is no more and no less than a model. The most basic assumption of that theory is that all matter in the universe is composed of discrete particles called atoms. Based on and supported by experiment and observation, it is further supposed that each atom is composed of smaller particles in specific arrangements.

According to the strict mathematical principles of quantum mechanics, essentially all of the mass of each atom is located in a very small, dense nucleus that contains the two massive particles called protons and neutrons. Surrounding this nucleus is a much broader, but tenuous cloud containing the lightest subatomic particles, the electrons. Each proton carries a single electrical charge that has been designated as positive. Because like electrical charges repel each other, the presence of more than one proton in a nucleus requires the presence of roughly the same number of electrically neutral, equally massive particles called neutrons. The combined masses of the protons and neutrons account for no less than 99.98 percent of the mass of an atom, and the nuclear structure that they form places absolute restrictions on the properties of the surrounding electrons. Specifically, electrons can have only specific quantum energies and so are restricted to specifically defined regions of space around the nucleus.

At the miniscule size of atoms (it would require 6.023 × 10²³ of the simplest atoms containing just one proton and one electron to achieve a total mass of one gram), the physics of the macroscopic world simply do not apply. Each electron, for example, can exist and behave both as a particle with mass or as a photon having a specific wavelength but no mass; each electron also can exist as both a particle and a photon, at the same time. All normal chemistry takes place at the level of the outermost electrons and does not involve the nuclei of the atoms.

Isotope chemistry, however, is a nuclear process. Naturally occurring atoms, up to and including the ninety-second element, uranium, occur primarily as stable atoms having a specific number of protons and an equally specific number of neutrons in the nucleus. It is a fundamental principle of atomic theory that each atom of a specific element must contain exactly the same number of protons in the nucleus; otherwise, the atoms are of different elements with different chemical identities. The number of neutrons can vary from atom to atom, however, and atoms that have the same number of protons but different numbers of neutrons in their nuclei are called isotopes of that particular element.

The simplest element, hydrogen, is known in three isotopic forms: protium (generally called hydrogen), deuterium, and tritium. These forms have zero, one, and two neutrons, respectively, in their nuclei. Their respective atomic masses are one, two, and three daltons (also called atomic mass units [amu]). Uranium, with ninety-two protons in its nucleus, is known to exist in several isotopic forms, the most common of which have atomic masses of 235 and 238 daltons.

Radioactivity

It is one of the supreme ironies of atomic structure that the neutron, when present in specific numbers in the nucleus, imparts extreme stability to the nucleus of an atom. When the neutron is present in different numbers, however, the atomic nucleus becomes extremely unstable and spontaneously decomposes by the process of nuclear fission.

In nuclear fission, an unstable atomic nucleus ejects some of its subatomic structure in a repetitive process until a stable nucleus forms. This can occur by different mechanisms. A neutron may decompose into an electron and a proton, producing an atom of an element with a higher atomic number. The electron that is ejected from the nucleus is called a β-particle (beta particle). In another process, the nucleus may emit an α-particle (alpha particle), which is the same as the nucleus of a helium atom, consisting of two protons and two neutrons carrying two positive electrical charges. More rarely, the unstable nucleus may split apart into the nuclei of two lighter elements. The emission of charged subatomic particles by unstable nuclei is termed “radioactivity” because the energy associated with those emissions was first detected by radio interference. The processes produced activity in the radio frequency range of the electromagnetic spectrum; hence, they were radioactive. There are other modes of nuclear fission, but the foregoing three are the primary methods of relevance to isotope geochemistry.

It is important to remember that the mechanism of nuclear decomposition is very specific, in that discrete and well-defined subunits are removed or altered so that the product of each step is equally rigidly defined. Because of the specificity of nuclear fission mechanisms, and because of the precise mathematical description of the rate of nuclear decomposition, the relative amounts of specific isotopes in a material can be used to determine the age of the material, within experimental detection limits.

Mass Spectrometry

The mass spectrometer is a device that measures the behavior of a charged particle in a magnetic field. The charge-to-mass ratio of the particle determines the radius of a circular path that the charged particle will travel within a uniform magnetic field. In the mass spectrometer, the strength of the magnetic field can be continuously varied in strength so that the number of particles of different masses in a sample can be measured by their flight time through the mass spectrometer. The technique itself is quite straightforward in concept.

A material sample is prepared containing only the material to be studied and is injected into the mass spectrometer. Once injected, it is subjected to an electrical discharge that fragments the sample and imparts a single electrical charge to each fragment. Because the interior of the mass spectrometer operates under high vacuum, the fragments or particles are present in the vapor state and are easily accelerated through a grid system into the magnetic field sector of the spectrometer. Each particle bears the same total charge and is accelerated by the same energy as it passes through the grid system, so that when it enters the magnetic field chamber, it has a specific velocity determined only by its mass. The mass and velocity of the particle interact with the magnetic field to determine the particular radius of its circular path through the magnetic field sector.

The operating program of the spectrometer varies the strength of the magnetic field at a closely defined rate, which in turn alters the radii of the particle trajectories so that particles in the magnetic field are brought to the detector in order of their mass. The detection pattern of the different masses is recorded as a mass spectrum. A typical mass spectrum is a bar graph displaying the relative numbers of particles of each mass that have been detected in a specific period of time, determined by the rate at which the magnetic field strength is varied during the analysis. The masses are displayed in incremental units because the structures of the different particles differ by the loss of discrete mass units. Accordingly, a sample in which a radioactive nucleus has ejected a single neutron by radioactive decomposition will exhibit two peaks that differ by one mass unit, while a sample that has emitted an α-particle will exhibit two peaks that differ by exactly four mass units, and possibly a peak at four mass units corresponding to the α-particle (a helium nucleus).

The preparation of the sample is of paramount importance in analyzing the isotope content of a material. The experimental error limits of this stage of the process ultimately determine the accuracy of the analysis. If the analysis is being carried out to determine the age of a material by radiometric dating, the more precisely the quantities of different isotopes can be determined, the narrower the range of dates that can be ascribed to the material will be.

Half-Life and Radiometric Dating

Radioactive elements undergo nuclear fission processes by exponential decay, a process that has a precise and strict mathematical description. The process is absolutely described by the mathematical equation At = Aoe−kt, where At is the amount of material A at time t, Ao is the original amount of material A, t is the elapsed time, and k is a constant value for the specific process being described. A special relationship exists when At is exactly one-half of the value of Ao; the time interval associated with that change in value is called the half-life of the process. It should be noted that it does not matter what was the original amount of the material; the same amount of time is required for any starting quantity to become halved in value. That is to say, it takes exactly the same amount of time for one kilogram of the specific material to decompose to one-half of a kilogram as it does for one milligram to decompose to one-half of a milligram. Thus, by determining the relative quantities of the starting material and its daughter material or materials, the mathematical relationship allows the determination of the elapsed time, t. The relationship breaks down to the simple statement A/Ao = (1/2)n, where n is the number of half-lives that have passed.

If the half-life is known, it then becomes a simple matter to convert the factor n to a specific number of years. It is at this point that the precision of the measurement becomes exceedingly important, because the error limit of the measurement determines the corresponding valid range of time. An error range of only ±0.1 percent in the measurement of quantities can translate to a range of as much as one million years for a process with a very long half-life.

In isotope geochemistry, the atoms of interest are those that naturally occur in rock structures and other consistent environmental structures and processes. Research in geochemistry (literally the chemistry of the earth) has determined many of the basic methods and quantities by which radioactive materials are formed and how their decay processes progress over time. This has provided consistent values for the initial quantities of specific radionuclides in a material and a reasonably sound basis for the determination of the age of those materials within experimental error limits.

Principal Applications

Isotope geochemistry has its principal applications in three areas: radiometric dating, forensics, and isotopic signature identification. These three areas are discussed here.

The basic principle of radiometric dating is the mathematical relationship of exponential decay. The essential components for radiometric dating are knowledge of the specific mechanism of the fission reactions that are involved and the half-life of the specific process. Reference books such as the CRC Handbook of Chemistry and Physics (92d ed., 2011) list the known half-lives of all known radioactive isotopes and the specific type of particle that is ejected from the nucleus during fission. The half-lives listed range from 10⁻¹⁶ second to more than 10⁹ years. This range clearly provides the opportunity to employ an appropriate radiometric dating methodology for different ages. Each methodology requires that the fission process ends with the formation of stable elements so that the proportion of the starting radionuclide to the final element can be determined; thus the utility of the methodology is limited to the identification of an appropriate, single and unambiguous process.

The most commonly used nuclear processes for radiometric dating are carbon-14 and nitrogen-14 (C¹⁴ and N¹⁴), potassium-40 and argon-40 (K⁴⁰ and Ar⁴⁰), and uranium-238 and lead-206 (U²³⁸ and Pb²⁰⁶). 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. 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 fundamental premise of this application is that the influx of cosmic rays impinging on the upper atmosphere brings about a constant rate of conversion of normal carbon, C¹², to its heavier radionuclide, C¹⁴, in atmospheric carbon dioxide that is then incorporated into the photosynthetic process in the usual way.

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. These modes are used for dating rock structures and rely on all of the Pb²⁰⁶ and Ar⁴⁰ that are present in the rock coming from the original U²³⁸ and K⁴⁰ content. The helium that is produced by the ejection of α-particles in the nuclear fission process typically remains trapped within the rock until something happens to bring about its release.

The forensic application of isotope geochemistry is related to its use in isotopic signature identification. In essence, the relative populations of isotopes in any material are unique and can be characterized in much the same way as a human's personal characteristics, though they are perhaps not as unique as fingerprints. By determining the isotopic content of a soil or mineral sample, that particular sample can be identified with locations that have the identical isotopic composition. In forensic examinations of crime scene evidence, for example, this can be used to place a suspect at a location. In archaeological investigations, which are forensic investigations, the use of carbon-14 dating is an invaluable tool in determining the absolute age of an artifact and the relative ages of surrounding materials.

For geological research, the isotopic signature of a mineral sample provides an unambiguous association with the location and formation of that mineral and is key to determining the geological age of the strata and structures from which it was taken. An isotopic signature also can be artificially induced in a material to provide a means of tracking and detection, as is sometimes used with gemstones. Irradiation of diamonds and other gemstones is often used to impart a specific isotopic signature that does not affect the appearance of the stone, but which can be readily detected and verified for identification purposes.

Principal Terms

alpha (α) particle: a subatomic particle consisting of two protons and two neutrons, bearing two positive electrical charges, and emitted from an atomic nucleus through fission; the nucleus of a helium atom

beta (β) particle: an electron or positron emitted from the nucleus of an unstable atom through the spontaneous decomposition of a neutron into a proton

exponential decay: a process of decomposition or reaction, particularly in regard to nuclear fission, whose kinetics are described by the time-related function A_t = A_oe^−kt

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

forensic: the examination of material clues to determine the cause and progression of an event that occurred in the past

fusion: the combining of two separate nuclear entities to form a single entity having an identity different from either of the originals, as when a proton and an electron fuse to form a neutron

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

irradiation: the exposure of some material to radioactive emissions

radionuclides: atoms of the same element, containing the same number of protons but different numbers of neutrons in the nucleus; a synonym for isotopes

Bibliography

Baskaran, Mark, ed. Handbook of Environmental Isotope Geochemistry. Vol. 1. New York: Springer, 2011.

Dalrymple, G. Brent. Ancient Earth, Ancient Skies: The Age of Earth and Its Cosmic Surroundings. Stanford, Calif.: Stanford University Press, 2004.

Harbaugh, John W. and Brian Frederick Windley. "Isotope Geochemistry." Britannica, 9 Jan. 2025, www.britannica.com/science/geology/Isotopic-geochemistry. Accessed 10 Feb. 2025.

Hoefs, Jochen. Stable Isotope Geochemistry. 6th ed. New York: Springer, 2009.

Holland, Heinrich D., and Karl K. Turekian, eds. Isotope Geochemistry: From the Treatise on Geochemistry. San Diego, Calif.: Academic Press/Elsevier, 2011.

Van Kranendonk, Martin J., R. Hugh Smithies, and Vickie C. Bennett, eds. Earth's Oldest Rocks. Boston: Elsevier, 2007.