Isotope

An isotope is a form of a chemical element distinguished by the number of neutrons in its atomic nuclei. Isotopes of the same element contain identical numbers of protons but different numbers of neutrons, giving them the same atomic number and different mass numbers. They generally have similar chemical behavior, although their masses and nuclear properties differ. Some isotopes are stable; others undergo radioactive decay. The term describes a relationship between nuclear species, not a synonym for radioactive material. (goldbook.iupac.org)

Nuclear identity and notation

An atom consists of an atomic nucleus surrounded by electrons. The proton count, conventionally written $Z$, determines the element. The neutron count is $N$, and the mass number is their sum:

A particular nuclear species is called a nuclide. Nuclides with the same $Z$ but different $A$ are isotopes of one element. Adding a neutron therefore changes isotopic identity without changing elemental identity. (isotopes.gov)

Standard notation places the mass number above and to the left of the element symbol, with the atomic number below it: ${}^{A}_{Z}\mathrm{X}$. Carbon-14, for example, is ${}^{14}_{6}\mathrm{C}$, often shortened to ${}^{14}\mathrm{C}$ or C-14. Carbon-12, carbon-13, and carbon-14 each have six protons but respectively six, seven, and eight neutrons. Hydrogen provides another familiar example: protium, deuterium, and tritium have zero, one, and two neutrons respectively. (isotopes.gov)

Mass and isotopic abundance

Mass number is an integer particle count, not an exact measurement of atomic mass. Carbon-13 has mass number 13, but its measured atomic mass is approximately 13.003355 daltons. Carbon-12, by contrast, has an atomic mass of exactly 12 daltons because it defines the reference scale for relative atomic masses. (goldbook.iupac.org)

An element’s atomic weight in a sample depends on both the masses of its isotopes and their relative abundances. For isotope masses $m_i$ and amount fractions $x_i$, the average atomic mass is

Natural carbon is overwhelmingly carbon-12, with roughly one percent carbon-13 and much smaller quantities of carbon-14. The proportions are not identical in every material. Physical, chemical, and biological processes produce measurable variations, so standard atomic weights for some elements are expressed as intervals rather than single universal values. (ciaaw.org)

Stable and radioactive isotopes

Stable isotopes do not exhibit observed spontaneous radioactive decay. Radioactive isotopes, also called radioisotopes, have unstable nuclei that transform into other nuclear species while releasing particles or radiation. Their nuclear behavior can differ sharply despite their common elemental identity: carbon-12 is stable, whereas carbon-14 is radioactive. (isotopes.gov)

Radioactivity is described statistically. A radioactive isotope’s half-life is the time required for half the nuclei in an initially present population to decay. For a single population with constant decay constant $\lambda$,

Carbon-14 has a half-life of approximately 5,730 years and undergoes beta decay to nitrogen-14. A half-life characterizes a population’s decay rate; it does not specify when an individual nucleus will transform. (isotopes.gov)

Chemical behavior and fractionation

Neutral isotopic atoms have the same number of electrons, which largely determine their chemical behavior. Their reactions are consequently similar, but not necessarily identical. Changing isotopic composition can alter a reaction’s rate or equilibrium constant. These differences are called isotope effects and can help investigate chemical reactions. (isotopes.gov)

Isotope fractionation is the preferential distribution of isotopes between substances or phases. During evaporation and condensation of water, hydrogen and oxygen isotopes partition differently between liquid and vapor. Fractionation depends on conditions such as temperature and whether a process approaches equilibrium. Biological processes also discriminate between isotopes: photosynthesis, for example, commonly produces organic material depleted in carbon-13 relative to its carbon source. (wwwrcamnl.wr.usgs.gov)

Measurement and applications

Isotopic compositions are measured using specialized mass spectrometry, particularly isotope-ratio mass spectrometry. Measurements often compare a heavy-to-light isotope ratio in a sample with that of a reference material. Small relative differences are reported using delta notation, usually in parts per thousand. Consistent reference scales allow results from different laboratories and materials to be compared. (wwwrcamnl.wr.usgs.gov)

In geology, radiometric dating uses radioactive decay and parent–daughter isotope relationships to estimate ages. Different isotope systems suit different timescales. Carbon-14 is important for dating relatively recent carbon-bearing material, while potassium–argon and uranium–lead systems are used for much older geological materials. Reliable interpretation requires accounting for initial isotopic conditions and subsequent gains or losses of relevant elements. (pubs.usgs.gov)

Stable isotope ratios provide information about the origins and movement of materials. Hydrogen and oxygen isotopes help investigate groundwater recharge and water movement; carbon isotopes help reconstruct diets and past environments. Radioisotopes also have established applications in medicine, industrial investigation, and scientific research, where their detectable emissions distinguish them from surrounding material. (pubs.usgs.gov)

Historical development

Frederick Soddy introduced the term isotope in 1913 after research showed that some radioactive substances were variants of known elements rather than separate elements. His investigations into isotopes formed part of the work recognized by the 1921 Nobel Prize in Chemistry. Francis William Aston subsequently demonstrated isotopes in numerous nonradioactive elements using his mass spectrograph, work recognized by the 1922 chemistry prize. These findings established that elemental identity does not require every atom of an element to have the same mass. (nobelprize.org)