Mass number

Mass number
Kjerish · CC BY-SA 4.0 · source
Name	Mass number
Unit	none
Related	Atomic number, Isotope, Nuclide, Atomic mass, Nuclear binding energy

Mass number is the integer equal to the total count of nucleons (protons and neutrons) in an atomic nucleus. It distinguishes nuclides that share the same chemical element identity but differ in neutron content, and it appears in notation for isotopes alongside the atomic number and chemical symbol. Mass number is distinct from atomic mass and from quantities used in precision mass spectrometry, yet it remains central to nuclear chemistry, radiochemistry, nuclear physics, and applications in medicine and industry.

Definition and notation

Mass number is denoted by the letter A in nuclear science literature and placed as a superscript to the left of an element symbol in nuclide notation, for example as A–X where X is the element's chemical symbol. In many publications and databases from organizations such as the International Union of Pure and Applied Chemistry and the International Union of Pure and Applied Physics, mass number is used to label nuclides like 235-U and 14-C without implying exact atomic mass. Because mass number counts whole nucleons, it is always an integer and does not reflect isotopic mass defects produced by nuclear binding energy or by contributions from electron binding energies treated in high-precision measurements.

Relation to atomic number and isotopes

Mass number complements the atomic number Z, which counts protons and determines chemical identity and placement in the periodic table. A nuclide is uniquely specified by the ordered pair (Z, A); nuclides with the same Z but different A are known as isotopes of a given element, exemplified by pairs such as 235-U and 238-U or 12-C and 14-C. Isobars are nuclides that share the same A but have different Z, a relationship important in discussions involving beta decay, nuclear stability, and pathways in nucleosynthesis as studied in contexts like the s-process and r-process in stellar environments such as red giant stars and supernovae. The concept of isotones groups nuclides by equal neutron number N = A − Z, which is useful in nuclear shell-model analyses applied to nuclides near closed shells like those around lead-208.

Calculation and measurement

Mass number is determined by counting nucleons in a nucleus and is therefore an integer obtained from nuclear composition rather than measured mass. Practical determination of A for unknown nuclides relies on techniques from experimental facilities such as CERN, Lawrence Berkeley National Laboratory, and national accelerator centers where detectors for charged-particle spectroscopy, recoil separators, and decay-chain analysis are employed. Mass spectrometry instruments, including Penning trap spectrometers and time-of-flight mass spectrometers, measure atomic masses with high precision and allow inference of mass excess and binding energies; these measured masses are reconciled with integer mass-number assignments via nuclear reaction studies and decay schemes established by collaborations involving institutions like the National Institute of Standards and Technology and the European Organization for Nuclear Research. For very short-lived exotic nuclides produced in fragmentation or fusion-evaporation reactions, A is assigned through correlated decay tagging and identification systems used at facilities such as RIKEN and GSI Helmholtzzentrum für Schwerionenforschung.

Role in nuclear reactions and decay

In nuclear reactions and radioactive decay, conservation of nucleon number generally preserves the total mass number across the reaction or decay process, subject to the involvement of particles that change nucleon count such as neutrons, protons, alpha particles, or heavier fragments. For example, in alpha decay of 238-U to 234-Th, A decreases by four units due to emission of an alpha particle; in neutron capture processes relevant to reactor physics at facilities like Oak Ridge National Laboratory or in nucleosynthesis in asymptotic giant branch stars, A increases by one. Understanding changes in A underpins design and analysis of fission chains in reactors developed by organizations like the Manhattan Project and modern nuclear engineering programs, and informs decay heat calculations and isotope production for applications in medicine and industry.

Applications in chemistry and physics

Mass number plays a practical role in isotope labeling, radiometric dating, tracer studies, and isotope separation technologies used by laboratories and industries worldwide. Radiocarbon dating exploits the difference between 12-C and 14-C (A = 12 and A = 14) to estimate ages of archaeological samples analyzed by institutions such as the Smithsonian Institution and university laboratories. In nuclear medicine, isotopes selected by mass number—examples include 131-I and 99m-Tc—are chosen for diagnostic imaging or therapy in hospitals associated with institutions like Johns Hopkins Hospital and Mayo Clinic. In fundamental physics, experiments probing nuclear structure, neutrino interactions, and double beta decay select nuclides with specific A values, as in searches at facilities such as Gran Sasso National Laboratory and collaborations like the Sudbury Neutrino Observatory.

Historical development and terminology

The concept of mass number emerged from early 20th-century investigations into atomic weights, nuclear composition, and radioactivity carried out by researchers and laboratories including Ernest Rutherford, James Chadwick, and the laboratory at Cavendish Laboratory. Chadwick's discovery of the neutron provided a natural explanation for isotopes having equal atomic numbers but different atomic masses, leading to formal use of a nucleon-counting number in the literature. Standardized notation and terminology evolved through work by bodies such as IUPAC and during the development of nuclear data tables compiled at institutions like Brookhaven National Laboratory, resulting in the current convention of labeling nuclides by integers A alongside Z and chemical symbols.

Category:Nuclear physics