# Isobar (nuclide)
**Isobars** are nuclides (atomic nuclei of different chemical elements) that have the same mass number but different atomic numbers[1](https://goldbook.iupac.org/terms/view/I03263/html). The mass number A is the total number of nucleons, protons plus neutrons, in the nucleus, while the atomic number Z is the number of protons and fixes the element[2](https://nucwik.cinch-project.eu/textbook/nrctextbook/chapter2). Two isobars therefore belong to different elements and have different chemical properties, even though their nuclei contain the same total number of particles[3](https://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/problems/ex23_2a.html).
| Key fact | Detail |
|---|---|
| Definition | Different nuclides of equal mass number A but different atomic number Z[1](https://goldbook.iupac.org/terms/view/I03263/html) |
| Classic example | 40Ar, 40K, and 40Ca all have A = 40 and are isobars[3](https://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/problems/ex23_2a.html) |
| Another set | 35Ar, 35Cl, 35S, and 35P share the mass number 35[2](https://nucwik.cinch-project.eu/textbook/nrctextbook/chapter2) |
| Beta decay link | Beta decay converts a proton into a neutron or the reverse, keeping A constant, so it always connects isobars[4](https://www.hep.phy.cam.ac.uk/~chpotter/particleandnuclearphysics/Lecture_15_NuclearDecay.pdf) |
| Stability count | For odd A there is generally one beta-stable isobar; for even A there may be one, two, or three[5](https://physics.uwo.ca/~jlandstr/p467/lec7-nucl_mass/) |
| Mass spectrometry | Isobars have the same nominal mass but slightly different exact masses, for example 12C16O+ at 27.9944 Da versus N2+ at 28.0056 Da[6](https://www.sciencedirect.com/topics/engineering/atomic-mass) |
| Nuclear structure | States of the same isospin in a set of nuclei with the same mass number are isobaric analog states[7](https://www.sciencedirect.com/science/article/pii/S0146641006000743) |
## Definition and notation
A nuclide is an atomic nucleus with a fixed number of protons Z and neutrons N; the mass number is A = Z + N[2](https://nucwik.cinch-project.eu/textbook/nrctextbook/chapter2). Nuclides are written with the mass number as a superscript and the atomic number as a subscript to the left of the element symbol, for example 40/19K, although the subscript is usually omitted because the symbol already fixes Z[2](https://nucwik.cinch-project.eu/textbook/nrctextbook/chapter2). The IUPAC Compendium of Chemical Terminology defines isobars simply as "different nuclides of equal mass number"[1](https://goldbook.iupac.org/terms/view/I03263/html).
The term is one of a family of classifications of nuclides. Isotopes have the same atomic number but different mass numbers, and isotones have the same neutron number but different atomic numbers[8](https://goldbook.iupac.org/terms/view/I03331/pdf) • [9](https://goldbook.iupac.org/terms/view/I03321/pdf). On a nuclide chart, where neutron number runs along one axis and proton number along the other, isotopes appear as horizontal lines and isobars as diagonals[2](https://nucwik.cinch-project.eu/textbook/nrctextbook/chapter2).
## Isobars and beta decay
The concept matters most in beta decay. In beta-minus decay a neutron in the nucleus converts to a proton with emission of an electron and an antineutrino; in beta-plus decay a proton converts to a neutron with emission of a positron and a neutrino; electron capture achieves the same conversion by absorbing an orbital electron[4](https://www.hep.phy.cam.ac.uk/~chpotter/particleandnuclearphysics/Lecture_15_NuclearDecay.pdf). In all three modes no nucleons are lost, so A stays constant while Z changes by one: every beta decay moves a nucleus from one isobar to a neighboring one[5](https://physics.uwo.ca/~jlandstr/p467/lec7-nucl_mass/).
**Mass parabolas.** The [semi-empirical mass formula](https://www.edgepedia.org/semi-empirical-mass-formula) expresses the nuclear mass as a function of A and Z. For a fixed A the mass is quadratic in Z, so a plot of mass against Z for one set of isobars is a parabola, and the minimum of the parabola gives the most stable isobar for that mass number[4](https://www.hep.phy.cam.ac.uk/~chpotter/particleandnuclearphysics/Lecture_15_NuclearDecay.pdf). The minima of these parabolas across all A trace the valley of beta stability[10](https://ebooks.inflibnet.ac.in/phyp04/chapter/nuclear-models-2/).
The pairing term in the mass formula, which reflects the tendency of identical nucleons to form pairs, splits the picture by parity. For odd A the pairing term is zero and there is a single parabola, so only one beta-stable isobar is expected[10](https://ebooks.inflibnet.ac.in/phyp04/chapter/nuclear-models-2/). For even A the term takes opposite signs for even-even and odd-odd nuclei, producing two parabolas separated by twice the pairing energy[11](https://www.phenix.bnl.gov/WWW/publish/elke/EIC/BOOKs/ParticlesAndNuclei.pdf). On the lower (even-even) parabola one, two, or even three beta-stable isobars can occur, separated by unstable odd-odd nuclei[5](https://physics.uwo.ca/~jlandstr/p467/lec7-nucl_mass/).
**Worked examples.** For A = 101 the parabola has a single minimum at the stable isobar 101Ru, with proton-rich isobars decaying toward it by beta-plus emission[11](https://www.phenix.bnl.gov/WWW/publish/elke/EIC/BOOKs/ParticlesAndNuclei.pdf). For A = 106, both 106Pd and 106Cd sit on the lower even-even parabola; 106Cd is beta-stable because its two odd-odd neighbors lie above it, and its conversion to 106Pd is possible only through double beta decay, a process so improbable that 106Cd may be treated as stable[11](https://www.phenix.bnl.gov/WWW/publish/elke/EIC/BOOKs/ParticlesAndNuclei.pdf). A familiar decay chain runs 90Sr to 90Y to stable 90Zr, all isobars of A = 90, with the second decay releasing 2.27 MeV against 0.54 MeV for the first[5](https://physics.uwo.ca/~jlandstr/p467/lec7-nucl_mass/). Carbon-14 decays by beta-minus emission to nitrogen-14, keeping the mass number at 14 while the atomic number rises from 6 to 7[12](https://learnminto.com/what-are-isobars/).
## Isobaric analog states
Because the nuclear force does not distinguish between protons and neutrons, states of the same isospin quantum number T in a set of nuclei with the same mass number form an isobaric multiplet, and corresponding states are called isobaric analog states[7](https://www.sciencedirect.com/science/article/pii/S0146641006000743). Their near-identical structure demonstrates the power of the isospin concept, while their small energy differences, the Coulomb displacement energies, serve as sensitive probes of nuclear structure and as tests of shell-model calculations[7](https://www.sciencedirect.com/science/article/pii/S0146641006000743). Isobaric analog states can occur even in mass regions where isotopic spin is not a good quantum number[13](https://doi.org/10.1103/PhysRev.126.2170).
## Separating isobars in the laboratory
**Mass spectrometry.** Isobars of the same nominal mass differ slightly in exact mass because of unequal mass defects. The monoisotopic ion 12C16O+ has an accurate mass of 27.9944 Da, while the isobaric N2+ peak at nominal mass 28 has an accurate mass of 28.0056 Da; resolving such differences requires a mass analyzer accurate to a few parts per million, works only for compounds of a few hundred Da or less, and cannot discriminate between isobars of the same chemical formula[6](https://www.sciencedirect.com/topics/engineering/atomic-mass). In analytical mass spectrometry, isobaric compounds with identical or similar molar masses but distinct molecular formulas are a common source of interference and are often hard to separate without prior chromatographic separation[14](https://pmc.ncbi.nlm.nih.gov/articles/PMC11402307/).
**Accelerator mass spectrometry.** Because isobars are different elements, chemical methods can distinguish them, but most mass spectrometric setups cannot; accelerator mass spectrometry (AMS) therefore needs dedicated isobar separation[15](https://nucleus.iaea.org/sites/accelerators/AMS/SitePages/Advanced-AMS---isobars.aspx?web=1). One approach exploits the dependence of energy loss in matter on the nuclear charge z: with a suitable gas inside the magnet chamber, atomic collisions change the charge state, ions of different z acquire different average charge states, and the isobars follow distinct trajectories[15](https://nucleus.iaea.org/sites/accelerators/AMS/SitePages/Advanced-AMS---isobars.aspx?web=1). This becomes harder at higher z because the relative difference between neighboring isobars shrinks[15](https://nucleus.iaea.org/sites/accelerators/AMS/SitePages/Advanced-AMS---isobars.aspx?web=1). A high-powered laser can also be used for selective photodetachment, removing an electron from the interfering isobar or the molecular anion containing it[15](https://nucleus.iaea.org/sites/accelerators/AMS/SitePages/Advanced-AMS---isobars.aspx?web=1). In radiocarbon dating, the isobar problem is acute because nitrogen contamination cannot be avoided and a N+ beam would make detection of 14C practically impossible; switching to negative carbon ions and stripping the beam in gas destroys molecular isobars of mass 14 such as 13CH and 12CH[16](https://gnssn.iaea.org/main/ncp/Tunisia/lrae/documents/tracers/Volume_I.pdf).
## The term extended to molecules
Derived from the Greek isos (equal) and baros (weight), the term was originally used for nuclides, not molecules[17](https://www.degruyterbrill.com/document/doi/10.1515/pac-2025-0618/html). It later entered mass spectrometry, where recommendations by Murray and colleagues define isobars as atomic or molecular species with the same nominal mass but different exact masses[17](https://www.degruyterbrill.com/document/doi/10.1515/pac-2025-0618/html). Applied to chemical compounds, isobars can represent molecules with identical or similar molar masses but distinct molecular formulas[14](https://pmc.ncbi.nlm.nih.gov/articles/PMC11402307/). A recent IUPAC-backed analysis notes that for small-molecule analysis the meaning and practical relevance of the term is less clear than in nuclear chemistry[17](https://www.degruyterbrill.com/document/doi/10.1515/pac-2025-0618/html).
## References
1. [IUPAC Gold Book: isobars (I03263)](https://goldbook.iupac.org/terms/view/I03263/html)
2. [NucWik (CINCH): The structure of atom and nucleus, nuclides, isotopes, isobars](https://nucwik.cinch-project.eu/textbook/nrctextbook/chapter2)
3. [Purdue University ChemEd: Classify nuclides as isotopes, isobars, or isotones](https://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/problems/ex23_2a.html)
4. [Tina Potter, Particle and Nuclear Physics, Lecture 15: Nuclear Decay, University of Cambridge](https://www.hep.phy.cam.ac.uk/~chpotter/particleandnuclearphysics/Lecture_15_NuclearDecay.pdf)
5. [J. Landstreet, Nuclear sizes and ground states, Physics 467, University of Western Ontario](https://physics.uwo.ca/~jlandstr/p467/lec7-nucl_mass/)
6. [Atomic Mass, ScienceDirect Topics overview](https://www.sciencedirect.com/topics/engineering/atomic-mass)
7. [Coulomb energy differences between high-spin states in isobaric multiplets, Nuclear Physics A](https://www.sciencedirect.com/science/article/pii/S0146641006000743)
8. [IUPAC Gold Book: isotopes (I03331)](https://goldbook.iupac.org/terms/view/I03331/pdf)
9. [IUPAC Gold Book: isotones (I03321)](https://goldbook.iupac.org/terms/view/I03321/pdf)
10. [Nuclear Models-2, Nuclear and Particle Physics, INFLIBNET e-books](https://ebooks.inflibnet.ac.in/phyp04/chapter/nuclear-models-2/)
11. [Particles and Nuclei (Povh et al.), Chapter 3: Nuclear Stability, BNL copy](https://www.phenix.bnl.gov/WWW/publish/elke/EIC/BOOKs/ParticlesAndNuclei.pdf)
12. [What Are Isobars? Definition, Examples & Differences, Learn Minto](https://learnminto.com/what-are-isobars/)
13. [Isobaric States in Nonmirror Nuclei, Physical Review 126, 2170 (1962)](https://doi.org/10.1103/PhysRev.126.2170)
14. [Understanding isotopes, isomers, and isobars in mass spectrometry, PMC](https://pmc.ncbi.nlm.nih.gov/articles/PMC11402307/)
15. [IAEA: Advanced AMS, isobar separation](https://nucleus.iaea.org/sites/accelerators/AMS/SitePages/Advanced-AMS---isobars.aspx?web=1)
16. [Environmental Isotopes in the Hydrological Cycle, IAEA/GNSSN, Volume I](https://gnssn.iaea.org/main/ncp/Tunisia/lrae/documents/tracers/Volume_I.pdf)
17. [The correct use of the term isobar for molecules, Pure and Applied Chemistry (De Gruyter)](https://www.degruyterbrill.com/document/doi/10.1515/pac-2025-0618/html)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Particles and nuclei › Nuclear physics › Nuclear structure and models › Nuclear properties and isotopes › Nuclide concepts and nuclide charts*
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