TheInfoList

Isotopes are two or more types of atoms that have the same
atomic number 300px, The Rutherford–Bohr model of the hydrogen atom () or a hydrogen-like ion (). In this model it is an essential feature that the photon energy (or frequency) of the electromagnetic radiation emitted (shown) when an electron jumps from one ...
(number of
protons A proton is a subatomic particle, symbol or , with a positive electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric cha ...
in their
nuclei ''Nucleus'' (plural nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA ...
) and position in the
periodic table The periodic table, also known as the periodic table of (the) chemical elements, is a tabular display of the chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is ...

(and hence belong to the same
chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elements cannot be broken down into simp ...
), and that differ in
nucleon In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...
numbers (
mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of s and s (together known as s) in an . It is approximately equal to the of the expre ...
s) due to different numbers of
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...

s in their nuclei. While all isotopes of a given element have almost the same chemical properties, they have different atomic masses and physical properties. The term isotope is formed from the Greek roots isos ( ἴσος "equal") and topos ( τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the
periodic table The periodic table, also known as the periodic table of (the) chemical elements, is a tabular display of the chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is ...

. It was coined by Scottish doctor and writer Margaret Todd in 1913 in a suggestion to chemist
Frederick Soddy Frederick Soddy FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family Resource ...

. The number of protons within the atom's nucleus is called
atomic number 300px, The Rutherford–Bohr model of the hydrogen atom () or a hydrogen-like ion (). In this model it is an essential feature that the photon energy (or frequency) of the electromagnetic radiation emitted (shown) when an electron jumps from one ...
and is equal to the number of
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

s in the neutral (non-ionized) atom. Each atomic number identifies a specific element, but not the isotope; an atom of a given element may have a wide range in its number of
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...

s. The number of
nucleon In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...
s (both protons and neutrons) in the nucleus is the atom's
mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of s and s (together known as s) in an . It is approximately equal to the of the expre ...
, and each isotope of a given element has a different mass number. For example,
carbon-12 Carbon-12 (12C) is the more abundant of the two stable A stable is a building in which livestock Livestock is commonly defined as domesticated Domestication is a sustained multi-generational relationship in which one group of organisms ...

,
carbon-13Carbon-13 (13C) is a natural, stable isotope A stable is a building in which livestock, especially horses, are kept. It most commonly means a building that is divided into separate stalls for individual animals and livestock. There are many d ...

, and
carbon-14 Carbon-14 (14C), or radiocarbon, is a radioactive isotope A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ...

are three isotopes of the element
carbon Carbon (from la, carbo "coal") is a with the C and 6. It is lic and —making four s available to form s. It belongs to group 14 of the periodic table. Carbon makes up only about 0.025 percent of Earth's crust. Three occur naturally, ...

with mass numbers 12, 13, and 14, respectively. The atomic number of carbon is 6, which means that every carbon atom has 6 protons so that the neutron numbers of these isotopes are 6, 7, and 8 respectively.

# Isotope vs. nuclide

A
nuclide A nuclide (or nucleide, from nucleus ''Nucleus'' (plural nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic c ...

is a species of an atom with a specific number of protons and neutrons in the nucleus, for example carbon-13 with 6 protons and 7 neutrons. The ''nuclide'' concept (referring to individual nuclear species) emphasizes nuclear properties over chemical properties, whereas the ''isotope'' concept (grouping all atoms of each element) emphasizes
chemical A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which ...

over nuclear. The neutron number has large effects on nuclear properties, but its effect on chemical properties is negligible for most elements. Even for the lightest elements, whose ratio of neutron number to atomic number varies the most between isotopes, it usually has only a small effect although it matters in some circumstances (for hydrogen, the lightest element, the isotope effect is large enough to affect biology strongly). The term ''isotopes'' (originally also ''isotopic elements'', now sometimes ''isotopic nuclides'') is intended to imply comparison (like ''
synonym A synonym is a word, morpheme A morpheme is the smallest meaningful lexical item in a language. A morpheme is not a word. The difference between a morpheme and a word is that a morpheme bound and free morphemes, sometimes does not stand alone ...
s'' or ''
isomer In chemistry, isomers are molecules or polyatomic ions with identical molecular formulas — that is, same number of atoms of each element (chemistry), element — but distinct arrangements of atoms in space. Isomerism is existence or possibil ...

s''). For example, the nuclides , , are isotopes (nuclides with the same atomic number but different mass numbers), but , , are isobars (nuclides with the same mass number). However, ''isotope'' is the older term and so is better known than ''nuclide'' and is still sometimes used in contexts in which ''nuclide'' might be more appropriate, such as
nuclear technology 200px, A residential smoke detector is the most familiar piece of nuclear technology for some people Nuclear technology is technology that involves the nuclear reaction In nuclear physics Nuclear physics is the field of physics that studie ...
and
nuclear medicine Nuclear medicine is a medical specialty A medical specialty is a branch of medical practice that is focused on a defined group of patients, diseases, skills, or philosophy. Examples include children (paediatrics Pediatrics (American and Briti ...
.

# Notation

An isotope and/or nuclide is specified by the name of the particular element (this indicates the atomic number) followed by a hyphen and the mass number (e.g.
helium-3 Helium-3 (3He see also helion) is a light, stable isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons A proton is a subatomic particle, symbol or , with a positive electric charge Ele ...

,
helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consists ...

,
carbon-12 Carbon-12 (12C) is the more abundant of the two stable A stable is a building in which livestock Livestock is commonly defined as domesticated Domestication is a sustained multi-generational relationship in which one group of organisms ...

,
carbon-14 Carbon-14 (14C), or radiocarbon, is a radioactive isotope A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ...

,
uranium-235 Uranium-235 (235U) is an Isotopes of uranium, isotope of uranium making up about 0.72% of natural uranium. Unlike the predominant isotope uranium-238, it is fissile, i.e., it can sustain a nuclear chain reaction. It is the only fissile isotope th ...

and
uranium-239 Uranium Uranium is a chemical element with the Symbol (chemistry), symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valen ...
). When a
chemical symbol Chemical symbols are the abbreviations used in chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, beh ...
is used, e.g. "C" for carbon, standard notation (now known as "AZE notation" because ''A'' is the
mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of s and s (together known as s) in an . It is approximately equal to the of the expre ...
, ''Z'' the
atomic number 300px, The Rutherford–Bohr model of the hydrogen atom () or a hydrogen-like ion (). In this model it is an essential feature that the photon energy (or frequency) of the electromagnetic radiation emitted (shown) when an electron jumps from one ...
, and E for
element Element may refer to: Science * Chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all ...
) is to indicate the mass number (number of nucleons) with a
superscript Pro; the size of the subscript is about 62% of the original characters, dropped below the baseline by about 16%. The second typeface is Myriad A myriad (from Ancient Greek Ancient Greek includes the forms of the Greek language used in a ...

at the upper left of the chemical symbol and to indicate the atomic number with a
subscript A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the , while supersc ...

at the lower left (e.g. , , , , , and ). Because the atomic number is given by the element symbol, it is common to state only the mass number in the superscript and leave out the atomic number subscript (e.g. , , , , , and ). The letter ''m'' is sometimes appended after the mass number to indicate a
nuclear isomer A nuclear isomer is a state of an , in which one or more s (protons or neutrons) occupy than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited states have 100 to 1000 times longer than the half-lives of the e ...
, a
metastable In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's ground state, state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. I ...

or energetically-excited nuclear state (as opposed to the lowest-energy
ground state The ground state of a quantum-mechanical system is its lowest-energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destro ...
), for example (
tantalum-180m Natural tantalum (73Ta) consists of two stable isotope Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons b ...
). The common pronunciation of the AZE notation is different from how it is written: is commonly pronounced as helium-four instead of four-two-helium, and as uranium two-thirty-five (American English) or uranium-two-three-five (British) instead of 235-92-uranium.

# Radioactive, primordial, and stable isotopes

Some isotopes/nuclides are
radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus The atomic nucleus is the small, dense region consisting of s and s ...

, and are therefore referred to as radioisotopes or
radionuclide A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their ...
s, whereas others have never been observed to decay radioactively and are referred to as stable isotopes or
stable nuclide Stable nuclides are nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy stat ...
s. For example, is a radioactive form of carbon, whereas and are stable isotopes. There are about 339 naturally occurring nuclides on Earth, of which 286 are
primordial nuclide In geochemistry Geochemistry is the science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of Testability, ...
s, meaning that they have existed since the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

's formation. Primordial nuclides include 34 nuclides with very long
half-lives Half-life (symbol ''t''1⁄2) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents a ...
(over 100 million years) and 252 that are formally considered as "
stable nuclide Stable nuclides are nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy stat ...
s", because they have not been observed to decay. In most cases, for obvious reasons, if an element has stable isotopes, those isotopes predominate in the elemental abundance found on Earth and in the Solar System. However, in the cases of three elements (
tellurium Tellurium is a chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that ...

,
indium Indium is a chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that c ...

, and
rhenium Rhenium is a chemical element with the Symbol (chemistry), symbol Re and atomic number 75. It is a silvery-gray, heavy, third-row transition metal in group 7 element, group 7 of the periodic table. With an estimated average concentration of 1 pa ...

) the most abundant isotope found in nature is actually one (or two) extremely long-lived radioisotope(s) of the element, despite these elements having one or more stable isotopes. Theory predicts that many apparently "stable" isotopes/nuclides are radioactive, with extremely long half-lives (discounting the possibility of
proton decay #REDIRECT Proton decay#REDIRECT Proton decay In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of ...

, which would make all nuclides ultimately unstable). Some stable nuclides are in theory energetically susceptible to other known forms of decay, such as alpha decay or double beta decay, but no decay products have yet been observed, and so these isotopes are said to be "observationally stable". The predicted half-lives for these nuclides often greatly exceed the estimated age of the universe, and in fact, there are also 31 known radionuclides (see
primordial nuclide In geochemistry Geochemistry is the science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of Testability, ...
) with half-lives longer than the age of the universe. Adding in the radioactive nuclides that have been created artificially, there are 3,339 currently known nuclides. These include 905 nuclides that are either stable or have half-lives longer than 60 minutes. See
list of nuclides This list of nuclides shows observed nuclides that either are stable or, if radioactive, have half-lives longer than one hour. This represents isotopes of the first 105 elements, except for elements 87 (francium Francium is a chemical elemen ...
for details.

# History

The existence of isotopes was first suggested in 1913 by the radiochemist
Frederick Soddy Frederick Soddy FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family Resource ...

, based on studies of radioactive
decay chain In nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". Most Radionuclide, radioisotopes do not de ...
s that indicated about 40 different species referred to as ''radioelements'' (i.e. radioactive elements) between uranium and lead, although the periodic table only allowed for 11 elements between lead and uranium inclusive. Several attempts to separate these new radioelements chemically had failed.Scerri, Eric R. (2007) ''The Periodic Table'' Oxford University Press, pp. 176–179 For example, Soddy had shown in 1910 that mesothorium (later shown to be 228Ra),
radium Radium is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elem ...

(226Ra, the longest-lived isotope), and thorium X (224Ra) are impossible to separate. Attempts to place the radioelements in the periodic table led Soddy and
Kazimierz Fajans Kazimierz Fajans (Kasimir Fajans in many American publications; 27 May 1887 – 18 May 1975) was a Polish American Polish Americans ( pl, Polonia amerykańska) are Americans who have total or partial Poles, Polish ancestry. There are an estimate ...

independently to propose their radioactive displacement law in 1913, to the effect that produced an element two places to the left in the periodic table, whereas
beta decay In , beta decay (''β''-decay) is a type of in which a (fast energetic or ) is emitted from an , transforming the original to an of that nuclide. For example, beta decay of a transforms it into a by the emission of an electron accompanie ...

emission produced an element one place to the right. Soddy recognized that emission of an alpha particle followed by two beta particles led to the formation of an element chemically identical to the initial element but with a mass four units lighter and with different radioactive properties. Soddy proposed that several types of atoms (differing in radioactive properties) could occupy the same place in the table. For example, the alpha-decay of uranium-235 forms thorium-231, whereas the beta decay of actinium-230 forms thorium-230. The term "isotope", Greek for "at the same place", was suggested to Soddy by Margaret Todd, a Scottish physician and family friend, during a conversation in which he explained his ideas to her. He won the 1921
Nobel Prize in Chemistry ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "MD ...
in part for his work on isotopes. In 1914 T. W. Richards found variations between the atomic weight of lead from different mineral sources, attributable to variations in isotopic composition due to different radioactive origins.The origins of the conceptions of isotopes
Frederick Soddy, Nobel prize lecture

## Stable isotopes

The first evidence for multiple isotopes of a stable (non-radioactive) element was found by J. J. Thomson in 1912 as part of his exploration into the composition of
canal rays 200 px, Anode ray tube showing the rays passing through the perforated cathode and causing the pink glow above it. An anode ray (also positive ray or canal ray) is a beam of positive ions that is created by certain types of gas-discharge tubes. ...

(positive ions). Thomson channelled streams of
neon Neon is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior ...

ions through parallel magnetic and electric fields, measured their deflection by placing a photographic plate in their path, and computed their mass to charge ratio using a method that became known as the Thomson's parabola method. Each stream created a glowing patch on the plate at the point it struck. Thomson observed two separate parabolic patches of light on the photographic plate (see image), which suggested two species of nuclei with different mass to charge ratios. subsequently discovered multiple stable isotopes for numerous elements using a
mass spectrograph Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio The mass-to-charge ratio (''m''/''Q'') is a physical quantity A physical quantity is a physical property of a material or system that can be Quanti ...
. In 1919 Aston studied neon with sufficient
resolution Resolution(s) may refer to: Common meanings * Resolution (debate), the statement which is debated in policy debate * Resolution (law), a written motion adopted by a deliberative body * New Year's resolution, a commitment that an individual make ...
to show that the two isotopic masses are very close to the integers 20 and 22 and that neither is equal to the known molar mass (20.2) of neon gas. This is an example of Aston's
whole number rule In chemistry, the whole number rule states that the masses of the isotopes are Natural number, whole number multiples of the mass of the hydrogen atom. The rule is a modified version of Prout's hypothesis proposed in 1815, to the effect that atomic ...
for isotopic masses, which states that large deviations of elemental molar masses from integers are primarily due to the fact that the element is a mixture of isotopes. Aston similarly showed that the molar mass of
chlorine Chlorine is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemica ...

(35.45) is a weighted average of the almost integral masses for the two isotopes 35Cl and 37Cl.

# Variation in properties between isotopes

## Chemical and molecular properties

A neutral atom has the same number of electrons as protons. Thus different isotopes of a given element all have the same number of electrons and share a similar electronic structure. Because the chemical behavior of an atom is largely determined by its electronic structure, different isotopes exhibit nearly identical chemical behavior. The main exception to this is the
kinetic isotope effect In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. ...
: due to their larger masses, heavier isotopes tend to react somewhat more slowly than lighter isotopes of the same element. This is most pronounced by far for (),
deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes The term stable isotope has a meaning similar to stable nuclide, but is preferably used when speaking of nuclides of a specific elemen ...

(), and
tritium Tritium ( or , ) or hydrogen-3 (symbol T or H) is a rare and radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucl ...

(), because deuterium has twice the mass of protium and tritium has three times the mass of protium. These mass differences also affect the behavior of their respective chemical bonds, by changing the center of gravity (
reduced massIn physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Spac ...

) of the atomic systems. However, for heavier elements, the relative mass difference between isotopes is much less so that the mass-difference effects on chemistry are usually negligible. (Heavy elements also have relatively more neutrons than lighter elements, so the ratio of the nuclear mass to the collective electronic mass is slightly greater.) There is also an equilibrium isotope effect. Similarly, two
molecules A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon ...

that differ only in the isotopes of their atoms (
isotopologue Isotopologues are molecules that differ only in their Isotope, isotopic composition. They have the same chemical formula and bonding arrangement of atoms, but at least one atom has a different number of neutrons than the parent. An example is water ...
s) have identical electronic structures, and therefore almost indistinguishable physical and chemical properties (again with deuterium and tritium being the primary exceptions). The ''vibrational modes'' of a molecule are determined by its shape and by the masses of its constituent atoms; so different isotopologues have different sets of vibrational modes. Because vibrational modes allow a molecule to absorb
photon The photon ( el, φῶς, phōs, light) is a type of elementary particle In , an elementary particle or fundamental particle is a that is not composed of other particles. Particles currently thought to be elementary include the fundamental s ...

s of corresponding energies, isotopologues have different optical properties in the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior ...

range.

## Nuclear properties and stability

Atomic nuclei consist of protons and neutrons bound together by the residual strong force. Because protons are positively charged, they repel each other. Neutrons, which are electrically neutral, stabilize the nucleus in two ways. Their copresence pushes protons slightly apart, reducing the electrostatic repulsion between the protons, and they exert the attractive nuclear force on each other and on protons. For this reason, one or more neutrons are necessary for two or more protons to bind into a nucleus. As the number of protons increases, so does the ratio of neutrons to protons necessary to ensure a stable nucleus (see graph at right). For example, although the neutron:proton ratio of is 1:2, the neutron:proton ratio of is greater than 3:2. A number of lighter elements have stable nuclides with the ratio 1:1 (''Z'' = ''N''). The nuclide (calcium-40) is observationally the heaviest stable nuclide with the same number of neutrons and protons. All stable nuclides heavier than calcium-40 contain more neutrons than protons.

## Numbers of isotopes per element

Of the 80 elements with a stable isotope, the largest number of stable isotopes observed for any element is ten (for the element
tin Tin is a with the Sn (from la, ) and  50. Tin is a silvery-colored metal that characteristically has a faint yellow hue. Tin is soft enough to be cut with little force and a bar of tin can be bent by hand with little effort. When bent ...

). No element has nine or eight stable isotopes. Five elements have seven stable isotopes, eight have six stable isotopes, ten have five stable isotopes, nine have four stable isotopes, five have three stable isotopes, 16 have two stable isotopes (counting as stable), and 26 elements have only a single stable isotope (of these, 19 are so-called
mononuclidic element A mononuclidic element or monotopic element is one of the 21 chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuc ...
s, having a single primordial stable isotope that dominates and fixes the atomic weight of the natural element to high precision; 3 radioactive mononuclidic elements occur as well). In total, there are 252 nuclides that have not been observed to decay. For the 80 elements that have one or more stable isotopes, the average number of stable isotopes is 252/80 = 3.15 isotopes per element.

## Even and odd nucleon numbers

The proton:neutron ratio is not the only factor affecting nuclear stability. It depends also on evenness or oddness of its atomic number ''Z'', neutron number ''N'' and, consequently, of their sum, the mass number ''A''. Oddness of both ''Z'' and ''N'' tends to lower the
nuclear binding energy Nuclear binding energy in experimental physics is the minimum energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge ...
, making odd nuclei, generally, less stable. This remarkable difference of nuclear binding energy between neighbouring nuclei, especially of odd-''A'' isobars, has important consequences: unstable isotopes with a nonoptimal number of neutrons or protons decay by
beta decay In , beta decay (''β''-decay) is a type of in which a (fast energetic or ) is emitted from an , transforming the original to an of that nuclide. For example, beta decay of a transforms it into a by the emission of an electron accompanie ...

(including
positron emission Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic ...
),
electron capture Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom An atom is the smallest unit of ordinary matter In classical physics ...

, or other less common decay modes such as
spontaneous fission Spontaneous fission (SF) is a form of radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy b ...
and
cluster decay Cluster decay, also named heavy particle radioactivity or heavy ion radioactivity, is a rare type of nuclear decay in which an atomic nucleus emits a small "cluster" of neutron The neutron is a subatomic particle, symbol or , which has a ...
. The majority of stable nuclides are even-proton-even-neutron, where all numbers ''Z'', ''N'', and ''A'' are even. The odd-''A'' stable nuclides are divided (roughly evenly) into odd-proton-even-neutron, and even-proton-odd-neutron nuclides. Stable odd-proton-odd-neutron nuclei are the least common.

### Even atomic number

The 146 even-proton, even-neutron (EE) nuclides comprise ~58% of all stable nuclides and all have
spin Spin or spinning may refer to: Businesses * or South Pacific Island Network * , an American scooter-sharing system * , a chain of table tennis lounges Computing * , 's tool for formal verification of distributed software systems * , a Mach-like ...
0 because of pairing. There are also 24 primordial long-lived even-even nuclides. As a result, each of the 41 even-numbered elements from 2 to 82 has at least one stable isotope, and most of these elements have ''several'' primordial isotopes. Half of these even-numbered elements have six or more stable isotopes. The extreme stability of
helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consists ...

due to a double
pairing In mathematics, a pairing is an ''R''-Bilinear map#Modules, bilinear map from the Cartesian product of two ''R''-Module (mathematics), modules, where the underlying Ring (mathematics), ring ''R'' is Commutative ring, commutative. Definition Let ''R ...
of 2 protons and 2 neutrons prevents ''any'' nuclides containing five (, ) or eight () nucleons from existing for long enough to serve as platforms for the buildup of heavier elements via
nuclear fusion Nuclear fusion is a nuclear reaction, reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles (neutrons or protons). The difference in mass between the reactants and products ...

in stars (see
triple alpha process Triple is used in several contexts to mean "threefold" or a " treble": Sports * Triple (baseball), a three-base hit * A basketball three-point field goal * A figure skating jump with three rotations * In bowling terms, three strikes in a row * In ...
). 53 stable nuclides have an even number of protons and an odd number of neutrons. They are a minority in comparison to the even-even isotopes, which are about 3 times as numerous. Among the 41 even-''Z'' elements that have a stable nuclide, only two elements (argon and cerium) have no even-odd stable nuclides. One element (tin) has three. There are 24 elements that have one even-odd nuclide and 13 that have two odd-even nuclides. Of 35 primordial radionuclides there exist four even-odd nuclides (see table at right), including the
fissile In nuclear engineering Nuclear engineering is the branch of engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, veh ...
. Because of their odd neutron numbers, the even-odd nuclides tend to have large
neutron capture Neutron capture is a nuclear reaction In nuclear physics Nuclear physics is the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion a ...
cross-sections, due to the energy that results from neutron-pairing effects. These stable even-proton odd-neutron nuclides tend to be uncommon by abundance in nature, generally because, to form and enter into primordial abundance, they must have escaped capturing neutrons to form yet other stable even-even isotopes, during both the
s-process The slow neutron-capture process, or ''s''-process, is a series of reactions in nuclear astrophysics that occur in stars, particularly AGB stars. The ''s''-process is responsible for the creation ( nucleosynthesis) of approximately half the atomi ...
and
r-process In nuclear astrophysics Nuclear astrophysics is an interdisciplinary part of both nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. Other forms of nuclear matter are als ...

of neutron capture, during nucleosynthesis in stars. For this reason, only and are the most naturally abundant isotopes of their element.

### Odd atomic number

Forty-eight stable odd-proton-even-neutron nuclides, stabilized by their paired neutrons, form most of the stable isotopes of the odd-numbered elements; the very few odd-proton-odd-neutron nuclides comprise the others. There are 41 odd-numbered elements with ''Z'' = 1 through 81, of which 39 have stable isotopes (the elements
technetium Technetium is a chemical element with the Symbol (chemistry), symbol Tc and atomic number 43. It is the lightest element whose isotopes are all radioactive. Nearly all available technetium is produced as a synthetic element. Naturally occurring t ...

() and
promethium Promethium is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical ele ...

() have no stable isotopes). Of these 39 odd ''Z'' elements, 30 elements (including hydrogen-1 where 0 neutrons is even) have one stable odd-even isotope, and nine elements:
chlorine Chlorine is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemica ...

(),
potassium Potassium is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, b ...

(),
copper Copper is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elem ...

(),
gallium Gallium is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elemen ...

(),
bromine Bromine is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elemen ...

(),
silver Silver is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical ele ...

(),
antimony Antimony is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, be ...

(),
iridium Iridium is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, beh ...

(), and
thallium Thallium is a chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science tha ...

(), have two odd-even stable isotopes each. This makes a total 30 + 2(9) = 48 stable odd-even isotopes. There are also five primordial long-lived radioactive odd-even isotopes, , , , , and . The last two were only recently found to decay, with half-lives greater than 1018 years. Only five stable nuclides contain both an odd number of protons ''and'' an odd number of neutrons. The first four "odd-odd" nuclides occur in low mass nuclides, for which changing a proton to a neutron or vice versa would lead to a very lopsided proton-neutron ratio (, , , and ; spins 1, 1, 3, 1). The only other entirely "stable" odd-odd nuclide, (spin 9), is thought to be the rarest of the 252 stable isotopes, and is the only primordial
nuclear isomer A nuclear isomer is a state of an , in which one or more s (protons or neutrons) occupy than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited states have 100 to 1000 times longer than the half-lives of the e ...
, which has not yet been observed to decay despite experimental attempts. Many odd-odd radionuclides (like tantalum-180) with comparatively short half-lives are known. Usually, they beta-decay to their nearby even-even isobars that have paired protons and paired neutrons. Of the nine primordial odd-odd nuclides (five stable and four radioactive with long half-lives), only is the most common isotope of a common element. This is the case because it is a part of the CNO cycle. The nuclides and are minority isotopes of elements that are themselves rare compared to other light elements, whereas the other six isotopes make up only a tiny percentage of the natural abundance of their elements.

### Odd neutron number

Actinides with odd neutron number are generally
fissile In nuclear engineering Nuclear engineering is the branch of engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, veh ...
(with thermal neutrons), whereas those with even neutron number are generally not, though they are fissionable with fast neutrons. All observationally stable odd-odd nuclides have nonzero integer spin. This is because the single unpaired neutron and unpaired proton have a larger nuclear force attraction to each other if their spins are aligned (producing a total spin of at least 1 unit), instead of anti-aligned. See
deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes The term stable isotope has a meaning similar to stable nuclide, but is preferably used when speaking of nuclides of a specific elemen ...

for the simplest case of this nuclear behavior. Only , and have odd neutron number and are the most naturally abundant isotope of their element.

# Occurrence in nature

Elements are composed either of one nuclide (
mononuclidic element A mononuclidic element or monotopic element is one of the 21 chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuc ...
s), or of more than one naturally occurring isotopes. The unstable (radioactive) isotopes are either primordial nuclide, primordial or postprimordial. Primordial isotopes were a product of stellar nucleosynthesis or another type of nucleosynthesis such as cosmic ray spallation, and have persisted down to the present because their rate of decay is so slow (e.g. uranium-238 and potassium-40). Post-primordial isotopes were created by cosmic ray bombardment as cosmogenic nuclides (e.g.,
tritium Tritium ( or , ) or hydrogen-3 (symbol T or H) is a rare and radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucl ...

,
carbon-14 Carbon-14 (14C), or radiocarbon, is a radioactive isotope A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ...

), or by the decay of a radioactive primordial isotope to a radioactive radiogenic nuclide daughter (e.g. uranium to
radium Radium is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elem ...

). A few isotopes are naturally synthesized as nucleogenic nuclides, by some other natural nuclear reaction, such as when neutrons from natural nuclear fission are absorbed by another atom. As discussed above, only 80 elements have any stable isotopes, and 26 of these have only one stable isotope. Thus, about two-thirds of stable elements occur naturally on Earth in multiple stable isotopes, with the largest number of stable isotopes for an element being ten, for
tin Tin is a with the Sn (from la, ) and  50. Tin is a silvery-colored metal that characteristically has a faint yellow hue. Tin is soft enough to be cut with little force and a bar of tin can be bent by hand with little effort. When bent ...

(). There are about 94 elements found naturally on Earth (up to plutonium inclusive), though some are detected only in very tiny amounts, such as plutonium-244. Scientists estimate that the elements that occur naturally on Earth (some only as radioisotopes) occur as 339 isotopes (
nuclide A nuclide (or nucleide, from nucleus ''Nucleus'' (plural nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic c ...

s) in total. Only 252 of these naturally occurring nuclides are stable in the sense of never having been observed to decay as of the present time. An additional 34
primordial nuclide In geochemistry Geochemistry is the science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of Testability, ...
s (to a total of 286 primordial nuclides), are radioactive with known half-lives, but have half-lives longer than 100 million years, allowing them to exist from the beginning of the Solar System. See
list of nuclides This list of nuclides shows observed nuclides that either are stable or, if radioactive, have half-lives longer than one hour. This represents isotopes of the first 105 elements, except for elements 87 (francium Francium is a chemical elemen ...
for details. All the known
stable nuclide Stable nuclides are nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy stat ...
s occur naturally on Earth; the other naturally occurring nuclides are radioactive but occur on Earth due to their relatively long half-lives, or else due to other means of ongoing natural production. These include the afore-mentioned cosmogenic nuclides, the nucleogenic nuclides, and any radiogenic nuclides formed by ongoing decay of a primordial radioactive nuclide, such as radon and
radium Radium is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elem ...

from uranium. An additional ~3000 radioactive nuclides not found in nature have been created in nuclear reactors and in particle accelerators. Many short-lived nuclides not found naturally on Earth have also been observed by spectroscopic analysis, being naturally created in stars or supernovae. An example is aluminium-26, which is not naturally found on Earth but is found in abundance on an astronomical scale. The tabulated atomic masses of elements are averages that account for the presence of multiple isotopes with different masses. Before the discovery of isotopes, empirically determined noninteger values of atomic mass confounded scientists. For example, a sample of
chlorine Chlorine is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemica ...

contains 75.8% chlorine-35 and 24.2% chlorine-37, giving an average atomic mass of 35.5 atomic mass units. According to generally accepted physical cosmology, cosmology theory, only isotopes of hydrogen and helium, traces of some isotopes of lithium and beryllium, and perhaps some boron, were created at the Big Bang, while all other nuclides were synthesized later, in stars and supernovae, and in interactions between energetic particles such as cosmic rays, and previously produced nuclides. (See nucleosynthesis for details of the various processes thought responsible for isotope production.) The respective abundances of isotopes on Earth result from the quantities formed by these processes, their spread through the galaxy, and the rates of decay for isotopes that are unstable. After the initial coalescence of the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

, isotopes were redistributed according to mass, and the isotopic composition of elements varies slightly from planet to planet. This sometimes makes it possible to trace the origin of meteorites.

# Atomic mass of isotopes

The atomic mass (''m''r) of an isotope (nuclide) is determined mainly by its
mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of s and s (together known as s) in an . It is approximately equal to the of the expre ...
(i.e. number of
nucleon In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...
s in its nucleus). Small corrections are due to the binding energy of the nucleus (see mass defect), the slight difference in mass between proton and neutron, and the mass of the electrons associated with the atom, the latter because the electron:nucleon ratio differs among isotopes. The mass number is a dimensionless quantity. The atomic mass, on the other hand, is measured using the atomic mass unit based on the mass of the carbon-12 atom. It is denoted with symbols "u" (for unified atomic mass unit) or "Da" (for John Dalton, dalton). The atomic masses of naturally occurring isotopes of an element determine the atomic mass of the element. When the element contains ''N'' isotopes, the expression below is applied for the average atomic mass $\overline m_a$: $\overline m_a = m_1 x_1+m_2 x_2+...+m_Nx_N$ where ''m''1, ''m''2, ..., ''m''''N'' are the atomic masses of each individual isotope, and ''x''1, ..., ''x''''N'' are the relative abundances of these isotopes.

# Applications of isotopes

## Purification of isotopes

Several applications exist that capitalize on the properties of the various isotopes of a given element. Isotope separation is a significant technological challenge, particularly with heavy elements such as uranium or plutonium. Lighter elements such as lithium, carbon, nitrogen, and oxygen are commonly separated by gas diffusion of their compounds such as CO and NO. The separation of hydrogen and deuterium is unusual because it is based on chemical rather than physical properties, for example in the Girdler sulfide process. Uranium isotopes have been separated in bulk by gas diffusion, gas centrifugation, laser ionization separation, and (in the Manhattan Project) by a type of production mass spectrometry.

## Use of chemical and biological properties

* Isotope analysis is the determination of isotopic signature, the relative abundances of isotopes of a given element in a particular sample. Isotope analysis is frequently done by isotope ratio mass spectrometry. For biogenic substances in particular, significant variations of isotopes of C, N, and O can occur. Analysis of such variations has a wide range of applications, such as the detection of adulteration in food products or the geographic origins of products using isoscapes. The identification of Mars meteorite, certain meteorites as having originated on Mars is based in part upon the isotopic signature of trace gases contained in them. * Isotopic substitution can be used to determine the mechanism of a chemical reaction via the
kinetic isotope effect In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. ...
. * Another common application is isotopic labeling, the use of unusual isotopes as tracers or markers in chemical reactions. Normally, atoms of a given element are indistinguishable from each other. However, by using isotopes of different masses, even different nonradioactive stable isotopes can be distinguished by mass spectrometry or infrared spectroscopy. For example, in 'stable isotope labeling with amino acids in cell culture (SILAC)' stable isotopes are used to quantify proteins. If radioactive isotopes are used, they can be detected by the radiation they emit (this is called ''radioisotopic labeling''). * Isotopes are commonly used to determine the concentration of various elements or substances using the isotope dilution method, whereby known amounts of isotopically-substituted compounds are mixed with the samples and the isotopic signatures of the resulting mixtures are determined with mass spectrometry.

## Use of nuclear properties

* A technique similar to radioisotopic labeling is radiometric dating: using the known half-life of an unstable element, one can calculate the amount of time that has elapsed since a known concentration of isotope existed. The most widely known example is radiocarbon dating used to determine the age of carbonaceous materials. * Several forms of spectroscopy rely on the unique nuclear properties of specific isotopes, both radioactive and stable. For example, nuclear magnetic resonance (NMR) spectroscopy can be used only for isotopes with a nonzero nuclear spin. The most common nuclides used with NMR spectroscopy are 1H, 2D, 15N, 13C, and 31P. * Mössbauer spectroscopy also relies on the nuclear transitions of specific isotopes, such as 57Fe. * Radionuclides also have important uses. Nuclear power and nuclear weapons development require relatively large quantities of specific isotopes. Nuclear medicine and radiation oncology utilize radioisotopes respectively for medical diagnosis and treatment.

* Abundance of the chemical elements * Bainbridge mass spectrometer * Geotraces * Isotopomer * List of nuclides * List of particles * Mass spectrometry * Reference Materials for Stable Isotope Analysis, Reference materials for stable isotope analysis * Table of nuclides

# References

The Nuclear Science web portal Nucleonica

The Karlsruhe Nuclide Chart

National Nuclear Data Center
Portal to large repository of free data and analysis programs from NNDC
National Isotope Development Center
Coordination and management of the production, availability, and distribution of isotopes, and reference information for the isotope community
Isotope Development & Production for Research and Applications (IDPRA)
U.S. Department of Energy program for isotope production and production research and development
International Atomic Energy Agency
Homepage of International Atomic Energy Agency (IAEA), an Agency of the United Nations (UN)
Atomic Weights and Isotopic Compositions for All Elements
Static table, from NIST (National Institute of Standards and Technology)
Atomgewichte, Zerfallsenergien und Halbwertszeiten aller Isotope

at the LBNL
Current isotope research and information
isotope.info
Emergency Preparedness and Response: Radioactive Isotopes
by the CDC (Centers for Disease Control and Prevention)
Chart of Nuclides
Interactive Chart of Nuclides (National Nuclear Data Center)

* [http://www-nds.iaea.org/livechart The LIVEChart of Nuclides – IAEA] with isotope data.
Annotated bibliography for isotopes
from the Alsos Digital Library for Nuclear Issues
The Valley of Stability (video)
– a virtual "flight" through 3D representation of the nuclide chart, by French Alternative Energies and Atomic Energy Commission, CEA (France) {{Authority control Isotopes, Nuclear physics