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Isotopes are two or more types of atoms that have the same
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of eve ...
(number of
protons A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mas ...
in their nuclei) and position in the
periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
(and hence belong to the same
chemical element A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler s ...
), and that differ in
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons we ...
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 protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxi ...
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 beha ...
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 rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
. It was coined by Scottish doctor and writer Margaret Todd in 1913 in a suggestion to the British chemist
Frederick Soddy Frederick Soddy FRS (2 September 1877 – 22 September 1956) was an English radiochemist who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions. He also p ...
. The number of protons within the atom's nucleus is called its
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of eve ...
and is equal to the number of
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
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 beha ...
s. The number of
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons we ...
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 protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxi ...
, and each isotope of a given element has a different mass number. For example,
carbon-12 Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon ( carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 i ...
,
carbon-13 Carbon-13 (13C) is a natural, stable isotope of carbon with a nucleus containing six protons and seven neutrons. As one of the environmental isotopes, it makes up about 1.1% of all natural carbon on Earth. Detection by mass spectrometry A ma ...
, and
carbon-14 Carbon-14, C-14, or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and c ...
are three isotopes of the element
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon m ...
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, 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 state. The word ''nuclide'' was coined by Tru ...
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 having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., w ...
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, or phrase that means exactly or nearly the same as another word, morpheme, or phrase in a given language. For example, in the English language, the words ''begin'', ''start'', ''commence'', and ''initiate'' are a ...
s'' or ''
isomer In chemistry, isomers are molecules or polyatomic ions with identical molecular formulae – that is, same number of atoms of each element – but distinct arrangements of atoms in space. Isomerism is existence or possibility of isomers. Iso ...
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 Nuclear technology is technology that involves the nuclear reactions of atomic nuclei. Among the notable nuclear technologies are nuclear reactors, nuclear medicine and nuclear weapons. It is also used, among other things, in smoke detect ...
and
nuclear medicine Nuclear medicine or nucleology is a medical specialty involving the application of radioactive substances in the diagnosis and treatment of disease. Nuclear imaging, in a sense, is "radiology done inside out" because it records radiation emitt ...
.

# 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 of helium with two protons and one neutron (the most common isotope, helium-4, having two protons and two neutrons in contrast). Other than protium (ordinary hydrogen), helium-3 is ...
,
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 consis ...
,
carbon-12 Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon ( carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 i ...
,
carbon-14 Carbon-14, C-14, or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and c ...
,
uranium-235 Uranium-235 (235U or U-235) is an 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 that ex ...
and
uranium-239 Uranium (92U) is a naturally occurring radioactive element that has no stable isotope. It has two primordial isotopes, uranium-238 and uranium-235, that have long half-lives and are found in appreciable quantity in the Earth's crust. The decay p ...
). When a
chemical symbol Chemical symbols are the abbreviations used in chemistry for chemical elements, functional groups and chemical compounds. Element symbols for chemical elements normally consist of one or two letters from the Latin alphabet and are written with th ...
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 protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxi ...
, ''Z'' the
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of eve ...
, and E for
element Element or elements may refer to: Science * Chemical element, a pure substance of one type of atom * Heating element, a device that generates heat by electrical resistance * Orbital elements, parameters required to identify a specific orbit of o ...
) is to indicate the mass number (number of nucleons) with a
superscript 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 baseline, whil ...
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 baseline, whil ...
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 metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited states have ...
, a
metastable In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball ...
or energetically excited nuclear state (as opposed to the lowest-energy
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...
), for example (
tantalum-180m Natural tantalum (73Ta) consists of two stable isotopes: 181Ta (99.988%) and (0.012%). There are also 35 known artificial radioisotopes, the longest-lived of which are 179Ta with a half-life of 1.82 years, 182Ta with a half-life of 114.43 days ...
). 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 loses energy by radiation. A material containing unstable nuclei is cons ...
, and are therefore referred to as radioisotopes or
radionuclide 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 ways: emitted from the nucleus as gamma radiation; transfer ...
s, whereas others have never been observed to decay radioactively and are referred to as stable isotopes or
stable nuclide Stable nuclides are nuclides that are not radioactive and so (unlike radionuclides) do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes. Th ...
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, geophysics and nuclear physics, primordial nuclides, also known as primordial isotopes, are nuclides found on Earth that have existed in their current form since before Earth was formed. Primordial nuclides were present in th ...
s, meaning that they have existed since the
Solar System The Solar System Capitalization 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 "Solar ...
's formation. Primordial nuclides include 35 nuclides with very long
half-lives Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
(over 100 million years) and 251 that are formally considered as "
stable nuclide Stable nuclides are nuclides that are not radioactive and so (unlike radionuclides) do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes. Th ...
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 with the symbol Te and atomic number 52. It is a brittle, mildly toxic, rare, silver-white metalloid. Tellurium is chemically related to selenium and sulfur, all three of which are chalcogens. It is occasionally ...
,
indium Indium is a chemical element with the symbol In and atomic number 49. Indium is the softest metal that is not an alkali metal. It is a silvery-white metal that resembles tin in appearance. It is a post-transition metal that makes up 0.21 part ...
, and
rhenium Rhenium is a chemical element with the symbol Re and atomic number 75. It is a silvery-gray, heavy, third-row transition metal in group 7 of the periodic table. With an estimated average concentration of 1 part per billion (ppb), rhenium is o ...
) 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, 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, geophysics and nuclear physics, primordial nuclides, also known as primordial isotopes, are nuclides found on Earth that have existed in their current form since before Earth was formed. Primordial nuclides were present in th ...
) 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) and 102 ( nobelium). At least 3, ...
for details.

# History

The existence of isotopes was first suggested in 1913 by the radiochemist
Frederick Soddy Frederick Soddy FRS (2 September 1877 – 22 September 1956) was an English radiochemist who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions. He also p ...
, 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 radioisotopes do not decay direc ...
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 with the symbol Ra and atomic number 88. It is the sixth element in group 2 of the periodic table, also known as the alkaline earth metals. Pure radium is silvery-white, but it readily reacts with nitrogen (ra ...
(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 independently to propose their radioactive displacement law in 1913, to the effect that
alpha decay Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an a ...
produced an element two places to the left in the periodic table, whereas
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. F ...
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 received 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 "M ...
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 (positive ions). Thomson channelled streams of
neon Neon is a chemical element with the symbol Ne and atomic number 10. It is a noble gas. Neon is a colorless, odorless, inert monatomic gas under standard conditions, with about two-thirds the density of air. It was discovered (along with kryp ...
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. F. W. Aston subsequently discovered multiple stable isotopes for numerous elements using a mass spectrograph. In 1919 Aston studied neon with sufficient resolution 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 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 in 1920 that the molar mass of
chlorine Chlorine is a chemical element with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine i ...
(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 when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for ...
: 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 protium (),
deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one ...
(), and
tritium Tritium ( or , ) or hydrogen-3 (symbol T or H) is a rare and radioactive isotope of hydrogen with half-life about 12 years. The nucleus of tritium (t, sometimes called a ''triton'') contains one proton and two neutrons, whereas the nucleus ...
(), 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 mass In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the m ...
) 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 a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioc ...
that differ only in the isotopes of their atoms (
isotopologue In chemistry, isotopologues are molecules that differ only in their 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 exampl ...
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 A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they ...
s of corresponding energies, isotopologues have different optical properties in the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from aroun ...
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 chemical element with the symbol Sn (from la, stannum) and atomic number 50. Tin is a silvery-coloured metal. 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 elements, 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 251 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 251/80 ≈ 3.14 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 that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is alway ...
, 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 nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. F ...
(including
positron emission Positron emission, beta plus decay, or β+ decay is a subtype of radioactive decay called beta decay, in which a proton inside a radionuclide nucleus is converted into a neutron while releasing a positron and an electron neutrino (). Positron emi ...
),
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 absorbs an inner atomic electron, usually from the K or L electron shells. Th ...
, or other less common decay modes such as
spontaneous fission Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements. The nuclear binding energy of the elements reaches its maximum at an atomic mass number of about 56 (e.g., iron-56); spontaneous brea ...
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 neutrons and protons, more than in an alpha particle, but less than a typic ...
. 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 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 consis ...
due to a double
pairing In mathematics, a pairing is an ''R''- bilinear map from the Cartesian product of two ''R''- modules, where the underlying ring ''R'' is commutative. Definition Let ''R'' be a commutative ring with unit, and let ''M'', ''N'' and ''L'' be ''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 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 is manif ...
in stars (see
triple alpha process The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon. Triple-alpha process in stars Helium accumulates in the cores of stars as a result of the proton– ...
). 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, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be ty ...
. Because of their odd neutron numbers, the even-odd nuclides tend to have large
neutron capture Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, ...
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 asymptotic giant branch stars. The ''s''-process is responsible for the creation ( nucleosynthesis) of approxi ...
and
r-process In nuclear astrophysics, the rapid neutron-capture process, also known as the ''r''-process, is a set of nuclear reactions that is responsible for the creation of approximately half of the atomic nuclei heavier than iron, the "heavy elements ...
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 Tc and atomic number 43. It is the lightest element whose isotopes are all radioactive. All available technetium is produced as a synthetic element. Naturally occurring technetium is a spontaneous ...
() and
promethium Promethium is a chemical element with the symbol Pm and atomic number 61. All of its isotopes are radioactive; it is extremely rare, with only about 500–600 grams naturally occurring in Earth's crust at any given time. Promethium is one of onl ...
() 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 with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine i ...
(),
potassium Potassium is the chemical element with the symbol K (from Neo-Latin '' kalium'') and atomic number19. Potassium is a silvery-white metal that is soft enough to be cut with a knife with little force. Potassium metal reacts rapidly with atmo ...
(),
copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
(),
gallium Gallium is a chemical element with the symbol Ga and atomic number 31. Discovered by French chemist Paul-Émile Lecoq de Boisbaudran in 1875, Gallium is in group 13 of the periodic table and is similar to the other metals of the group (alumi ...
(),
bromine Bromine is a chemical element with the symbol Br and atomic number 35. It is the third-lightest element in group 17 of the periodic table ( halogens) and is a volatile red-brown liquid at room temperature that evaporates readily to form a si ...
(),
silver Silver is a chemical element with the symbol Ag (from the Latin ', derived from the Proto-Indo-European ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, white, lustrous transition metal, it exhibits the highest electrical ...
(),
antimony Antimony is a chemical element with the symbol Sb (from la, stibium) and atomic number 51. A lustrous gray metalloid, it is found in nature mainly as the sulfide mineral stibnite (Sb2S3). Antimony compounds have been known since ancient t ...
(),
iridium Iridium is a chemical element with the symbol Ir and atomic number 77. A very hard, brittle, silvery-white transition metal of the platinum group, it is considered the second-densest naturally occurring metal (after osmium) with a density o ...
(), and
thallium Thallium is a chemical element with the symbol Tl and atomic number 81. It is a gray post-transition metal that is not found free in nature. When isolated, thallium resembles tin, but discolors when exposed to air. Chemists William Crookes and ...
(), have two odd-even stable isotopes each. This makes a total 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 251 stable nuclides, and is the only primordial
nuclear isomer A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited states have ...
, which has not yet been observed to decay despite experimental attempts. Many odd-odd radionuclides (such as the ground state of 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 CNO cycle (for carbon– nitrogen–oxygen; sometimes called Bethe–Weizsäcker cycle after Hans Albrecht Bethe and Carl Friedrich von Weizsäcker) is one of the two known sets of fusion reactions by which stars convert hydrogen to heli ...
. 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

Actinide The actinide () or actinoid () series encompasses the 15 metallic chemical elements with atomic numbers from 89 to 103, actinium through lawrencium. The actinide series derives its name from the first element in the series, actinium. The info ...
s with odd neutron number are generally
fissile In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be ty ...
(with
thermal neutron The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term ''temperature'' is used, since hot, thermal and cold neutrons are moderated in a medium with ...
s), whereas those with even neutron number are generally not, though they are
fissionable In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be ty ...
with
fast neutron The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term ''temperature'' is used, since hot, thermal and cold neutrons are moderated in a medium with ...
s. 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 The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nucle ...
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 of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one ...
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 elements), or of more than one naturally occurring isotopes. The unstable (radioactive) isotopes are either
primordial Primordial may refer to: * Primordial era, an era after the Big Bang. See Chronology of the universe * Primordial sea (a.k.a. primordial ocean, ooze or soup). See Abiogenesis * Primordial nuclide, nuclides, a few radioactive, that formed before t ...
or postprimordial. Primordial isotopes were a product of
stellar nucleosynthesis Stellar nucleosynthesis is the creation (nucleosynthesis) of chemical elements by nuclear fusion reactions within stars. Stellar nucleosynthesis has occurred since the original creation of hydrogen, helium and lithium during the Big Bang. As a ...
or another type of nucleosynthesis such as
cosmic ray spallation Cosmic ray spallation, also known as the x-process, is a set of naturally occurring nuclear reactions causing nucleosynthesis; it refers to the formation of chemical elements from the impact of cosmic rays on an object. Cosmic rays are highly ener ...
, and have persisted down to the present because their rate of decay is so slow (e.g.
uranium-238 Uranium-238 (238U or U-238) is the most common isotope of uranium found in nature, with a relative abundance of 99%. Unlike uranium-235, it is non-fissile, which means it cannot sustain a chain reaction in a thermal-neutron reactor. However, i ...
and
potassium-40 Potassium-40 (40K) is a radioactive isotope of potassium which has a long half-life of 1.25 billion years. It makes up about 0.012% (120 ppm) of the total amount of potassium found in nature. Potassium-40 undergoes three types of radioactiv ...
). Post-primordial isotopes were created by
cosmic ray Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our o ...
bombardment as cosmogenic nuclides (e.g.,
tritium Tritium ( or , ) or hydrogen-3 (symbol T or H) is a rare and radioactive isotope of hydrogen with half-life about 12 years. The nucleus of tritium (t, sometimes called a ''triton'') contains one proton and two neutrons, whereas the nucleus ...
,
carbon-14 Carbon-14, C-14, or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and c ...
), or by the decay of a radioactive primordial isotope to a radioactive radiogenic nuclide daughter (e.g.
uranium Uranium is a chemical element with the 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 valence electrons. Uranium is weakly ...
to
radium Radium is a chemical element with the symbol Ra and atomic number 88. It is the sixth element in group 2 of the periodic table, also known as the alkaline earth metals. Pure radium is silvery-white, but it readily reacts with nitrogen (ra ...
). A few isotopes are naturally synthesized as nucleogenic nuclides, by some other natural
nuclear reaction In nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformation ...
, such as when neutrons from natural
nuclear fission Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of r ...
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 chemical element with the symbol Sn (from la, stannum) and atomic number 50. Tin is a silvery-coloured metal. 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 Plutonium is a radioactive chemical element with the symbol Pu and atomic number 94. It is an actinide metal of silvery-gray appearance that tarnishes when exposed to air, and forms a dull coating when oxidized. The element normally exhibi ...
inclusive), though some are detected only in very tiny amounts, such as
plutonium-244 Plutonium-244 (244Pu) is an isotope of plutonium that has a half-life of 80 million years. This is longer than any of the other isotopes of plutonium and longer than any other actinide isotope except for the three naturally abundant ones: uranium ...
. 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, 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 state. The word ''nuclide'' was coined by Tru ...
s) in total. Only 251 of these naturally occurring nuclides are stable, in the sense of never having been observed to decay as of the present time. An additional 35
primordial nuclide In geochemistry, geophysics and nuclear physics, primordial nuclides, also known as primordial isotopes, are nuclides found on Earth that have existed in their current form since before Earth was formed. Primordial nuclides were present in th ...
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) and 102 ( nobelium). At least 3, ...
for details. All the known
stable nuclide Stable nuclides are nuclides that are not radioactive and so (unlike radionuclides) do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes. Th ...
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 A radiogenic nuclide is a nuclide that is produced by a process of radioactive decay. It may itself be radioactive (a radionuclide) or stable (a stable nuclide). Radiogenic nuclides (more commonly referred to as radiogenic isotopes) form some of ...
nuclides formed by ongoing decay of a primordial radioactive nuclide, such as
radon Radon is a chemical element with the symbol Rn and atomic number 86. It is a radioactive, colourless, odourless, tasteless noble gas. It occurs naturally in minute quantities as an intermediate step in the normal radioactive decay chains through ...
and
radium Radium is a chemical element with the symbol Ra and atomic number 88. It is the sixth element in group 2 of the periodic table, also known as the alkaline earth metals. Pure radium is silvery-white, but it readily reacts with nitrogen (ra ...
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
supernova A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or wh ...
e. An example is
aluminium-26 Aluminium-26 (26Al, Al-26) is a radioactive isotope of the chemical element aluminium, decaying by either positron emission or electron capture to stable magnesium-26. The half-life of 26Al is 7.17 (717,000) years. This is far too short for th ...
, 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 with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine i ...
contains 75.8% chlorine-35 and 24.2% chlorine-37, giving an average atomic mass of 35.5
atomic mass unit The dalton or unified atomic mass unit (symbols: Da or u) is a non-SI unit of mass widely used in physics and chemistry. It is defined as of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at r ...
s. According to generally accepted 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 The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
, 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 Nucleosynthesis is the process that creates new atomic nuclei from pre-existing nucleons (protons and neutrons) and nuclei. According to current theories, the first nuclei were formed a few minutes after the Big Bang, through nuclear reactions in ...
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 System Capitalization 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 "Solar ...
, 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
meteorite A meteorite is a solid piece of debris from an object, such as a comet, asteroid, or meteoroid, that originates in outer space and survives its passage through the atmosphere to reach the surface of a planet or moon. When the original obje ...
s.

# Atomic mass of isotopes

The
atomic mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&nb ...
(''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 protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxi ...
(i.e. number of
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons we ...
s in its nucleus). Small corrections are due to the
binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
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 A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or ...
. The atomic mass, on the other hand, is measured using the
atomic mass unit The dalton or unified atomic mass unit (symbols: Da or u) is a non-SI unit of mass widely used in physics and chemistry. It is defined as of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at r ...
based on the mass of the carbon-12 atom. It is denoted with symbols "u" (for unified atomic mass unit) or "Da" (for dalton). The atomic masses of naturally occurring isotopes of an element determine the
standard atomic weight The standard atomic weight of a chemical element (symbol ''A''r°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, ...
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 Isotope separation is the process of concentrating specific isotopes of a chemical element by removing other isotopes. The use of the nuclides produced is varied. The largest variety is used in research (e.g. in chemistry where atoms of "marker" n ...
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 The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
) by a type of production
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a '' mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is u ...
.

## Use of chemical and biological properties

*
Isotope analysis Isotope analysis is the identification of isotopic signature, abundance of certain stable isotopes of chemical elements within organic and inorganic compounds. Isotopic analysis can be used to understand the flow of energy through a food ...
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 Isotope-ratio mass spectrometry (IRMS) is a specialization of mass spectrometry, in which mass spectrometric methods are used to measure the relative abundance of isotopes in a given sample. This technique has two different applications in the ea ...
. For
biogenic substance A biogenic substance is a product made by or of life forms. While the term originally was specific to metabolite compounds that had toxic effects on other organisms, it has developed to encompass any constituents, secretions, and metabolites of ...
s 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 certain meteorites as having originated on
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...
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 A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaki ...
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 when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for ...
. * Another common application is
isotopic labeling Isotopic labeling (or isotopic labelling) is a technique used to track the passage of an isotope (an atom with a detectable variation in neutron count) through a reaction, metabolic pathway, or cell. The reactant is 'labeled' by replacing specif ...
, 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 isotope The term stable isotope has a meaning similar to stable nuclide, but is preferably used when speaking of nuclides of a specific element. Hence, the plural form stable isotopes usually refers to isotopes of the same element. The relative abundan ...
s can be distinguished by
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a '' mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is u ...
or
infrared spectroscopy Infrared spectroscopy (IR spectroscopy or vibrational spectroscopy) is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functio ...
. For example, in 'stable isotope labeling with amino acids in cell culture (
SILAC Stable Isotope Labeling by/with Amino acids in Cell culture (SILAC) is a technique based on mass spectrometry that detects differences in protein abundance among samples using non-radioactive isotopic labeling. It is a popular method for quantitati ...
)' stable isotopes are used to quantify
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, res ...
s. 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 Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a '' mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is u ...
.

## Use of nuclear properties

* A technique similar to radioisotopic labeling is
radiometric dating Radiometric dating, radioactive dating or radioisotope dating is a technique which is used to date materials such as rocks or carbon, in which trace radioactive impurities were selectively incorporated when they were formed. The method compares ...
: using the known
half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable a ...
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 Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon. The method was ...
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 Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...
(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. *
Radionuclide 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 ways: emitted from the nucleus as gamma radiation; transfer ...
s also have important uses.
Nuclear power Nuclear power is the use of nuclear reactions to produce electricity. Nuclear power can be obtained from nuclear fission, nuclear decay and nuclear fusion reactions. Presently, the vast majority of electricity from nuclear power is produ ...
and
nuclear weapon A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions ( thermonuclear bomb), producing a nuclear explosion. Both b ...
s development require relatively large quantities of specific isotopes.
Nuclear medicine Nuclear medicine or nucleology is a medical specialty involving the application of radioactive substances in the diagnosis and treatment of disease. Nuclear imaging, in a sense, is "radiology done inside out" because it records radiation emitt ...
and
radiation oncology Radiation therapy or radiotherapy, often abbreviated RT, RTx, or XRT, is a therapy using ionizing radiation, generally provided as part of cancer treatment to control or kill malignant cells and normally delivered by a linear accelerator. Radiat ...
utilize radioisotopes respectively for medical diagnosis and treatment.

*
Abundance of the chemical elements The abundance of the chemical elements is a measure of the occurrence of the chemical elements relative to all other elements in a given environment. Abundance is measured in one of three ways: by the mass-fraction (the same as weight fraction); ...
* Bainbridge mass spectrometer * Geotraces *
Isotopomer Isotopomers or isotopic isomers are isomers with isotopic atoms, having the same number of each isotope of each element but differing in their positions. The result is that the molecules are either constitutional isomers or stereoisomers solely ...
*
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) and 102 ( nobelium). At least 3, ...
*
List of particles This is a list of known and hypothesized particles. Elementary particles Elementary particles are particles with no measurable internal structure; that is, it is unknown whether they are composed of other particles. They are the fundamental ob ...
*
Mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a '' mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is u ...
* 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 The International Atomic Energy Agency (IAEA) is an intergovernmental organization that seeks to promote the peaceful use of nuclear energy and to inhibit its use for any military purpose, including nuclear weapons. It was established in 195 ...
(IAEA), an Agency of the
United Nations The United Nations (UN) is an intergovernmental organization whose stated purposes are to maintain international peace and security, develop friendly relations among nations, achieve international cooperation, and be a centre for harmoniz ...
(UN)
Atomic Weights and Isotopic Compositions for All Elements
Static table, from NIST (
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...
)
Atomgewichte, Zerfallsenergien und Halbwertszeiten aller Isotope

at the
LBNL Lawrence Berkeley National Laboratory (LBNL), commonly referred to as the Berkeley Lab, is a United States national laboratory that is owned by, and conducts scientific research on behalf of, the United States Department of Energy. Located in ...

Current isotope research and information
isotope.info
Emergency Preparedness and Response: Radioactive Isotopes
by the CDC (
Centers for Disease Control and Prevention The Centers for Disease Control and Prevention (CDC) is the national public health agency of the United States. It is a United States federal agency, under the Department of Health and Human Services, and is headquartered in Atlanta, Geor ...
)
Chart of Nuclides
Interactive Chart of Nuclides (National Nuclear Data Center)

* ttp://www-nds.iaea.org/livechart The LIVEChart of Nuclides – IAEAwith 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 CEA (France) {{Authority control Nuclear physics