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 but different numbers of neutrons in each atom.
The term isotope is formed from the Greek roots isos and topos, 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. It was coined by a Scottish doctor and writer Margaret Todd in 1913 in a suggestion to chemist Frederick Soddy.
The number of protons within the atom's nucleus is called atomic number and is equal to the number of electrons in the neutral 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 neutrons. The number of nucleons in the nucleus is the atom's mass number, and each isotope of a given element has a different mass number.
For example, carbon-12, carbon-13, and carbon-14 are three isotopes of the element carbon 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 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 emphasizes nuclear properties over chemical properties, whereas the isotope concept emphasizes chemical 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. The term isotopes is intended to imply comparison. For example, the nuclides,, are isotopes, but,, are isobars. 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 and nuclear medicine.

Notation

An isotope and/or nuclide is specified by the name of the particular element followed by a hyphen and the mass number. When a chemical symbol is used, e.g. "C" for carbon, standard notation is to indicate the mass number with a superscript at the upper left of the chemical symbol and to indicate the atomic number with a subscript at the lower left. 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. The letter m is sometimes appended after the mass number to indicate a nuclear isomer, a metastable or energetically-excited nuclear state, for example .
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 or uranium-two-three-five instead of 235-92-uranium.

Radioactive, primordial, and stable isotopes

Some isotopes/nuclides are radioactive, and are therefore referred to as radioisotopes or radionuclides, whereas others have never been observed to decay radioactively and are referred to as stable isotopes or stable nuclides. 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 nuclides, meaning that they have existed since the Solar System's formation.
Primordial nuclides include 34 nuclides with very long half-lives and 252 that are formally considered as "stable nuclides", 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 the most abundant isotope found in nature is actually one extremely long-lived radioisotope 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. 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 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 for details.

History

Radioactive isotopes

The existence of isotopes was first suggested in 1913 by the radiochemist Frederick Soddy, based on studies of radioactive decay chains that indicated about 40 different species referred to as radioelements 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. For example, Soddy had shown in 1910 that mesothorium, radium, and thorium X 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 produced an element two places to the left in the periodic table, whereas beta decay 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 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 in part for his work on isotopes.
's photographic plate are the separate impact marks for the two isotopes of neon: neon-20 and neon-22.
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.

Stable isotopes

The first evidence for multiple isotopes of a stable element was found by J. J. Thomson in 1912 as part of his exploration into the composition of canal rays. Thomson channelled streams of neon 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, 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 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 that the molar mass of chlorine 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: 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, and tritium, 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 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.
Similarly, two molecules that differ only in the isotopes of their atoms have identical electronic structure, and therefore almost indistinguishable physical and chemical properties. 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 photons of corresponding energies, isotopologues have different optical properties in the infrared 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. 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. The nuclide 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. No element has nine stable isotopes. Xenon is the only element with eight stable isotopes. Four 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, and 26 elements have only a single stable isotope. 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

p,nEEOOEOOETotal
Stable14655348252
Long-lived2243534
All primordial16895653286

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, 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, electron capture, or other less common decay modes such as spontaneous fission and cluster decay.
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 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 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 due to a double pairing 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 in stars.
DecayHalf-life
beta7.7 a
alpha1.06 a
alpha7.04 a

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 have no even-odd stable nuclides. One element 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, including the fissile. Because of their odd neutron numbers, the even-odd nuclides tend to have large neutron capture 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 and r-process 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 and promethium have no stable isotopes). Of these 39 odd Z elements, 30 elements have one stable odd-even isotope, and nine elements: chlorine,
potassium,
copper,
gallium,
bromine,
silver,
antimony,
iridium,
and thallium, have two odd-even stable isotopes each. This makes a total 30 + 2 = 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. The only other entirely "stable" odd-odd nuclide, , is thought to be the rarest of the 252 stable isotopes, and is the only primordial nuclear isomer, which has not yet been observed to decay despite experimental attempts.
Many odd-odd radionuclides 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, 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

s with odd neutron number are generally fissile, 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, instead of anti-aligned. See deuterium 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, or of more than one naturally occurring isotopes. The unstable isotopes are either 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. Post-primordial isotopes were created by cosmic ray bombardment as cosmogenic nuclides, or by the decay of a radioactive primordial isotope to a radioactive radiogenic nuclide daughter. 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. There are about 94 elements found naturally on Earth, though some are detected only in very tiny amounts, such as plutonium-244. Scientists estimate that the elements that occur naturally on Earth occur as 339 isotopes 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 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 for details.
All the known stable nuclides 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 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 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 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. 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, 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 of an isotope is determined mainly by its mass number. Small corrections are due to the binding energy of the nucleus, 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" or "Da".
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 :
where m1, m2,..., mN are the atomic masses of each individual isotope, and x1,..., xN are the relative abundances of these isotopes.

Applications of isotopes

Purification of isotopes

Several applications exist that capitalize on 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 by a type of production mass spectrometry.

Use of chemical and biological properties