Isotope

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 (i.e. radioactive elements) between uranium and lead, although the periodic table only allowed for 11 elements between lead and uranium inclusive.[11][12][13]

Several attempts to separate these new radioelements chemically had failed.[14] For example, Soddy had shown in 1910 that mesothorium (later shown to be ²²⁸Ra), radium (²²⁶Ra, the longest-lived isotope), and thorium X (²²⁴Ra) are impossible to separate.[15] 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.[16][17][18][19] 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.[13] For example, the alpha-decay of uranium-235 forms thorium-231, whereas the beta decay of actinium-230 forms thorium-230.[14] The term "isotope", Greek for "at the same place",[13] was suggested to Soddy by Margaret Todd, a Scottish physician and family friend, during a conversation in which he explained his ideas to her.[15][20][21][22][23][24] He won the 1921 Nobel Prize in Chemistry in part for his work on isotopes.[25]

In the bottom right corner of J. J. Thomson'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.[14][25]

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).[26][27] 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 (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 that the molar mass of chlorine (35.45) is a weighted average of the almost integral masses for the two isotopes ³⁵Cl and ³⁷Cl.[28]

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 (¹
H
), deuterium (²
H
), and tritium (³
H
), 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) 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.

Isotope half-lives. Z = number of protons. N = number of neutrons. The plot for stable isotopes diverges from the line Z = N as the element number Z becomes larger

Similarly, two molecules that differ only in the isotopes of their atoms (isotopologues) have identical electronic structure, 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 photons of corresponding energies, isotopologues have different optical properties in the infrared range.

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 ³
₂He
is 1:2, the neutron:proton ratio of ²³⁸
₉₂U
is greater than 3:2. A number of lighter elements have stable nuclides with the ratio 1:1 (Z = N). The nuclide ⁴⁰
₂₀Ca
(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.

Of the 80 elements with a stable isotope, the largest number of stable isotopes observed for any element is ten (for the element tin). 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 ^180m
₇₃Ta
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).[29] 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.

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 (including positron emission), 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 (roughly evenly) into odd-proton-even-neutron, and even-proton-odd-neutron nuclides. Stable odd-proton-odd-neutron nuclei are the least common.

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 due to a double pairing of 2 protons and 2 neutrons prevents any nuclides containing five (⁵
₂He
, ⁵
₃Li
) or eight (⁸
₄Be
) nucleons from existing for long enough to serve as platforms for the buildup of heavier elements via nuclear fusion in stars (see triple alpha process).

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 ²³⁵
₉₂U
. 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 ¹⁹⁵
₇₈Pt
and ⁹
₄Be
are the most naturally abundant isotopes of their element.

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 (
₄₃Tc
) and promethium (
₆₁Pm
) 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 (
₁₇Cl
), potassium (
₁₉K
), copper (
₂₉Cu
), gallium (
₃₁Ga
), bromine (
₃₅Br
), silver (
₄₇Ag
), antimony (
₅₁Sb
), iridium (
₇₇Ir
), and thallium (
₈₁Tl
), have two odd-even stable isotopes each. This makes a total 30 + 2(9) = 48 stable odd-even isotopes.

There are also five primordial long-lived radioactive odd-even isotopes, ⁸⁷
₃₇Rb
, ¹¹⁵
₄₉In
, ¹⁸⁷
₇₅Re
, ¹⁵¹
₆₃Eu
, and ²⁰⁹
₈₃Bi
. 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 (²
₁H
, ⁶
₃Li
, ¹⁰
₅B
, and ¹⁴
₇N
; spins 1, 1, 3, 1). The only other entirely "stable" odd-odd nuclide, ^180m
₇₃Ta
(spin 9), 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.[30]

Many odd-odd radionuclides (like tantalum-180) with comparatively short half lives are known. Usually, they beta-decay to their nearby even-even isobars that have paired protons and paired neutrons. Of the nine primordial odd-odd nuclides (five stable and four radioactive with long half lives), only ¹⁴
₇N
is the most common isotope of a common element. This is the case because it is a part of the CNO cycle. The nuclides ⁶
₃Li
and ¹⁰
₅B
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.

Actinides with odd neutron number are generally fissile (with thermal neutrons), whereas those with even neutron number are generally not, though they are fissionable with fast neutrons. All observationally stable odd-odd nuclides have nonzero integer spin. This is because the single unpaired neutron and unpaired proton have a larger nuclear force attraction to each other if their spins are aligned (producing a total spin of at least 1 unit), instead of anti-aligned. See deuterium for the simplest case of this nuclear behavior.

Only ¹⁹⁵
₇₈Pt
, ⁹
₄Be
and ¹⁴
₇N
have odd neutron number and are the most naturally abundant isotope of their element.

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 (in the Manhattan Project) by a type of production mass spectrometry.

• Isotope analysis is the determination of isotopic signature, the relative abundances of isotopes of a given element in a particular sample. Isotope analysis is frequently done by isotope ratio mass spectrometry. For biogenic substances in particular, significant variations of isotopes of C, N and O can occur. Analysis of such variations has a wide range of applications, such as the detection of adulteration in food products[32] or the geographic origins of products using isoscapes. The identification of certain meteorites as having originated on Mars is based in part upon the isotopic signature of trace gases contained in them.[33]
• Isotopic substitution can be used to determine the mechanism of a chemical reaction via the kinetic isotope effect.
• Another common application is isotopic labeling, the use of unusual isotopes as tracers or markers in chemical reactions. Normally, atoms of a given element are indistinguishable from each other. However, by using isotopes of different masses, even different nonradioactive stable isotopes can be distinguished by mass spectrometry or infrared spectroscopy. For example, in 'stable isotope labeling with amino acids in cell culture (SILAC)' stable isotopes are used to quantify proteins. If radioactive isotopes are used, they can be detected by the radiation they emit (this is called radioisotopic labeling).
• Isotopes are commonly used to determine the concentration of various elements or substances using the isotope dilution method, whereby known amounts of isotopically-substituted compounds are mixed with the samples and the isotopic signatures of the resulting mixtures are determined with mass spectrometry.

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