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Isotope

An isotope is an of a that has the same (number of protons) as other s of that but differs in the number of neutrons in its , leading to variations in . Isotopes of the same exhibit nearly identical chemical properties because they possess the same number of electrons and thus the same , but they can have significantly different nuclear properties, including and mass. Stable isotopes do not undergo , whereas unstable (radioactive) isotopes decay over time, emitting and transforming into other isotopes or s. There are 254 known stable isotopes across all s, with approximately 339 naturally occurring isotopes in total, while over 3,000 additional radioactive isotopes have been artificially produced in laboratories. The concept of isotopes emerged from early 20th-century research on ; in 1913, British chemist introduced the term to describe chemically identical substances with different atomic weights observed in series, for which he received the in 1921. Isotopes are denoted using superscript notation for the (protons plus neutrons) and subscript for the , such as ^{12}_{6}\text{C} for , or more simply as carbon-12. Isotopes have diverse applications across , , and due to their unique nuclear behaviors. In , radioactive isotopes like enable diagnostic imaging of organs and tissues, while others such as are used in targeted cancer therapies. isotopes serve as tracers in biological and , and radioactive ones like facilitate of archaeological and geological samples by measuring decay rates with half-lives such as 5,730 years. Additionally, isotopes contribute to fields like oil and gas exploration through and basic research in .

Definitions and Fundamentals

Isotope vs. Nuclide

In , a is defined as a species of atom characterized by its , , and nuclear energy state, provided the mean lifetime in that state is long enough to be observable. This term encompasses any specific , including those in ground states or excited nuclear isomers./Atomic_Theory/Nuclide_Atomic_Number_mass_number) An isotope, in contrast, refers specifically to nuclides that have the same but different . Since the atomic number determines the , isotopes are variants of the same differing only in the number of neutrons in their nuclei, which affects the mass number without altering chemical properties significantly. The key distinction is that all isotopes are nuclides, but not all nuclides are isotopes; isotopes form a subset of nuclides that share the same ./Atomic_Theory/Nuclide_Atomic_Number_mass_number) Nuclides with different atomic numbers belong to different s and thus cannot be isotopes of one another. For example, and are isotopes of carbon, as both have an atomic number of 6 but mass numbers of 12 and 14, respectively, differing by two neutrons. Similarly, the —protium (hydrogen-1), (hydrogen-2), and (hydrogen-3)—all have one proton but zero, one, or two neutrons, respectively, making them nuclides of the same element. These examples illustrate how isotopes represent nuclear variations within a single element, while each is distinctly identified as a nuclide by its full nuclear composition.

Notation

The standard notation for a nuclide, as recommended by the International Union of Pure and Applied Chemistry (IUPAC), is ^{A}_{Z}\mathrm{X}, where \mathrm{X} is the for the , Z is the (number of protons), and A is the (total number of protons and neutrons in the ). This format uniquely identifies a by specifying its proton and composition, with the subscript positioned to the left of the symbol and the superscripted above it. For example, is denoted as ^{14}_{6}\mathrm{C}, indicating 6 protons and a total of 14 s. The subscript is often omitted when the symbol alone suffices to identify Z, simplifying the notation to ^{A}\mathrm{X} in contexts where ambiguity is unlikely. Alternative formats are commonly used for brevity or in specific fields. The hyphen notation, such as \mathrm{C}-$14 or carbon-14, places the mass number immediately after the element symbol or name, separated by a hyphen; this is prevalent in general scientific literature and applied sciences like radiochemistry. For well-known isotopes, especially in nuclear engineering or medicine, the element symbol may be abbreviated with just the mass number, as in U-235 for uranium-235. These variants prioritize readability while conveying the mass number, though they lack the explicit atomic number detail of the full IUPAC form unless context provides it. The neutron number N = A - Z is not typically included in standard symbols but may be specified separately if required for nuclear physics discussions, emphasizing the primary role of A and Z in isotopic identification. The notation for isotopes and nuclides evolved significantly from its origins in the early . Prior to 1913, and collaborators referred to radioactive species using descriptive names tied to their position in decay chains, such as "uranium X" or "radium A," reflecting chemical similarities without numerical mass distinctions. The introduction of by Francis Aston in 1919 enabled precise measurement of atomic masses, leading to the adoption of integer mass numbers ( approximating A) and notations like ^{12}\mathrm{C} for the first observed stable isotopes of light elements. By the mid-20th century, IUPAC formalized the ^{A}_{Z}\mathrm{X} convention through joint recommendations with the International Union of Pure and Applied Physics (IUPAP), first outlined in 1953 for chemical nuclides and refined in subsequent publications like the IUPAC Green Book to ensure consistency across disciplines. This standardization, building on Soddy's conceptual foundation, replaced ad hoc naming with a systematic, quantifiable system aligned with periodic table organization.

History

Discovery of Radioactive Isotopes

The discovery of radioactivity began in 1896 when French physicist observed that salts emit rays capable of penetrating opaque materials and exposing photographic plates, even without exposure to light, marking the first identification of spontaneous radiation from an element. This phenomenon, initially thought to be related to , was soon recognized as a distinct property inherent to itself, independent of external stimuli. Building on Becquerel's findings, Pierre and Marie Curie in 1898 isolated two new radioactive elements, and , from through laborious chemical , revealing substances far more active than and exhibiting nearly identical chemical spectra to and , respectively. Their work demonstrated that pitchblende contained multiple "elements" with similar chemical behaviors but varying intensities of , challenging the notion of elements as uniquely defined by atomic weight. Further studies of chains, pioneered by and , showed that successive transformations in series like the uranium-radium chain produced daughter products with the same () but different mass numbers (A), leading to chemically indistinguishable species despite distinct radioactive properties. In 1913, formalized this observation by coining the term "isotope" (from Greek, meaning "same place") to describe chemically identical elements occupying the same position in the periodic table but differing in atomic weight due to their origins in decay sequences. reconciled the apparent multiplicity of radioelements, such as the four (, radiothorium, , and leads) identified in decay chains, all sharing identical chemical traits. Concurrently, J.J. Thomson's positive ray analysis in 1913 provided early mass-based evidence for isotopes in , detecting ions at masses 20 and 22 with the same chemical identity, extending the isotope idea beyond to stable elements and validating Soddy's framework through instrumental means.

Discovery of Stable Isotopes and Neutrons

The concept of isotopes, initially proposed by in to describe chemically identical radioactive elements with different atomic weights, laid the groundwork for understanding atomic variations beyond radioactivity. Soddy's work, based on observations of decay chains, suggested that such entities occupied the same position in the periodic table despite mass differences. This idea, though focused on unstable nuclides, prompted further investigation into whether stable elements exhibited similar properties. In 1919, Francis Aston at the developed the first mass spectrograph, a device that ionized elements and separated them by using magnetic and , enabling precise measurement of atomic masses. Applying it to gas, Aston identified two stable isotopes: neon-20 (mass approximately 20) and neon-22 (mass approximately 22), present in a of about 10:1, which accounted for the 's average atomic weight of 20.2. This marked the first demonstration of stable isotopes in a non-radioactive , confirming Soddy's isotopic extended to common and challenging the notion of atoms as indivisible units with fixed masses. Aston's instrument soon revealed isotopes in other elements, including chlorine, where mass spectra of compounds like HCl showed two primary lines corresponding to chlorine-35 and chlorine-37, with an abundance ratio of roughly 3:1 that matched the observed atomic weight of 35.5. By the early , Aston had compiled initial isotopic tables for light elements, listing masses close to whole numbers and supporting his "whole number rule" that isotopic masses approximate integers. These findings spurred the development of comprehensive isotopic catalogs, integrating data from multiple elements to map natural abundance variations. The puzzle of mass differences without corresponding charge variations persisted until 1932, when James Chadwick at the Cavendish Laboratory discovered the neutron through experiments bombarding beryllium with alpha particles, producing neutral radiation that ejected protons from paraffin with energies inconsistent with known particles. Chadwick's analysis showed this radiation consisted of uncharged particles with mass similar to the proton, which he termed neutrons, explaining isotopes as nuclei with varying neutron counts around a fixed proton number. This breakthrough refined nuclear models in the 1930s, shifting scientific views from indivisible atoms to composite structures of protons and neutrons, and enabled accurate predictions of isotopic masses.

Classification

Stable, Radioactive, and Primordial Isotopes

Stable isotopes are nuclides whose nuclei do not undergo to any measurable extent, remaining unchanged over timescales comparable to the age of the . These isotopes constitute the foundation of naturally occurring in their most persistent forms, with examples including (¹²C), which is the primary isotope of carbon, and (¹⁶O), the most abundant isotope of oxygen. Approximately 254 stable nuclides are known across 80 of the periodic table, representing the only nuclides observed without evidence of decay using current detection methods. Radioactive isotopes, in contrast, possess unstable nuclei that spontaneously decay, emitting particles or electromagnetic radiation to reach a more stable configuration. This category encompasses both naturally occurring and artificially synthesized nuclides, with carbon-14 (¹⁴C) serving as a well-known example of a natural radioactive isotope, characterized by a half-life of 5730 years. Over 3,800 radioactive nuclides have been identified as of 2024, vastly outnumbering stable ones among the approximately 4,100 total known nuclides. Many radioactive isotopes are transient, with short half-lives, while others persist due to longer decay periods. Primordial isotopes are those present since the formation of approximately 4.54 billion years ago, having either never decayed or decayed so slowly that significant amounts remain. This group includes all 254 known s as well as 35 long-lived radioactive nuclides from 28 elements, such as (²³⁸U), which has a on the order of billions of years. These isotopes originated from processes in stars and the , incorporated into planetary material during solar system formation. Beyond isotopes, natural radioactive isotopes can be categorized by their mechanisms. Cosmogenic isotopes form continuously through interactions of cosmic rays with atmospheric or surface atoms, yielding nuclides like (¹⁰Be). Radiogenic isotopes, on the other hand, arise as products of primordial radioactive isotopes, exemplified by lead-206 (²⁰⁶Pb) generated from the chain of uranium-238. This distinction highlights how Earth's isotopic inventory evolves through ongoing and processes, separate from the original primordial endowment.

Even and Odd Nucleon Numbers

The stability of atomic nuclei is significantly influenced by the (even or odd number) of their proton (Z) and (N) counts, a phenomenon rooted in the interaction among . Even-even nuclei, which have even numbers of both protons and neutrons, exhibit the highest due to the pairing that allows nucleons to form spin-paired configurations, lowering the overall state. For example, (Z=6, N=6) is a prototypical even-even renowned for its exceptional stability. This pairing effect is quantified in the (SEMF) through the pairing term \delta, where \delta \approx 11 A^{-1/2} MeV for even-even nuclei (with A being the mass number), contributing a positive addition to the binding energy. In contrast, odd-odd nuclei, with odd Z and odd N, are the least stable because they lack complete pairing, resulting in unpaired nucleons that increase the nuclear energy and promote decay. Lithium-6 (Z=3, N=3) exemplifies this, as one of the few stable odd-odd isotopes despite its relative rarity and lower binding efficiency. The SEMF pairing term assigns a negative value (\delta \approx -11 A^{-1/2} MeV) to odd-odd nuclei, reducing their binding energy compared to other configurations. Nuclei with even Z and odd N, or odd Z and even N (even-odd or odd-even), display intermediate stability, as one type of nucleon can pair fully while the other remains partially unpaired. The SEMF sets \delta = 0 for these cases, reflecting no net pairing contribution. This ordering—even-even > even-odd/odd-even > odd-odd—manifests in statistical trends among stable isotopes: approximately 50% are even-even, with even-odd and odd-even each comprising about 25%, while odd-odd account for fewer than 2% (only five known stable examples). These patterns underscore the dominance of pairing in determining isotopic occurrence and .

Isotopes per Element

The number of isotopes per element varies significantly across the periodic table, with lighter elements generally exhibiting fewer isotopes than heavier ones. For instance, hydrogen has two stable isotopes, protium (¹H) and deuterium (²H), while tritium (³H) is radioactive but semi-stable with a half-life of about 12.3 years, resulting in three isotopes that are relevant in natural contexts. Similarly, helium has two stable isotopes, ³He and ⁴He. In contrast, heavier elements like tin possess a greater diversity, with ten stable isotopes ranging from ¹¹²Sn to ¹²⁴Sn. This trend toward increasing isotopic variety with atomic number reflects the broader range of neutron numbers that can form bound nuclei as proton count rises, up to a point. Dysprosium exemplifies a high among stable isotopes, with seven: ¹⁵⁶Dy, ¹⁵⁸Dy, ¹⁶⁰Dy, ¹⁶¹Dy, ¹⁶²Dy, ¹⁶³Dy, and ¹⁶⁴Dy. Bismuth, however, represents a narrower case, with no truly stable isotopes; its sole primordial isotope, ²⁰⁹Bi, is radioactive with an extraordinarily long half-life of approximately 1.9 × 10¹⁹ years, effectively behaving as stable, alongside shorter-lived radioactive variants. Overall, 80 of the first 82 elements in the periodic table possess at least one stable isotope, totaling around 254 stable nuclides. Nuclear shell closures play a key role in this distribution, as they enhance stability for nuclei near "magic numbers" of protons or neutrons (such as 2, 8, 20, 28, 50, 82, 126), allowing a wider window of neutron-to-proton ratios and thus more stable isotopes per element in those regions. Elements beyond (Z > 83) generally lack stable isotopes, with all heavier natural and synthetic ones being radioactive; transuranic elements, starting from (Z = 93), are entirely radioactive and artificially produced. For superheavy synthetic elements like (Z = 118), only a few isotopes have been synthesized, such as ²⁹⁴Og with a of 0.7 milliseconds, and theoretical models predict no stable variants but potential longer-lived ones near predicted shell closures.

Properties

Chemical and Molecular Properties

Isotopes of the same element possess nearly identical chemical properties because they share the same , resulting in the same and thus identical interactions with other atoms in chemical bonding. For elements heavier than (Z > 1), these properties are virtually indistinguishable, as the relative mass differences between isotopes are small and do not significantly alter electronic behavior or reactivity patterns. However, the mass differences arising from varying counts introduce subtle isotopic effects, primarily influencing molecular vibrations and rotational energies rather than the core chemical bonding. These mass-dependent effects manifest in shifts to vibrational frequencies, where heavier isotopes reduce the frequency of molecular oscillations due to increased in bonds. For instance, in , the replacement of protium (¹H) with (²H) yields (D₂O), which has a higher boiling point of 101.4 °C compared to ordinary (H₂O) at 100 °C, attributable to lower zero-point vibrational energy and slightly stronger hydrogen bonding in the heavier . Such differences are pronounced for hydrogen isotopes (protium, , ) owing to their large relative mass disparity, but diminish for heavier elements. A key consequence is the (KIE), where reactions involving heavier isotopes proceed more slowly than those with lighter ones, stemming from the higher required to overcome the reduced vibrational amplitude in the . This primary KIE is particularly evident in enzyme-catalyzed reactions; for example, the of by propionyl-CoA carboxylase shows a ¹³C KIE, with the heavier ¹³C isotope reacting slower than ¹²C due to mass-sensitive bond vibrations at the catalytic site. Equilibrium isotope fractionation further illustrates these effects, as lighter isotopes preferentially occupy phases with weaker bonding or higher , leading to isotopic enrichment during chemical equilibria. In the , for instance, ¹²C enriches in gaseous CO₂ relative to solid carbonates, with fractionation factors decreasing with temperature (e.g., approximately 1.01 at 25 °C for CO₃²⁻–CO₂ exchange), reflecting vibrational partitioning in molecular species. Deuterium-enriched exemplifies practical utility, serving as a in ¹H NMR because deuterium's nuclear spin (I=1) produces no interfering proton signals, allowing clear observation of sample resonances without solvent background.

Nuclear Properties and Stability

Nuclear stability is fundamentally determined by the binding energy per , which quantifies the energy required to disassemble the into its constituent protons and neutrons. This peaks at approximately 8.8 MeV for the isotope , marking it as one of the most stable nuclei, with only and iron-58 exhibiting slightly higher values. For lighter isotopes, the binding increases with , favoring processes, while for heavier ones, it decreases, promoting as a pathway to greater ./University_Physics_III_-Optics_and_Modern_Physics(OpenStax)/10:_Nuclear_Physics/10.03:_Nuclear_Binding_Energy) The distribution of stable isotopes forms the "valley of stability" when plotted as neutron number N versus proton number Z, where stable nuclides cluster along a narrow band. For light elements (Z < 20), the N/Z ratio is near 1, but it rises to about 1.5 for heavy elements like lead, reflecting the need for additional neutrons to counter proton repulsion. Isotopes deviating significantly from this band are unstable and undergo radioactive decay to approach the valley. Stability criteria require nuclei to lie within the proton and neutron drip lines, boundaries beyond which the separation energy for two protons or neutrons becomes negative, allowing unbound emission. Enhanced stability occurs at "magic numbers" of protons or neutrons—2, 8, 20, 28, 50, 82, and 126—corresponding to completed nuclear shells that minimize energy and resist decay. Doubly magic nuclei, with both proton and neutron numbers at these values, exhibit exceptional stability. Even-even configurations (even protons and even neutrons) further bolster stability through nucleon pairing. Unstable isotopes decay through specific modes to achieve greater binding energy: alpha decay emits a helium-4 nucleus (reducing Z by 2 and mass number A by 4), beta-minus decay converts a neutron to a proton (increasing Z by 1), beta-plus decay does the reverse, and gamma decay releases high-energy photons from excited nuclear states without altering A or Z. Half-lives of these decays span from nanoseconds for highly unstable isotopes to over $10^{15} years for long-lived primordial radionuclides. The semi-empirical mass formula provides a predictive model for binding energy and thus stability, approximating it as B(A,Z) \approx a_v A - a_s A^{2/3} - a_c \frac{Z(Z-1)}{A^{1/3}} - a_{sym} \frac{(A-2Z)^2}{A} \pm a_p A^{-1/2}, where a_v \approx 15.5 MeV (volume term, favoring larger nuclei), a_s \approx 16.8 MeV (surface term, penalizing small surface-to-volume ratios), a_c \approx 0.72 MeV (Coulomb term, accounting for proton repulsion), a_{sym} \approx 23 MeV (asymmetry term, penalizing N \neq Z), and a_p \approx 34 MeV / A^{1/2} (pairing term, with sign depending on even-odd nucleon counts). This formula reproduces the observed trends in the binding energy curve and valley of stability.

Atomic Mass

The atomic mass of an isotope refers to the rest mass of a neutral atom, expressed in atomic mass units (u), where 1 u is defined as exactly one-twelfth the mass of a in its nuclear and electronic ground state. This definition ensures a standardized scale for comparing atomic masses across elements and isotopes, with the carbon-12 isotope serving as the reference point. Isotopic masses deviate from integer values due to the mass defect arising from nuclear binding energy, which converts a portion of the nucleons' mass into energy that holds the nucleus together. For instance, carbon-12 has an exact mass of 12 u by definition, while carbon-13 has a measured mass of approximately 13.003355 u, reflecting the additional neutron's contribution adjusted for binding effects./20%253A_Radioactivity_and_Nuclear_Chemistry/20.08%253A_Converting_Mass_to_Energy-_Mass_Defect_and_Nuclear_Binding_Energy) These variations are small but critical for precise calculations in nuclear and chemical contexts. Atomic masses are measured using mass spectrometry techniques, such as Penning trap mass spectrometry, which achieve precisions on the order of 10^{-9} u or better by comparing cyclotron frequencies of ions. This high accuracy allows for the determination of isotopic masses with uncertainties as low as parts per billion, essential for applications in nuclear physics and geochemistry. The standard atomic weight listed in the periodic table represents the weighted average of an element's isotopic masses, based on their natural abundances. For chlorine, with isotopes chlorine-35 (mass 34.968853 u, abundance 75.76%) and chlorine-37 (mass 36.965903 u, abundance 24.24%), the standard atomic weight is approximately 35.45 u, calculated as (0.7576 × 34.968853) + (0.2424 × 36.965903). These weighted averages inform the periodic table's mass values and are fundamental to stoichiometry, enabling accurate predictions of reactant and product quantities in chemical reactions through molar mass calculations.

Natural Occurrence

Sources in Nature

Isotopes in nature arise from distinct production mechanisms that span cosmic, geological, and atmospheric processes. Primordial isotopes, those inherited from the early universe and solar system formation, primarily originate from Big Bang nucleosynthesis and stellar nucleosynthesis. During Big Bang nucleosynthesis, which occurred within the first few minutes after the at temperatures around 1 MeV, the lightest elements were formed through nuclear fusion reactions involving protons and neutrons. This process yielded the isotopes ^1H (protium), ^2H (deuterium), ^3He, ^4He, and ^7Li, with trace amounts of ^6Li and possibly beryllium and boron isotopes, though the latter remain undetected. These abundances reflect the neutron-to-proton freeze-out ratio of approximately 1/6 and span nine orders of magnitude, with ^4He dominating at a mass fraction of about 0.245 and deuterium at a number ratio D/H of roughly $2.5 \times 10^{-5}. Stellar nucleosynthesis extends the production of primordial isotopes to elements up to iron in the cores of massive stars. In main-sequence stars, hydrogen fuses into via the proton-proton chain or CNO cycle, releasing energy and building heavier nuclei. Advanced stages in massive stars (>8 solar masses) involve helium burning to carbon and oxygen, followed by carbon, , oxygen, and burning, culminating in the synthesis of iron-peak isotopes like ^{56}Fe through exothermic . These processes occur over the star's lifetime, with iron representing the endpoint of energy-producing due to its high per . Upon stellar death, core-collapse supernovae eject these isotopes into the , enriching subsequent generations of stars and planets. Radiogenic isotopes form on Earth through the radioactive decay of primordial unstable isotopes embedded in planetary materials. These decay chains involve sequential alpha, , and sometimes gamma emissions, transforming heavy parent nuclides into stable daughters. For instance, (^{232}Th), with a of approximately 14 billion years, undergoes a series of 10 decays—six alpha and four —to reach stable lead-208 (^{208}Pb). Similarly, (^{238}U), with a of 4.468 billion years, decays through 14 steps, including intermediates like , thorium-230, radium-226, and , ultimately producing lead-206 (^{206}Pb). These chains contribute to the inventory of lighter isotopes in and , with the stable endpoints accumulating over geological time. Cosmogenic isotopes are continuously produced in Earth's atmosphere and surface by high-energy cosmic rays interacting with target nuclei via spallation reactions. Cosmic rays, primarily protons and alpha particles from galactic sources, collide with atmospheric constituents, fragmenting them into lighter isotopes. A key example is carbon-14 (^{14}C), generated when secondary neutrons from cosmic ray cascades react with nitrogen-14: ^{14}\mathrm{N} + \mathrm{n} \to ^{14}\mathrm{C} + \mathrm{p} This isotope, with a half-life of 5,730 years, mixes into the atmosphere and , while other cosmogenic nuclides like ^7Be, ^{10}Be, and ^{36}Cl form through similar on oxygen and other elements. Production rates vary with solar activity and geomagnetic field strength, but these isotopes remain trace components compared to abundances. In the cosmic context, heavy isotopes beyond the iron peak are forged in explosive stellar events, particularly core-collapse , via rapid neutron-capture processes. The r-process occurs in neutron-rich environments during supernova explosions or , where seed nuclei rapidly capture neutrons to form neutron-heavy isotopes up to , followed by beta decays to stability. This mechanism accounts for roughly half of elements heavier than iron, including gold, platinum, and uranium isotopes, with supernova ejecta seeding the . Observations of events like the confirm r-process through emissions rich in heavy elements. Anthropogenic isotopes, such as those from nuclear fission (e.g., ^{137}Cs, ^{90}Sr), arise from human activities like reactor operations and weapons testing and were negligible in natural systems prior to the 1940s, as these isotopes are almost purely synthetic and did not exist in significant quantities in the environment before nuclear tests began in 1945.

Isotopic Abundance and Variation

Isotopic abundances refer to the relative proportions of different isotopes of an element occurring naturally on Earth, as determined through precise mass spectrometric measurements and standardized by international bodies. For carbon, the standard abundances are [98.84%, 99.04%] for ^{12}C and [0.96%, 1.16%] for ^{13}C (as of 2023). Similarly, oxygen exhibits [99.738%, 99.776%] ^{16}O, [0.0367%, 0.0400%] ^{17}O, and [0.187%, 0.222%] ^{18}O, while hydrogen consists of [99.972%, 99.999%] ^1H and [0.00001%, 0.00028%] ^2H (deuterium). These values represent ranges for terrestrial materials and are compiled in periodic tables maintained by the International Union of Pure and Applied Chemistry (IUPAC), with updates reflecting refined measurements from global sampling. Isotopic abundances are not uniform but exhibit variations due to physical and chemical processes that preferentially incorporate lighter or heavier isotopes, known as isotopic . For instance, during of , the vapor becomes depleted in heavier isotopes, resulting in a lower D/H ratio compared to the residual , with fractionation factors around 0.9839 for relative to protium diffusivity. Such effects are quantified using delta notation (δ), where δD or δ¹⁸O values describe deviations in parts per thousand from international standards like (VSMOW). These variations influence hydrological cycles and are observed in , where rain is typically isotopically lighter than source vapor. In geological records, isotopic ratios serve as proxies for paleoenvironmental conditions. Shifts in δ¹³C values in sedimentary , often ranging from -25‰ to -20‰, reflect changes in vegetation cover, CO₂ levels, and , with more negative values indicating enhanced input from plants during humid periods. For example, positive excursions in sediments during glacial maxima correlate with increased productivity and carbon burial, providing evidence of past oscillations over millions of years. Cosmic isotopic abundances differ from terrestrial norms, revealing formation histories across the and beyond. The D/H ratio in cometary varies from 1 to 3 times the Earth's ocean value of approximately 1.56 × 10⁻⁴, with comets showing enrichments up to 3 × 10⁻⁴, higher than the medium's ~1.5 × 10⁻⁵. These discrepancies suggest ion-molecule reactions in cold molecular clouds concentrated , contrasting with the more uniform ratios in bodies like chondrites. IUPAC and related commissions periodically revise abundance data to incorporate such measurements, ensuring consistency in isotopic studies.

Applications

Purification and Separation

Isotope separation, also known as isotope enrichment, involves isolating specific isotopes from a based on subtle differences in their physical or chemical properties, such as or characteristics. This process is essential for applications requiring high-purity isotopes, and its efficiency is fundamentally limited by the relative difference between isotopes, denoted as ΔM/M, where small values around 1%—as seen in and (ΔM/M ≈ 1.26%)—pose significant challenges due to the need for multiple stages to achieve meaningful enrichment. Physical methods predominate, leveraging mass-dependent phenomena like rates or centrifugal forces, while chemical approaches exploit isotopic effects on bonding. Gaseous diffusion was a pioneering industrial-scale for enrichment, particularly during the , where (UF₆) gas is forced through porous barriers. Lighter UF₆ molecules containing diffuse faster than those with , enabling partial separation per stage; thousands of cascaded stages were required for weapons-grade enrichment. This technique, operational at facilities like Oak Ridge's plant, consumed vast electricity but proved reliable for large-scale production until phased out in favor of more efficient alternatives. Gas offers higher efficiency than by spinning UF₆ gas at high speeds in cylindrical rotors, generating centrifugal forces that drive heavier molecules outward while lighter concentrates near the center. Modern centrifuges, often arranged in cascades, achieve separation factors per stage of about 1.2–1.5 for isotopes, reducing energy use by orders of magnitude compared to ; they now dominate global uranium enrichment capacity. Electromagnetic separation, exemplified by the developed during the , ionizes tetrachloride vapor and accelerates the ions through a , where mass-to-charge differences cause spatial deflection and collection of isotopes on separate targets. Operated at Oak Ridge's Y-12 plant, calutrons provided the bulk of for the first atomic bomb but were energy-intensive and low-throughput, yielding only about 1% efficiency per unit; they remain viable for small-scale, high-purity separations of various elements today. Laser-based methods, such as atomic vapor laser isotope separation (AVLIS), utilize precisely tuned to selectively excite and ionize atoms of a target isotope in a vapor stream, followed by electrostatic collection of the ions. Developed at , AVLIS achieves high selectivity (up to 10:1 per stage for ) due to isotope-specific electronic transitions, offering precision for elements with small mass differences; while it faced commercialization challenges and was deprioritized for in the late 1990s, as of 2025, AVLIS is being actively developed for and other isotopes like , with recent milestones such as SILEX Systems' enrichment achievement in October 2025 and Hexium's scaling efforts funded in April 2025. Chemical exchange methods rely on differences in equilibrium constants for isotopic exchange reactions between phases, often enhanced by selective complexation agents. For lithium isotopes, crown ethers like facilitate separation by preferentially binding lithium-6 or lithium-7 in organic-aqueous systems, achieving separation factors around 1.05–1.10 per stage; these are combined with ion-exchange resins or ionic liquids for continuous processing. Such techniques are particularly suited for light elements where mass effects are pronounced relative to atomic size.

Chemical and Biological Uses

Stable isotopes serve as tracers in chemical and biological to track molecular pathways without introducing . For instance, nitrogen-15 (¹⁵N) is widely used to quantify uptake in , enabling precise measurement of nitrogen derived from applied fertilizers in agro-ecosystems. In greenhouse and field experiments, ¹⁵N-enriched fertilizers have demonstrated utilization efficiencies ranging from 35% in controlled settings to 78% under optimal banding applications on , highlighting the isotope's role in assessing nutrient dynamics and optimizing agricultural practices. Oxygen-18 (¹⁸O) provides insights into the water cycle by revealing evaporative processes and in various environments. In ponds, δ¹⁸O values ranging from -14.4‰ to -7.3‰ indicate evaporative enrichment due to prolonged ice-free periods and rising temperatures, while Andean lakes show minimal shifts (-12.1‰ to -5.9‰) owing to high inputs. These isotopic signatures, analyzed via local lines, help model hydrological responses to variability. Nuclear magnetic resonance (NMR) spectroscopy exploits isotopes such as ¹H, ¹³C, and ³¹P to elucidate molecular structures in chemical and biological samples. These nuclei, with I = 1/2, produce high-resolution spectra that identify chemical shifts and couplings, allowing non-invasive analysis of metabolites in body fluids, cell extracts, and biopsies without prior separation. In biological applications, ¹H-NMR detects proton environments, ¹³C-NMR maps carbon skeletons, and ³¹P-NMR monitors phosphorus-containing compounds like , facilitating for classifying normal versus pathological states and tracking stable isotope-enriched pathways in . Isotopic labeling with deuterium (²H) enhances pharmaceutical research by enabling metabolism tracking through kinetic isotope effects, where C-D bonds resist enzymatic cleavage compared to C-H bonds. Deuterium incorporation at metabolically labile sites, such as α-positions in amines, slows oxidative degradation by enzymes, allowing precise monitoring of drug absorption, distribution, metabolism, and excretion () via . Examples include , the first FDA-approved deuterated drug for , which exhibits extended half-life due to reduced O-demethylation, and AVP-786 for dementia , where deuteration mitigates N- and O-demethylation pathways. Heavy water (D₂O) finds applications in biological studies as a solvent and metabolic probe, substituting for H₂O to label biomolecules via incorporation. In microbial research, D₂O enables to detect active in and by identifying C-D vibrations (2040-2300 cm⁻¹), revealing metabolic activity and carbon source preferences at the single-cell level, as seen in studies of phosphate-releasing soil microbes and groundwater communities. Additionally, D₂O supports tracking of cellular processes like in non-pathogenic organisms, leveraging its stability for long-term experiments.

Nuclear and Medical Uses

Isotopes play a crucial role in generation through controlled reactions. , enriched to increase its concentration in fuel rods, undergoes when struck by neutrons, releasing energy that heats water to produce for in most commercial reactors. , produced as a in uranium-fueled reactors, serves as an alternative , enabling mixed-oxide fuel cycles that extend fuel resources and support designs. For space applications, powers radioisotope thermoelectric generators (RTGs), where its heat is converted to for missions like Voyager and , providing reliable power in environments without sunlight. In , radioactive isotopes enable non-invasive diagnostics by emitting detectable radiation. , with a of approximately 110 minutes, is incorporated into fluorodeoxyglucose for () scans, allowing visualization of metabolic activity in cancers, neurological disorders, and cardiac conditions. , boasting a 6-hour , is the most widely used isotope for (), forming complexes that target organs like the heart, bones, and for and . Radiotherapy leverages isotopes' to destroy malignant cells while sparing healthy tissue. , administered orally or intravenously, is selectively absorbed by tissue, delivering particles to treat and by ablating overactive or cancerous cells. , used in external beam teletherapy units, emits high-energy gamma rays to irradiate deep-seated tumors, historically providing a reliable source for whole-body or targeted treatments in resource-limited settings. Isotopic dating relies on to establish timelines in and . , with a of about 5,730 years, enables of organic remains up to approximately 50,000 years old, revolutionizing archaeological chronologies for prehistoric human artifacts and environmental changes. , using the decay of to lead-206 ( 4.5 billion years) and to lead-207 ( 704 million years) in crystals, provides precise ages for ancient rocks, underpinning geological understandings of Earth's and tectonic events. Recent advancements in targeted alpha therapy highlight isotopes' potential in precision oncology. Actinium-225, an alpha emitter with a half-life of 10 days, conjugates to prostate-specific membrane antigen (PSMA) ligands for radioligand therapy, selectively delivering high-energy, short-range alpha particles to metastatic prostate cancer cells, showing promising response rates in post-2020 clinical trials with reduced off-target toxicity. As of 2025, ongoing clinical trials, including the first using accelerator-produced Ac-225 starting in summer 2025, continue to demonstrate potent efficacy, as presented in new data at conferences like SNMMI 2025.