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History of atomic theory

The history of atomic theory traces the conceptual and experimental development of the atom as the basic unit of matter, from philosophical speculations in to the quantum mechanical models of the that describe subatomic particles and probabilistic wave functions. In the 5th century BCE, philosophers and proposed the first atomic hypothesis, positing that all matter consists of eternal, indivisible particles called atoms (from the atomos, meaning uncuttable) differing in shape, size, and arrangement, moving through an infinite void to form the diversity of substances. This ancient , though speculative and lacking empirical support, influenced later thinkers but was largely overshadowed by Aristotelian views of continuous matter until the . The revival of atomism in the 17th century, advanced by figures like through his corpuscular philosophy and experiments on air pressure, laid groundwork for a mechanistic view of chemistry, emphasizing discrete particles over continuous substances. A major breakthrough came in 1803 when English chemist formulated the first modern atomic theory, based on quantitative and chemical combination ratios, asserting that elements consist of identical, indivisible atoms with specific weights, that compounds form from fixed atomic ratios, and that atoms rearrange but are neither created nor destroyed in reactions. Dalton's indestructible "billiard ball" atoms explained laws of conservation and definite proportions, transforming chemistry into a rigorous . By the late 19th century, evidence from experiments led J.J. Thomson in 1897 to discover the as a , proposing the " where electrons are embedded in a positively charged atomic sphere, challenging Dalton's indivisibility. In 1911, Ernest Rutherford's gold foil experiment revealed that atoms have a dense, positively charged occupying minimal volume, with electrons orbiting at a distance, implying vast empty space and leading to the nuclear model. Building on this, introduced his 1913 quantized model for the , where electrons occupy fixed energy levels or "orbits" without radiating energy, incorporating early quantum ideas to explain lines. The limitations of Bohr's planetary model, particularly for multi-electron atoms, spurred the development of in the . Werner Heisenberg's 1925 matrix mechanics treated atomic properties mathematically without classical trajectories, while Erwin Schrödinger's 1926 described electrons as probability waves in orbitals around the , with both formulations proven equivalent. These advancements, further refined by contributions like Paul Dirac's relativistic quantum equation, established the modern of the atom, emphasizing uncertainty, superposition, and cloud distributions over deterministic paths. Subsequent discoveries, such as the in and , continue to expand our understanding of atomic structure and its role in and chemistry.

Ancient and Philosophical Origins

Democritean Atomism

Democritean atomism, originating in the 5th century BCE, was primarily developed by the philosophers and his student , who proposed that the universe consists fundamentally of indivisible particles called atoms moving through empty space, or void. is credited as the founder, positing an infinite number of atoms eternally traversing an infinite void to explain the diversity of the natural world without invoking supernatural causes. expanded this framework, describing atoms as solid, eternal, and unchangeable entities that cannot be created or destroyed. These atoms differ only in their shape, size, and arrangement, which account for the variety of perceptible substances; for instance, smooth and round atoms might form air, while jagged ones could constitute iron. The void serves as the necessary counterpart to atoms, providing the empty space that enables their and interactions, as without it, motion would be impossible in a fully filled . Atoms are in constant, random motion, colliding and combining through mechanical processes to form larger compounds and structures, such as the aggregation into worlds or living beings, all governed by natural necessity rather than design. Philosophically, Democritean atomism implies a deterministic , where every results from the prior positions, shapes, and velocities of atoms, eliminating chance or from natural explanations. This mechanistic perspective rejects in physical phenomena, asserting that gods, if they exist, operate within the same atomic framework and do not interfere with human affairs or cosmic order. Such ideas challenged prevailing religious and Eleatic philosophies, promoting a materialist understanding of reality based solely on principles extended to the scale of atoms. The doctrine profoundly influenced later Epicurean atomism, particularly as articulated by the Roman poet in his 1st-century BCE work , which popularized these concepts through verse. To reconcile atomic with human , Epicureans introduced the concept of the "swerve" (), a spontaneous deviation in atomic paths that introduces indeterminacy and allows for voluntary action without collapsing the materialist system. This adaptation preserved the core Democritean emphasis on atoms and void while addressing ethical concerns about agency.

Indian and Other Ancient Views

In ancient Indian philosophy, the Vaisheshika school, attributed to the sage Kanada around the 6th century BCE, developed one of the earliest systematic atomic theories. Kanada posited paramanu—indivisible, eternal particles—as the fundamental building blocks of the universe, comprising four primary substances: earth, water, fire, and air. These atoms were described as infinitesimal, possessing no internal parts or causes, and inferred through logical analysis of observable effects rather than direct perception. The atoms in thought were eternal and inherently active, capable of combining under natural tendencies or external influences like to form perceptible . Specifically, two paramanu could conjoin to create a dvyanuka (dyad), which served as the basis for larger aggregates such as tryanuka (triads) and visible composites, with the properties of the resulting substances determined by the arrangement and proportions of the atoms. This combination process explained the diversity of material forms without invoking creation or destruction of the atoms themselves. The school, closely allied with in what became known as the Nyaya-Vaisheshika tradition, refined these ideas through a focus on and . Nyaya philosophers elaborated on atomic particularity (vishesha), emphasizing how atoms of different elements retained distinct qualities like smell for or fluidity for , while integrating them into broader categories of substance and causation. Unlike more unified views, this tradition maintained a pluralistic where atoms formed the for all non-eternal objects, analyzed through inference and debate rather than experimentation. Buddhist schools, particularly in the Abhidharma traditions, offered a contrasting atomic perspective centered on impermanence. Atoms were conceived as kshanika—momentary and transient entities—that arose and ceased in instantaneous flashes, underscoring the doctrine of constant flux in all phenomena. This rejected eternal substances, viewing atoms not as stable particles but as dynamic aggregates of forces or dharmas (fundamental elements of experience), imperceptible and existing only in relation to consciousness. Jain philosophy presented yet another variant of atomism, positing paramanu as eternal, indivisible units of matter that inherently possessed qualities such as color, taste, touch, and shape. These atoms, uniform in type but variable in attributes, combined into aggregates (skandha) through adhesion or vibration, forming all extended objects while remaining point-like and omnipresent in space. The theory integrated atoms into a cosmology of infinite cycles, where their interactions explained the multiplicity of worldly forms without empirical measurement. Across these Indian traditions, atomic concepts served primarily metaphysical and epistemological purposes, exploring the of , causation, and within cosmological frameworks. Unlike mechanistic models emphasizing motion in void spaces, these views lacked empirical testing or quantitative predictions, prioritizing logical and philosophical to resolve questions of divisibility and permanence.

19th-Century Chemical Foundations

Dalton's Atomic Theory

John Dalton, an English , , and , developed the first scientifically grounded atomic theory in the early , marking a pivotal shift from philosophical speculation to empirical chemical principles. His work established atoms as the fundamental, indivisible building blocks of , explaining observed chemical behaviors through quantitative relationships. This formulation built briefly on ancient Democritean ideas but was rooted in contemporary experiments rather than metaphysics. Dalton first presented his atomic theory in the inaugural volume of A New System of Chemical Philosophy, published in 1808 in . The theory's core postulates, derived from analyses of chemical combinations, are as follows:
  • All matter consists of tiny, indivisible particles known as atoms, which cannot be created or destroyed in chemical reactions.
  • Atoms of the same are identical in mass, size, and other properties, while atoms of different differ in these characteristics.
  • Compounds form when atoms of different elements combine in simple, fixed whole-number ratios by mass to produce molecules.
  • Chemical reactions involve the rearrangement of atoms, with no change in their total number or identity.
Dalton's theory drew significant influence from French chemist Joseph Louis Proust's , first articulated in a 1794 paper on iron oxides, which demonstrated that pure chemical compounds always contain elements in consistent mass ratios regardless of preparation method. Proust's findings, debated during the Berthollet-Proust , provided Dalton with empirical support for atomic combinations in fixed ratios, enabling him to assign relative atomic weights—such as setting at 1 and initially estimating oxygen at 7—to quantify elemental differences. In A New System of Chemical Philosophy, Dalton applied these ideas to explain the fixed composition of , proposing it as a compound of one and one oxygen atom, thus accounting for its invariable elemental proportions under the postulate of simple atomic unions. Despite its foundational impact, Dalton's theory included initial inaccuracies, notably the rule that equal volumes of gases at the same temperature and pressure contain equal numbers of atoms—a assumption that led to errors in determining atomic weights and molecular formulas, such as underestimating water's hydrogen-oxygen ratio. This gas-volume postulate was later refuted and refined by Amedeo Avogadro's , which distinguished atoms from molecules and clarified that equal gas volumes hold equal numbers of molecules.

Laws of Multiple Proportions and Definite Proportions

The law of definite proportions, formulated by French chemist Joseph Proust, asserts that a given chemical compound always contains the same elements combined in the same fixed ratio by mass, irrespective of the method of preparation or the source of the materials. Proust arrived at this conclusion through meticulous analyses of various metal oxides, carbonates, and sulfates between 1794 and 1804, demonstrating, for instance, that copper(II) carbonate consistently exhibited a mass ratio of approximately 5:1:4 for copper, carbon, and oxygen, regardless of whether it was derived from natural malachite or synthesized in the laboratory. This law challenged prevailing notions of variable composition in compounds and provided a cornerstone for quantitative chemistry by emphasizing the constancy of elemental proportions in pure substances. Building upon Proust's findings, English chemist proposed the in 1803, which states that if two elements form more than one compound, the different masses of one element that combine with a fixed mass of the other element bear a simple of small whole numbers to one another. Dalton derived this from his experimental studies on oxides of and other compounds, observing that the law aligned with the idea of discrete atomic combinations. For example, in and , 12 grams of carbon combines with 16 grams of oxygen in the former and 32 grams in the latter, yielding a mass for oxygen of 1:2 relative to the fixed carbon mass. Similarly, and oxygen form , where 2 grams of combine with 16 grams of oxygen, and , where the same 2 grams of combine with 32 grams of oxygen, again resulting in a 1:2 for oxygen. These empirical laws offered quantitative validation for atomic combinations, enabling to estimate relative atomic weights based on the simplest whole-number ratios observed in compounds. In 1811, Italian physicist extended these principles to gaseous compounds with his hypothesis that equal volumes of different gases, at the same temperature and pressure, contain equal numbers of molecules, which helped reconcile volume ratios in gas reactions with mass-based laws but was largely ignored until the 1860s.

Isomerism and Molecular Evidence

In the early 19th century, chemists encountered compounds with identical elemental compositions but distinct chemical and physical properties, challenging the simplicity of Dalton's atomic theory. This phenomenon was first systematically recognized through the work of in 1828, who synthesized silver cyanate (AgCNO) and noted its identical to silver fulminate (also AgCNO), previously analyzed by and , yet the two substances exhibited markedly different behaviors—silver cyanate being stable and soluble, while silver fulminate was explosive and insoluble. Wöhler's observation, building on earlier analyses, provided concrete evidence that atomic ratios alone could not account for all chemical diversity, prompting a reevaluation of atomic arrangements. Jöns Jacob Berzelius formalized this discovery in 1830 by introducing the term "isomerism" to describe such compounds, deriving it from Greek roots meaning "equal parts," and emphasizing that isomers shared the same atoms in the same proportions but differed in their internal structure or arrangement. Berzelius's concept, applied to Wöhler's silver salts as a paradigmatic example, marked a pivotal shift toward recognizing complexity within molecules, influencing subsequent investigations into organic substances like alcohols and acids that displayed similar discrepancies. By the mid-1850s, the limitations of mere proportional laws became evident in , where numerous isomers defied explanation without considering atomic connectivity. In 1858, and Archibald Scott Couper independently developed the structural theory of organic compounds, proposing that carbon atoms exhibit tetravalency and can link to form chains or rings, thereby accounting for isomerism through different bonding patterns rather than just mass ratios. illustrated this with examples from the series, where isomers such as d-tartaric acid, l-tartaric acid, and meso-tartaric acid—despite identical compositions (C4H6O6)—arose from variations in the spatial arrangement of carbon chains and hydroxyl groups, a insight that extended to explaining the optical activity observed by a decade earlier. Couper, in parallel publications, emphasized carbon's self-linking ability () using linear bond notations, applying it to compounds like acetic acid and glucose to demonstrate how structural differences produced functional diversity. Concurrently, Stanislao Cannizzaro's 1858 pamphlet, presented at the Congress, revived Amedeo Avogadro's 1811 hypothesis by distinguishing between atoms and molecules, arguing that equal volumes of gases contain equal numbers of molecules, which could be diatomic or polyatomic, thus resolving inconsistencies in atomic weights and supporting the molecular from isomerism. Cannizzaro's approach used vapor measurements to assign correct molecular formulas to isomers, such as confirming as rather than simpler variants, thereby reinforcing the structural insights of Kekulé and Couper. These developments collectively transformed atomic theory from Dalton's indivisible, rigid particles into a framework of dynamic molecular architectures, where bonding and valency enabled complex isomerism and underscored the need for molecular-level evidence in chemical identity. This shift not only validated Avogadro's ideas but also paved the way for modern by prioritizing connectivity over mere composition.

Periodic Classification and Opposition

Mendeleev's Periodic Table

In 1869, Russian chemist published a periodic table that arranged the 63 known chemical elements in order of increasing atomic weight, grouping those with similar chemical and physical properties into vertical columns, or families. He observed that these properties recurred at regular intervals, or periods, as atomic weights increased, leading him to formulate the periodic law, which posited that the properties of elements are a of their atomic weights. This arrangement built upon the concept of atomic weights established in John Dalton's early 19th-century atomic theory, providing a systematic framework for understanding elemental behavior. Mendeleev's table included gaps for undiscovered elements, and he boldly predicted their existence and properties based on the patterns he identified. For instance, he forecasted an element below aluminum in Group III, which he termed eka-aluminum, describing it as a soft metal with an atomic weight of about 68, a of 6.0 g/cm³, and a low ; this was confirmed in 1875 with the discovery of , whose properties closely matched his predictions. Similarly, for eka-silicon, placed below in Group IV, Mendeleev anticipated a gray metal with an atomic weight near 72, of 5.5 g/cm³, and specific and formulas; germanium, discovered in 1886, fulfilled these expectations with remarkable accuracy. He also predicted other elements like eka-boron (later ) and eka-manganese (), enhancing the table's predictive power and credibility. Independently, German chemist developed a similar periodic table in , arranging elements by atomic weight and noting the periodicity of properties such as atomic volume and . Meyer's work, published more comprehensively in 1870, emphasized graphical representations of property trends but did not include explicit predictions for missing elements. Discrepancies in element ordering, such as those involving and iodine where atomic weight suggested reversal but properties did not align, were resolved by prioritizing valency groups—classifying elements by their combining capacity (e.g., monovalent, divalent)—which reinforced the periodic recurrence and Mendeleev's adjustments for chemical similarity over strict atomic weight sequence. Mendeleev's periodic system had profound implications for atomic theory, suggesting that the observed periodicity arose from an underlying atomic structure that governed chemical behavior and interactions, beyond mere empirical classification. This framework implied a fundamental order in the constitution of atoms, influencing subsequent developments in understanding elemental properties and their combinations.

Challenges to Atomic Theory

In the late , atomic theory encountered substantial philosophical and scientific opposition, particularly from the school of , which posited a continuous view of matter devoid of discrete particles. , a leading physical chemist, rejected as an unnecessary and unverifiable , advocating instead for —a framework explaining physical and chemical phenomena solely through transformations of without reference to atoms. , a and philosopher, similarly opposed the atomic on positivist grounds, arguing that unobservable entities like atoms were metaphysical speculations that could not be justified by and should be treated as mere calculational tools. These views gained traction among some scientists in the and , as appeared to align with observable laws while avoiding the perceived fictions of invisible atoms. Ludwig Boltzmann mounted a vigorous defense of through his development of , which interpreted thermodynamic laws as probabilistic outcomes of atomic interactions. A key challenge came from mathematician in , who invoked Poincaré's to argue that, in a finite atomic system governed by reversible mechanics, states would eventually recur, contradicting the irreversible and thus undermining atomic explanations. Boltzmann countered that the second law reflects overwhelmingly probable trends rather than absolute certainties, with recurrence events being statistically negligible over cosmic timescales, thereby preserving the validity of atomic models for practical predictions. This , spanning 1896–1897, highlighted the tension between mechanistic atomism and energeticist critiques. Advances in provided indirect support for atomic discreteness, as exemplified by William Henry Perkin's accidental synthesis of , the first synthetic violet dye, in 1856 through oxidation of derived from . This breakthrough relied on emerging structural theories assuming specific atomic arrangements to predict and replicate complex molecular behaviors, yet skeptics like Ostwald dismissed such successes as phenomenological descriptions rather than proof of atomic reality, insisting on direct observation. Mendeleev's periodic table offered additional corroboration by classifying elements as discrete units with predictable properties. The longstanding debate resolved in the early 1900s as experimental evidence from and irrefutably demonstrated the existence of atoms, leading Ostwald himself to concede their reality in a letter, marking the triumph of .

Kinetic and Statistical Developments

Kinetic Theory of Gases

The emerged in the as an early attempt to explain gas behavior through the motion of microscopic particles, with providing the foundational quantitative model in his 1738 work . Bernoulli modeled gas pressure as arising from the impacts of rapidly moving particles on the walls of a container, deriving by assuming particles travel in straight lines between elastic collisions with the walls and each other. This approach treated gases as composed of tiny, elastic spheres in constant motion, linking macroscopic pressure to the average of the particles. The theory gained renewed attention in the mid-19th century amid advances in thermodynamics. In 1845, John James Waterston submitted a manuscript to the Royal Society outlining a kinetic model where gas pressure results from molecular collisions, incorporating ideas of equipartition of energy among translational degrees of freedom; though initially rejected and unpublished until 1892, it anticipated key developments. Rudolf Clausius independently revived and refined Bernoulli's ideas in his 1857 paper, emphasizing that pressure stems from the momentum transfer during molecular impacts on container walls, while assuming molecules have negligible volume compared to the gas as a whole and undergo elastic collisions. Clausius's work introduced the mean free path concept, quantifying the average distance molecules travel between collisions, and calculated molecular speeds for gases like oxygen and hydrogen at room temperature, bridging kinetic models to experimental data on viscosity and diffusion. James Clerk Maxwell advanced the theory significantly in his 1860 paper "Illustrations of the Dynamical Theory of Gases," deriving the of molecular velocities under the assumptions of random motion and elastic collisions. Maxwell's distribution function for speeds is given by f(v) = 4\pi v^2 \left( \frac{m}{2\pi k T} \right)^{3/2} \exp\left( -\frac{m v^2}{2 k T} \right), where m is the , k is Boltzmann's constant, T is temperature, and v is speed; this yields the most probable speed v_p = \sqrt{2kT/m}, average speed \langle v \rangle = \sqrt{8kT/(\pi m)}, and root-mean-square speed v_{rms} = \sqrt{3kT/m}, explaining why faster molecules contribute disproportionately to pressure. extended these ideas in 1872, formulating the H-theorem to demonstrate how molecular collisions drive systems toward , linking microscopic to the irreversible increase in S = -k \int f \ln f \, d^3v. The H-theorem posits that the quantity H = \int f \ln f \, d^3v decreases over time (dH/dt \leq 0), with equality only at , thus providing a statistical foundation for the second law of from chaotic . Central to the kinetic theory are several key assumptions shared across these developments: molecules are point-like with negligible volume relative to the container; they move randomly in straight lines with no intermolecular forces except during instantaneous, collisions; and the number of molecules is vast, justifying statistical averaging over their velocities. These postulates enable derivations of like the PV = NkT and transport properties, treating as proportional to average \frac{3}{2}kT per .

Brownian Motion and Molecular Reality

In 1827, Scottish botanist Robert Brown observed the irregular, continuous motion of tiny particles, such as grains suspended in water, when viewed under a ; this phenomenon, later termed , appeared independent of external forces like currents or . In 1905, provided a theoretical explanation for within the framework of the kinetic theory, attributing the random displacements of suspended particles to collisions with invisible molecules in the fluid; he derived that the mean square displacement \langle x^2 \rangle in one dimension follows \langle x^2 \rangle = 2Dt, where D is the coefficient and t is time. Independently, in 1906, Polish physicist developed a similar kinetic theory of , deriving comparable relations for particle and emphasizing the role of molecular impacts in suspensions. Between 1908 and 1911, French physicist conducted meticulous experiments using uniform colloidal particles (such as or mastic resins) suspended in , tracking their paths over time to verify Einstein's and Smoluchowski's predictions; by measuring displacements and relating them to , , and particle size via the , Perrin calculated Avogadro's number as approximately $6.8 \times 10^{23} molecules per , aligning closely with values from other physical methods. These quantitative results not only confirmed the molecular-kinetic model but also provided the first empirical determination of atomic-scale parameters from observable macroscopic effects. For this work, Perrin received the 1926 , recognizing his demonstration of the discontinuous structure of matter through . Perrin's experiments decisively refuted the positivist skepticism of figures like and , who had dismissed atoms as unobservable metaphysical entities; by linking the erratic motion to quantifiable molecular collisions, Perrin established the physical reality of atoms on an empirical basis previously lacking.

Subatomic Discoveries

Electron Discovery

The late 19th century saw heightened interest in , mysterious streams of observed in partially evacuated tubes during electrical discharges, amid recent breakthroughs in studies. In 1895, discovered X-rays while experimenting with similar vacuum tubes, revealing invisible rays capable of penetrating materials and exposing photographic plates. This finding spurred investigations into related phenomena. The following year, identified in salts, noting their ability to emit penetrating rays independently of , further challenging classical views of . Joseph John Thomson, at the Cavendish Laboratory, sought to determine the nature of cathode rays through systematic experiments using modified cathode ray tubes. He observed that these rays were deflected toward the positive plate in an electric field and toward the negative pole in a magnetic field, indicating they consisted of negatively charged particles rather than waves. By applying perpendicular electric and magnetic fields of equal strength, Thomson balanced the deflections, allowing him to calculate the particles' charge-to-mass ratio (e/m) as approximately $1.76 \times 10^{11} C/kg, corresponding to a mass about 1/1,800 times that of a hydrogen ion. These particles, produced from cathodes of various metals and gases, exhibited identical properties, suggesting they were a fundamental constituent of all matter, which Thomson termed "corpuscles" (later known as electrons). In his seminal 1897 paper, Thomson concluded that cathode rays were streams of these lightweight, negatively charged particles, marking the first identification of a subatomic entity and overturning the long-held notion of atoms as indivisible. This discovery implied atoms were composite structures, with electrons accounting for phenomena like ionization in gases and electrolytes. To reconcile atomic neutrality, Thomson proposed in 1904 the "plum pudding" model, envisioning atoms as uniform spheres of positive charge embedding mobile electrons, akin to plums in a pudding, which maintained overall electrical balance while allowing for observed deflections and stability. The electron's universality across elements underscored its role as a building block, paving the way for refined atomic models that incorporated a central .

Nuclear Atom Model

In 1909, and conducted experiments under Ernest Rutherford's supervision, directing alpha particles from a radioactive source onto thin metal foils, particularly , and observing their patterns using a fluorescent screen. They found that while most alpha particles passed through the foil with minimal deflection, a small fraction—about 1 in 8000—were scattered at large angles, up to 180 degrees, indicating backscattering rather than the gradual deviations expected from Thomson's . Rutherford interpreted these results in his 1911 paper, proposing that the observed large-angle scattering could only occur if the positive charge and most of the 's mass were concentrated in a tiny, dense central region, which he termed the , rather than distributed throughout the . This nuclear model depicted the as a miniature solar system, with negatively charged orbiting the central positive to maintain overall neutrality, building briefly on J.J. Thomson's prior identification of the as the 's fundamental negative constituent. Rutherford estimated the radius to be on the order of $10^{-14} m, vastly smaller than the of approximately $10^{-10} m, implying that are mostly empty space with the occupying a minute fraction of the volume. In 1913, introduced the concept of isotopes, describing chemically identical elements with different atomic masses as variants arising from differences in nuclear composition, which aligned with the emerging view of the as the site of mass and stability. This work supported early identifications of the as composed of positively charged particles akin to the , providing a basis for understanding nuclear identity beyond configurations. Despite its groundbreaking insights, Rutherford's model faced a critical flaw: according to , orbiting electrons would accelerate and continuously radiate energy, leading to spiraling decay into the and atomic instability, which contradicted observed atomic permanence. This instability highlighted the need for a new theoretical framework to resolve the model's shortcomings.

Isotopes and Proton Identification

In 1913, proposed the concept of isotopes while studying chains, observing that certain elements, such as , exhibited variants that were chemically indistinguishable but differed in atomic weight and radioactive properties. For instance, different forms of lead from the and decay series were found to have identical chemical behaviors yet distinct atomic weights, leading Soddy to coin the term "isotopes" to describe these "same place" elements in the periodic table. This discovery resolved anomalies in where decay products mimicked the chemical identity of parent elements despite mass differences. Building on Soddy's work, Francis Aston developed the mass spectrograph in 1919, an instrument that ionized elements and separated them based on their mass-to-charge ratios using , providing precise measurements that confirmed the existence of isotopes. Aston's device revealed, for example, that consisted of isotopes with masses around 20 and 22, explaining variations in average atomic weights observed in natural samples. His measurements demonstrated that isotopes were not limited to radioactive elements but were a general feature of , with non-integer average atomic masses arising from mixtures of these variants. In 1920, identified the proton as the fundamental positively charged particle within atomic nuclei, naming it after its origin in the atom's . Drawing from earlier canal ray experiments by , which produced beams of positive ions, Rutherford proposed that the —observed in scattering experiments and ionization tracks—was a basic building block present in all nuclei, with the number of protons determining the element's identity. This built upon his 1911 nuclear model by specifying the proton's role. The identification of isotopes and protons provided a key explanation for periodic table irregularities, such as variable atomic weights, by attributing an element's mass primarily to the protons in its while allowing isotopic variations to account for chemical similarities across mass differences. This framework clarified why elements like exhibited atomic weights between integers, due to isotopic abundances rather than fundamental ambiguity in atomic structure.

Neutron Discovery

In 1930, physicists and Herbert Becker at the Max Planck Institute bombarded targets with alpha particles emitted from sources, observing a of exceptional penetrating power that they initially identified as high-energy gamma rays arising from excitation. This unexpected emission, with an absorption coefficient in lead far lower than typical gamma , suggested energies exceeding 10 million volts, prompting further investigation into reactions induced by alpha particles. Building on this work, Irène and at the in replicated the beryllium bombardment in early 1932 and discovered that the emitted radiation could eject protons from light substances like and hydrogenous materials at velocities up to 3 × 10^9 cm/s. They measured this effect using an and interpreted the protons' recoil as resulting from Compton-like of ultra-penetrating gamma rays with energies around 50 MeV, though the required seemed anomalously high for known processes. Their observations, published in 1932, highlighted the radiation's ability to transfer momentum to protons without electrical deflection, but they did not propose a particulate nature for the emitter. James Chadwick at the Cavendish Laboratory in Cambridge pursued these findings with more precise measurements later in 1932, using a polonium-beryllium source to generate the radiation and directing it onto to observe proton ejections via an and . He calculated that the maximum proton velocity of approximately 3.3 × 10^9 cm/s could only be achieved if the incident particles had a mass roughly equal to that of the proton—about 1 unit—and carried no electrical charge, as evidenced by the lack of deflection in electric or magnetic fields. The reaction was identified as ^9Be + ^4He → ^12C + ^1n, where the neutral particle, dubbed the "," was emitted with energies around 5 MeV; this resolved discrepancies in prior interpretations by confirming the radiation as a stream of massive, uncharged particles rather than photons. The neutron's discovery provided a crucial piece for understanding atomic nuclei, positing them as composites of positively charged protons and electrically neutral neutrons—collectively termed —that together account for nearly all nuclear mass while mitigating electrostatic repulsion through the strong . This model explained isotopic mass variations without invoking additional charged particles, as neutrons contribute to mass differences observed in elements like and . Shortly thereafter, developed a theoretical framework in mid-1932, treating protons and neutrons as two states of the nucleon bound by exchange forces, laying the groundwork for quantum descriptions of nuclear stability. For his experimental confirmation of the neutron, Chadwick received the 1935 .

Quantum Mechanical Evolution

Bohr Atomic Model

In 1913, Niels Bohr proposed a model for the hydrogen atom that incorporated quantum ideas to resolve the classical instability of electrons spiraling into the nucleus in Rutherford's nuclear model. Bohr's approach assumed electrons occupy discrete, stationary orbits around the nucleus without radiating energy, defying classical electromagnetic theory but ensuring atomic stability. Bohr introduced two key postulates: first, electrons exist in stable orbits where they do not emit , behaving according to ; second, is quantized such that L = n \frac{h}{2\pi}, where n = 1, 2, 3, \dots is the principal , h is Planck's , and electrons transition between orbits by absorbing or emitting with frequency \nu = \frac{E' - E''}{h}, where E' and E'' are the energies of the initial and final orbits. Applying this to , Bohr derived quantized levels E_n = -\frac{13.6 \, \text{eV}}{n^2}, leading to predictions that matched the , where transitions from higher n to n=2 produce visible wavelengths like 656 nm (H-alpha line) observed experimentally. In 1916, extended Bohr's model by allowing elliptical orbits, introducing a second k for the eccentricity and incorporating to account for the splitting in spectra, such as the slight deviation in Balmer line positions due to orbital . This refinement improved agreement with spectroscopic data for hydrogen-like atoms but retained the semi-classical framework. Despite its successes, Bohr's model is limited to hydrogen and single-electron ions, failing to predict spectra for multi-electron atoms due to unaccounted electron-electron interactions and ignoring the wave nature of electrons.

Wave-Particle Duality and Modern Models

In 1924, proposed that particles of matter, such as electrons, exhibit wave-like properties, hypothesizing a wavelength \lambda = h / p where h is Planck's constant and p is the particle's . This hypothesis extended the wave-particle duality observed in to all matter, suggesting that electrons orbiting the could be understood as standing waves. Building on earlier quantization ideas, de Broglie's concept provided a conceptual bridge toward a more complete . Experimental confirmation came in 1927 through the Davisson-Germer experiment, which demonstrated by a , producing patterns consistent with de Broglie's predicted for electrons accelerated to specific energies. The observed diffraction maxima aligned with the Bragg condition for wave scattering, verifying that electrons behave as waves under suitable conditions. In 1926, developed wave mechanics by formulating the , a governing the evolution of the wave function \psi that describes the of a particle's position. The time-dependent form is i [\hbar](/page/H-bar) \frac{\partial \psi}{\partial t} = \hat{H} \psi, where \hat{H} is the operator incorporating kinetic and potential energies, and \hbar = h / 2\pi. For stationary states, the time-independent \hat{H} \psi = E \psi was solved for the , yielding quantized energy levels and spatial probability distributions known as orbitals, replacing Bohr's fixed orbits with probabilistic clouds. Independently, Werner Heisenberg introduced matrix mechanics in 1925, formulating quantum theory using non-commuting arrays (matrices) to represent observables like position and momentum, where products do not commute, leading to inherently probabilistic outcomes. This approach, developed with Max Born and Pascual Jordan, proved mathematically equivalent to Schrödinger's wave mechanics. In 1927, Heisenberg articulated the uncertainty principle, stating that the product of uncertainties in position and momentum satisfies \Delta x \Delta p \geq \hbar / 2, highlighting fundamental limits on simultaneous measurement precision. In 1925, Wolfgang Pauli proposed the exclusion principle, asserting that no two fermions, such as electrons, can occupy the same quantum state simultaneously, which explains the structure of electron shells in atoms and periodic table properties. In 1928, Paul Dirac extended quantum mechanics to include special relativity with the Dirac equation, i \hbar \frac{\partial \psi}{\partial t} = c \vec{\alpha} \cdot \vec{p} \psi + \beta m c^2 \psi, where \psi is a four-component spinor and \vec{\alpha}, \beta are matrices. This relativistic wave equation successfully predicted electron spin and the existence of antimatter, laying groundwork for quantum electrodynamics. Post-World War II developments in the late 1940s solidified (QFT) as the foundational framework for atomic theory, addressing infinities in calculations through techniques pioneered by , , and Sin-Itiro Tomonaga. Their work, building on Hans Bethe's 1947 calculation of the , enabled precise predictions for atomic spectra and particle interactions, establishing QFT as the modern synthesis of and for multi-particle systems.

References

  1. [1]
    Ancient Atomism - Stanford Encyclopedia of Philosophy
    Oct 18, 2022 · Little is known about Leucippus, while the ideas of his student Democritus—who is said to have taken over and systematized his teacher's theory— ...Ancient Greek Atomism · The Legacy of Ancient Atomism · Bibliography
  2. [2]
    Atomism from the 17th to the 20th Century
    Jun 30, 2005 · The status of atomism underwent a transformation when John Dalton formulated his version of chemical atomism early in the nineteenth century.
  3. [3]
    Leucippus and Democritus
    The first proponents of an atomic theory were the Greek philosophers Leucippus and Democritus who proposed the following model in the fifth century BC.
  4. [4]
    The atomic theory of matter - Richard Fitzpatrick
    Atomic theory was invented by the ancient Greek philosophers Leucippus and Democritus, who speculated that the world essentially consists of myriads of tiny ...
  5. [5]
    John Dalton
    Experiments with gases that first became possible at the turn of the nineteenth century led John Dalton in 1803 to propose a modern theory of the atom based on ...
  6. [6]
    1.7: Indivisible – The Atomic Theory - Maricopa Open Digital Press
    Dalton's modern atomic theory, which he proposed about 1803, is a fundamental concept that states that all elements are composed of atoms. Previously, we ...
  7. [7]
    Who first discovered that atoms are made up of other particles and ...
    John Dalton (1766-1844), a great chemist, really started the modern atomic hypothesis. His atom however was like a solid billiard ball. Later, J.J. Thomson ( ...
  8. [8]
    [PDF] J. J. Thomson and The Electron: 1897–1899 An Introduction
    Jul 19, 2025 · Thomson's 1897 paper proposed cathode rays as subatomic "corpuscles" (later electrons), and his 1898 and 1899 papers further developed this ...
  9. [9]
    Modeling the Atom | The Engines of Our Ingenuity
    In 1910, Ernest Rutherford discovered there was an awful lot of empty space in atoms, leading him to postulate yet a new model of the atom, in which electrons ...Missing: scholarly | Show results with:scholarly
  10. [10]
    [PDF] RePoSS #10: Before Bohr: Theories of atomic structure 1850-1913
    The first really successful theory of atomic structure was proposed by Niels Bohr in his epoch-making paper in Philosophical Magazine of July 1913.
  11. [11]
    Niels Bohr
    Model of the Atom (Niels Bohr)​​ In 1913 one of Rutherford's students, Niels Bohr, proposed a model for the hydrogen atom that was consistent with Rutherford's ...
  12. [12]
    Copenhagen Interpretation of Quantum Mechanics
    May 3, 2002 · In 1913 Bohr, visiting Rutherford in Manchester, put forward a mathematical model of the atom which provided the first theoretical support ...
  13. [13]
    [PDF] Atoms and Quantum Mechanics - Duke Physics
    Schrödinger was able to show that his version of quantum mechanics and Heisenberg's are mathematically equivalent; Schrödinger's is generally regarded as ...
  14. [14]
    [PDF] Chapter 7. Quantum Theory and Atomic Structure
    Applying wave mathematics to the electron wave, Erwin. Schrödinger derived an equation that is the basis for the quantum-mechanical model of hydrogen atom.
  15. [15]
    Leucippus - Stanford Encyclopedia of Philosophy
    Aug 14, 2004 · The Greek tradition regarded Leucippus as the founder of atomism in ancient Greek philosophy. Little is known about him, and his views are ...Life and Works · Atomist Doctrine · Bibliography
  16. [16]
    Democritus - Stanford Encyclopedia of Philosophy
    Aug 15, 2004 · Democritus' theory of perception depends on the claim that eidôla or images, thin layers of atoms, are constantly sloughed off from the surfaces ...Life and Works · Atomist Doctrine · Theory of Perception · Theory of Knowledge
  17. [17]
    Lucretius - Stanford Encyclopedia of Philosophy
    Sep 22, 2023 · Titus Lucretius Carus (mid-90s to mid-50s BCE) was the author of a Latin, six-book didactic poem on Epicurean physics, the De rerum natura, henceforth DRN.
  18. [18]
    Epicurus - Stanford Encyclopedia of Philosophy
    Jan 10, 2005 · The philosophy of Epicurus (341–270 BCE) was a complete and interdependent system, involving a view of the goal of human life (happiness)3. Physical Theory · 4. Psychology And Ethics · Critical Studies
  19. [19]
    [PDF] Nyaya-Vaisheshika: The Indian Tradition of Physics - arXiv
    Kanada, one of the early philosophers of Vaisheshika, is known for his atomic view of the world. He uses the term 'Vishesha' to mean particularity of an atom ...
  20. [20]
    None
    ### Summary of Buddhist and Jain Atomism from the Document
  21. [21]
    Dalton's atomic theory (article) | Khan Academy
    This article will discuss John Dalton's atomic theory, which was the first complete attempt to describe all matter in terms of atoms and their properties.
  22. [22]
    Postulates of Dalton's Atomic Theory - Chemistry LibreTexts
    Jan 29, 2023 · John Dalton, a British school teacher, published his theory about atoms in 1808. His findings were based on experiments and the laws of chemical combination.
  23. [23]
    Proust's Law of Constant Proportion - Chemistry LibreTexts
    Jan 29, 2023 · Joseph Proust​​ The law was first published in a paper on iron oxides in 1794. Proust's law was attacked by the respected French chemist Claude- ...
  24. [24]
    Proust Establishes the Law of Definite Proportions | Research Starters
    Proust did publish a paper in 1794 in which he clearly recognized that iron not only had two oxides but also two sulfates, and he went on to state that all ...
  25. [25]
    A new system of chemical philosophy : Dalton, John, 1766-1844
    Jan 15, 2008 · 1808-27. Topics: Atomic theory, Chemistry, Inorganic. Publisher ... FULL TEXT download · download 1 file · HOCR download · download 1 file.
  26. [26]
    Chapter 9 Equal Numbers in Equal Volumes: Avogadro - Le Moyne
    This chapter includes Avogadro's law, that equal volumes of gas contain equal numbers of particles, presented as a hypothesis. Combined with Dalton's atomic ...
  27. [27]
    Historical and Recent Developments in the Chemistry of Cyanate ...
    Jun 11, 2025 · ... isomerism”, closely tied to the cyanate ion. Wöhler and Liebig discovered that silver cyanate (9) and silver fulminate (10−12) shared the ...
  28. [28]
    Friedrich Wöhler - MSU Chemistry
    Earlier (1824) Wöhler found that silver cyanate had the same composition as found for silver fulminate by Gay-Lussac and Liebig (see portrait). These pairs ...
  29. [29]
    Philosophy of Chemistry
    Mar 14, 2011 · Kekulé's ideas about bonding between atoms were important steps toward understanding isomerism. Yet his presentations of structure theory lacked ...
  30. [30]
    [PDF] Isotopomers and Isotopologues
    The term isomers is of much older vintage. It was coined by the great Swedish chemist Jöns Jacob Berzelius in 1830 [7]:. Unter isomerischen Körpern verstehe ...
  31. [31]
    August Kekulé and Archibald Scott Couper - Science History Institute
    The discovery by these two scientists depended on Kekulé's theory, proposed in 1857, that carbon is tetravalent, valence being defined at the time as the ...
  32. [32]
    Stanislao Cannizzaro | Science History Institute
    He used the hypothesis of a fellow Italian, Amedeo Avogadro, who had died just two years earlier, as a pathway out of the confusion rampant among chemists about ...
  33. [33]
    [PDF] In 1858, a new theory revolutionised organic chemistry, but its ...
    At this point, Couper and Kekulé independently realised that the discrepancy could be explained by assuming that the carbon atoms could soak up each other's ...
  34. [34]
    Mendeleev's Periodic Table | Origins
    Mar 18, 2019 · In these places he not only predicted there were as-yet-undiscovered elements, but he predicted their atomic weights and their characteristics.
  35. [35]
    A brief history of the periodic table
    Feb 7, 2021 · In 1869, Russian chemist Dmitri Mendeleev created the framework that became the modern periodic table, leaving gaps for elements that were yet to be discovered.
  36. [36]
    Periodic Table of Elements - PubChem - NIH
    The creator of the periodic table, Dmitri Mendeleev, in 1869 began collecting and sorting known properties of elements, like he was playing a game.
  37. [37]
    4.8: Mendeleev and Periodic Table - Chemistry LibreTexts
    May 25, 2021 · 1 : Comparison of the Properties Predicted by Mendeleev in 1869 for eka-Aluminum and eka-Silicon with the Properties of Gallium (discovered in ...
  38. [38]
    Mendeleev's Legacy: The Periodic System - Science History Institute
    Mendeleev's greatest achievement was not the periodic table so much as the recognition of the periodic system on which it was based.
  39. [39]
    Julius Lothar Meyer and Dmitri Ivanovich Mendeleev
    Mendeleev succeeded in arranging all known elements into one table. Meyer then published his classic paper of 1870 (“Die Natur der chemischen Elemente als ...
  40. [40]
    Prediction and the periodic table - ScienceDirect.com
    Mendeleev predicted that eka-silicon is a refractory substance as predicted by Mendeleev. In fact it melts at the relatively low temperature of 950°C. If, in ...
  41. [41]
    The periodic law of the chemical elements - PubMed Central - NIH
    Aug 17, 2020 · The work of Mendeleev has lately thrown a new light upon the relations existing between the atomic weights of the elements and their properties.
  42. [42]
    [PDF] ENERGY AS A PRIMITIVE ONTOLOGY FOR THE PHYSICAL WORLD
    Jun 16, 2025 · Ostwald inverted this view and was rejected as anti-atomistic, because his Energetics was conceived and seen as an alternative to atomic theory.
  43. [43]
    [PDF] 1981 OF BOLTZMANN WITH MACH, OSTWALD AND PLANCK ...
    Now why did Mach, a progressive person, struggle against atomism? No doubt his Opposition was rooted in his positivist philosophy, and this philosophy, as I ...
  44. [44]
    [PDF] Backstory to Atomism - The Quantum Measurement Problem
    Mach also dismissed atomism but criticized energism as being an abstract theory. His objections were partly philosophic ones and also being a physiologist, he.Missing: opposition energeticists<|control11|><|separator|>
  45. [45]
    [PDF] Zermelo, Boltzmann, and the recurrence paradox
    In late 1896 and 1897 Ernst Zermelo and Ludwig Boltz- mann debated whether statistical mechanics could adequa- tely explain the laws of thermodynamics.
  46. [46]
    [PDF] Recurrence - The Information Philosopher
    Boltzmann replied that his argument was statistical. He only claimed that entropy increase was overwhelmingly more prob- able than Zermelo's predicted decrease.
  47. [47]
    Zermelo, Boltzmann, and the recurrence paradox - ADS
    The papers exchanged by Ludwig Boltzmann and Ernst Zermelo concerning the recurrence paradox are summarized. The historical context of the paradox, ...Missing: atomic theory
  48. [48]
    William Henry Perkin | Science History Institute
    In 1856 Perkin accidentally discovered mauvine—the first commercialized synthetic dye—and introduced a new era in the chemical industry.
  49. [49]
    Boltzmann's Work in Statistical Physics
    Nov 17, 2004 · ... recurrence objection (Zermelo). Ostwald and Mach clearly resisted the atomic view of matter (although for different reasons). Boltzmann ...
  50. [50]
    Arrhenius, the Atomic Hypothesis, and the 1908 Nobel Prizes in ...
    In 1908 the rapid accumulation of experimental evidence in support of this hypothesis made Wilhelm Ostwald, the best known and most persistent of the skeptics, ...Missing: motion | Show results with:motion
  51. [51]
    [PDF] History of the Kinetic Theory of Gases* by Stephen G. Brush** Table ...
    The Swiss mathematical physicist Daniel Bernoulli (1700-1782) formulated a quantitative kinetic theory in his book on hydrodynamics. He derived Boyle's law for ...
  52. [52]
    I. On the physics of media that are composed of free and perfectly ...
    On the physics of media that are composed of free and perfectly elastic molecules in a state of motion. J. J. Waterston.<|separator|>
  53. [53]
    [PDF] The Nature of the Motion which we call Heat - Galileo Unbound
    111. Page 2. 112. SELECTED READINGS IN PHYSICS: KINETIC THEORY. The ratio of the vis viva of translatory motion to the total vis viva is found to be equal to 3( ...
  54. [54]
    Revival of Kinetic Theory by Clausius (1857 - 1858) - UMD MATH
    Aug 24, 2001 · Near the end of his 1857 paper Clausius calculated the average speeds of molecules of oxygen, nitrogen, and hydrogen at the temperature of ...
  55. [55]
    [PDF] 2 Further Studies on the Thermal Equilibrium of Gas Molecules
    SUMMARY. According to the mechanical theory of heat, the thermal properties of gases and other substances obey perfectly definite laws in spite of the fact ...
  56. [56]
    August 1827: Robert Brown and Molecular Motion in a Pollen-filled ...
    Aug 1, 2016 · A paper on the motion of small particles suspended in a stationary liquid. That work was rooted in the observations of a 19th century Scottish botanist named ...
  57. [57]
    [PDF] brownian movement - albert einstein, ph.d.
    I N this paper it will be shown that according to the molecular-kinetic theory of heat, bodies of microscopically-visible size suspended in a.Missing: source | Show results with:source
  58. [58]
    [PDF] PRIORITY AND THE EINSTEIN PAPERS ON “BROWNIAN MOTION”
    His discovery was reported in a paper given at the 1904 Australasian Association for the Advancement of. Science conference at Dunedin, New Zealand and ...Missing: original source
  59. [59]
    Jean Baptiste Perrin – Nobel Lecture - NobelPrize.org
    Briefly, and in spite of the variety of experimental conditions and techniques, the study of the emulsions gave me for Avogadro's number: 68 x 1022 by means of ...
  60. [60]
    Jean Baptiste Perrin – Facts - NobelPrize.org
    He also substantiated Einstein's theory that Brownian motion—the random movement of small particles in a liquid—was due to collisions between the particles and ...
  61. [61]
    FROM SEMANTICS TO METAPHYSICS by Joshua D. Brown A ...
    existence of atoms persisted until Perrin's experiments on Brownian motion in 1908. (Indeed, Duhem and Mach denied the reality of atoms until they died ...
  62. [62]
    Henri Becquerel and the Discovery of Radioactivity
    Dec 13, 2011 · French physicist Antoine Henri Becquerel, who discovered a completely unknown property of matter in March 1896.
  63. [63]
    Discovery of the Electron: J. J. Thomson - Le Moyne
    In 1897 he reported that "cathode rays" were actually negatively charged particles in motion; he argued that the charged particles weighed much less than the ...Missing: primary | Show results with:primary
  64. [64]
    October 1897: The Discovery of the Electron
    Oct 1, 2000 · Thomson boiled down the findings of his 1897 experiments into three primary hypotheses: (1) Cathode rays are charged particles, which he called ...Missing: source | Show results with:source
  65. [65]
    On a diffuse reflection of the α-particles - Journals
    (2025) Analogical models to introduce high school students to modern physics: an inquiry-based activity on Rutherford's gold foil experiment, Physics Education, ...
  66. [66]
    Rutherford's Nucleus Paper of 1911
    Geiger,* who found that the distribution for particles deflected between 30° and 150° from a thin gold-foil was in substantial agreement with the theory. A more ...
  67. [67]
    May, 1911: Rutherford and the Discovery of the Atomic Nucleus
    May 1, 2006 · The experiment involved firing alpha particles from a radioactive source at a thin gold foil. Any scattered particles would hit a screen coated ...
  68. [68]
    The Radio-Elements and the Periodic Law - Nature
    The Radio-Elements and the Periodic Law. FREDERICK SODDY. Nature volume 91, pages 57–58 (1913)Cite this article.<|separator|>
  69. [69]
    Experimental Evidence for the Structure of the Atom - Stanford
    Mar 23, 2017 · The Rutherford Gold Foil Experiment offered the first experimental evidence that led to the discovery of the nucleus of the atom as a small, dense, and ...
  70. [70]
    Künstliche Erregung von Kern-γ-Strahlen | Zeitschrift für Physik A ...
    Cite this article. Bothe, W., Becker, H. Künstliche Erregung von Kern-γ-Strahlen. Z. Physik 66, 289–306 (1930). https://doi.org/10.1007/BF01390908. Download ...Missing: paper | Show results with:paper
  71. [71]
    [PDF] JAMES CHADWICK - The neutron and its properties - Nobel Lecture ...
    atoms, when each neutron is bound to two protons and each proton to two neutrons. Thus two neutrons and two protons form a closed system - the α-particle.
  72. [72]
  73. [73]
    James Chadwick – Facts - NobelPrize.org
    James Chadwick, born in 1891 and died in 1974, won the 1935 Nobel Prize for discovering the neutron, a neutral particle with mass similar to a proton.
  74. [74]
    [PDF] Niels Bohr - Nobel Lecture
    atom is transformed back from the latter stationary state to the former. While the first postulate has in view the general stability of the atom, the second ...
  75. [75]
    Hydrogen energies and spectrum - HyperPhysics
    The basic structure of the hydrogen energy levels can be calculated from the Schrodinger equation. The energy levels agree with the earlier Bohr model, and ...
  76. [76]
    [PDF] {How Sommerfeld extended Bohr's model of the atom (1913–1916)}
    Jan 30, 2014 · The main problem concerned the quantization of orbits which are deformed from the circular or elliptical shape. Sommerfeld received the decisive ...
  77. [77]
    [PDF] XXXV. A Tentative Theory of Light Quanta. By LOUIS DE BROGLIE
    On the theoretical side Bohr's theory, which is supported by so many experimental proofs, is grounded on the postulate that atoms can only emit or absorb.
  78. [78]
    [PDF] Louis de Broglie - Nobel Lecture
    This hypothesis is necessary to explain how, in the case of light interferences, the light energy is con- centrated at the points where the wave intensity is ...
  79. [79]
    Heisenberg's Breakthrough - American Institute of Physics
    The first page of Heisenberg's break-through paper on quantum mechanics, published in the Zeitschrift für Physik, 33 (1925), 879-893, received 29 July 1925.
  80. [80]
    Diffraction of Electrons by a Crystal of Nickel | Phys. Rev.
    Davisson and Germer showed that electrons scatter from a crystal the way x rays do, proving that particles of matter can act like waves. See ...
  81. [81]
    [PDF] diffraction of electrons by a crystal of nickel
    December, 1927. Vol. 30, No. 6. THE. PHYSICAL REVIEW. DIFFRACTION OF ELECTRONS BY A CRYSTAL OF NICKEL. BY C. DAVISSON AND L. H. GERMER. ABSTRACT. The intensity ...
  82. [82]
    An Undulatory Theory of the Mechanics of Atoms and Molecules
    The paper gives an account of the author's work on a new form of quantum theory. §1. The Hamiltonian analogy between mechanics and optics.
  83. [83]
    [PDF] An undulatory theory of the mechanics of atoms and molecules - ISY
    The paper gives an account of the author's work on a new form of quantum theory. §1. The Hamiltonian analogy between mechanics and optics. §2. The.
  84. [84]
    Schrodinger's original quantum-mechanical solution for hydrogen
    Jul 24, 2020 · In 1926, Erwin Schrodinger wrote a series of papers that invented wave mechanics and set the foundation for much of the single-particle quantum ...
  85. [85]
    Understanding Heisenberg's 'Magical' Paper of July 1925 - arXiv
    Apr 1, 2004 · In July 1925 Heisenberg published a paper [Z. Phys. 33, 879-893 (1925)] which ended the period of `the Old Quantum Theory' and ushered in the new era of ...
  86. [86]
    The Uncertainty Principle - Heisenberg Web Exhibit
    Heisenberg presented his discovery and its consequences in a 14-page letter to Pauli in February 1927. The letter evolved into a published paper in which ...
  87. [87]
    [PDF] On the Connexion between the Completion of Electron Groups in an ...
    Apr 16, 2010 · PAULI. Z. Physik 31, 765ff (1925). Especially in connexion with Millikan and Landé's observation that the alkali doublet can be represented ...
  88. [88]
    The quantum theory of the electron - Journals
    Husain N (2025) Quantum Milestones, 1928: The Dirac Equation Unifies Quantum Mechanics and Special Relativity, Physics, 10.1103/Physics.18.20, 18. Shah R ...
  89. [89]
    [PDF] The Quantum Theory of the Electron - UCSD Math
    Oct 26, 2013 · By P. A. M. DIRAC, St. John's College, Cambridge. (Communicated by R. H. Fowler, F.R.S.-Received January 2, 1928.) The new quantum mechanics, ...
  90. [90]
    [PDF] The Search for Unity: Notes for a History of Quantum Field Theory
    Quantum field theory is the theory of matter and its interactions, which grew out of the fusion of quantum mechanics and special relativity in the late.Missing: post- seminal
  91. [91]
    January 1928: The Dirac equation unifies quantum mechanics and ...
    Nov 19, 2024 · A seminal paper by Paul Dirac, who relied on mathematical intuition, laid the foundation for quantum electrodynamics.