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  Web Book Home Page | Chemogenesis Main Index Foreword:  Chemogenesis & Chemical Education Part I   Atoms | Elements | Periodic Tables 1.1  Introduction to Chemogenesis 1.2  Nucleosynthesis of The Elements 1.3  The Segrè Chart 1.4  Quantum Numbers to Periodic Tables 1.5  The Periodic Table: What Is It Showing? 1.6  The INTERNET Database of Periodic Tables 1.7  Periodicity Part II   Structure | Bonding | Material Type 2.1  Mono-Bond Typed Binary Compounds 2.2  Binary Compound Synthlet 2.3  Electronegativity 2.4  van Arkel-Ketelaar Triangles of Bonding 2.5  Tetrahedra of Structure, Bonding & Material Type 2.6  Structure, Bonding & Material Synthlet 2.7  The Classification of Matter: Chemical Stuff Part III   Interactions | Reactions | Mechanisms 3.1  The Chemogenesis Analysis: An Overview 3.2  Lewis and Brønsted Models of Acidity 3.3  The Hard Soft [Lewis] Acid Base Principle 3.4  Main Group Elemental Hydrides 3.5  Five Hydrogen Probe Experiments 3.6  Congeneric Dots, Series & Planars 3.7  Quantifying Congeneric Behaviour 3.8  Ligand Replacement Congeneric Series 3.9  Congeneric Array Interactions 3.10  Emergence of Organic Chemistry 3.11  Congeneric Array Database 3.12  The Five Reaction Chemistries 3.13  Lewis Acids & Lewis Bases: A New Analysis 3.14  The Lewis Acid/Base Interaction Matrix 3.15  Patterns in Reaction Chemistry Poster 3.16  Lewis Acid/Base Interaction Matrix Database 3.17  Nucleophiles, Bases & The Fluoride Ion 3.18  Redox Chemistry 3.19  Redox Chemistry Synthlet 3.20  Radical Chemistry 3.21  Diradical Chemistry 3.22  Photochemistry 3.23  Species/Species Interactions 3.24  The Simplest Mechanistic Step: STAD 3.25  Unit & Compound Mechanistic Steps 3.26  The Mechanism Matrix 3.27  Addition To A Double Bond Synthlet 3.28  Pericyclic Reaction Chemistry Part IV   Chemical Theory 4.1  Why Do Chemical Reactions Occur? 4.2a  Thermochemistry: List Reactions Synthlet 4.2b  Thermochemistry: Play With Reaction Synthlet 4.2c  Thermochemistry: Bulid A Reaction Synthlet 4.3  Timeline of Structural Theory 4.4  Modern Lewis Theory 4.5  Valence Shell Electron Pair Repulsion: VSEPR 4.6  Diatomic Species by Molecular Orbital Theory 4.7  Polyatomic Species: Molecular Orbitals 4.8  Organic π-Systems 4.9  Functional Group Database Part V   Complexity & Emergence 5.1  Chemistry & Complexity: Systems 5.2  Linear Chemistry Systems 5.3  Chemical Systems Prone to Complexity Part VI   Extras 6.1  Chemogenesis Videos 6.2  Chemical Thesaurus Reaction Chemistry Database 6.3  Paper: Chemogenesis 6.4  Paper: Electronegativity as a Basic Elemental Property (FoC) 6.5  Workshop: What is Chemistry? 6.6  Paper: Scientific laws, Dalton’s postulates, chemical reactions
          and Wolfram’s NKS (FoC) 6.7  Literature References & Further Reading

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The INTERNET Database of Periodic Tables

There are thousands of periodic tables in web space, but this is the only comprehensive database of periodic tables & periodic system formulations. If you know of an interesting periodic table that is missing, please contact the database curator: Mark R. Leach Ph.D. The database holds information on periodic tables, the discovery of the elements, the elucidation of atomic weights and the discovery of atomic structure (and much, much more).

Elucidation of Atomic Structure: 1800 - 1948

Dalton introduced the idea of atoms and stoichiometric combination ratios in the early nineteenth century. Atomic weights were rationalised by Cannizzaro in 1858. Radioactivity was discovered in 1896, and around this time the Group 8/18 inert/rare/full-shell gases found. The years from 1900 to 1930 saw the quantum revolution in atomic physics and atomic structure develop. The Manhattan project advanced knowledge of the heavier and radioactive elements, leading to the Seaborg periodic table and the Segrè chart. (These would have been state secrets in 1944, but by 1948 they were in the public domain). By the late 1940s, understanding atomic structure was very good:

Dalton's Postulates About The Elements

Around the year 1803 in Manchester, John Dalton gave a series of lectures in which he presented his postulates:

• Elements are made of tiny particles called atoms.
• The atoms of a given element are different from those of any other element, and the atoms of different elements can be distinguished from one another by their respective relative atomic weigh/mass.
• All atoms of a given element are identical.
• Atoms of one element can combine with atoms of other elements to form chemical compounds, and a given compound always has the same relative numbers of types of atoms.
• Atoms cannot be created, divided into smaller particles, nor destroyed in the chemical process, and a chemical reaction simply changes the way atoms are grouped together.

From a very early notebook from around this time:

Dalton's Elements

Two pages from John Dalton's A New System of Chemical Philosophy in which he proposed his version of atomic theory based on scientific experimentation (see the scanned book, page 219):

• Dalton states that he is considering "chemical elements or ultimate particles"
• Dalton assigns hydrogen as having a relative weight of 1.
• Note the seemingly huge % errors in the atomic weights, compared with modern values.
• These errors occurred because while Dalton had deduced that atoms combine in fixed (stoichiometric) ratios in compounds, he not always know what the ratios were. Thus there were two unknowns: the atomic weights (masses) and the stoichiometric ratios.

By Mark Leach

Cannizzaro's Letter or Sunto

Letter of Professor Stanislao Cannizzaro to Professor S. De Luca: Sunto di un corso di filosofia chimica (Sketch of a Course of Chemical Philosophy) given in the Royal University of Genoa, Il Nuovo Cimento, vol. vii. (1858), pp. 321-366.

Many thanks to Carmen Giunta, Professor of Chemistry Emeritus, Le Moyne College who provided the information about, and link to, Cannizzaro's Letter. See a list of other classic chemistry papers.

Read the full letter/paper, in English translation, here. (The Italian version is here.)

Cannizzaro writes:

"I believe that the progress of science made in these last years has confirmed the hypothesis of Avogadro, of Ampère, and of Dumas on the similar constitution of substances in the gaseous state; that is, that equal volumes of these substances, whether simple or compound, contain an equal number of molecules: not however an equal number of atoms, since the molecules of the different substances, or those of the same substance in its different states, may contain a different number of atoms, whether of the same or of diverse nature."

From the Science History of Science Institute:

"In 1858 Cannizzaro outlined a course in theoretical chemistry for students at the University of Genoa,where he had to teach without benefit of a laboratory. 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 atomic weights and the fundamental structure of chemical compounds."

Mark Leach writes:

"Before a periodic table of the chemical elements – which orders the elements by atomic weight and then groups them by property – could be developed it was necessary to know the atomic weight values. However, to deduce the atomic weights was a problem as it was necessary to know the ratios of how the elements combined, the stoichiometry.

"Tables of atomic weight data by Dalton (1808), Wollaston (1813), Daubeny (1831) and Kopp & Will (1858) show progress, but the 1858 Cannizzaro letter was the first where the atomic weight data is more or less both complete and accurate, thus removing stiochiometric errors.

"I have extracted the element atomic weight data from the paper, and given the % error with respect to modern atomic weight/mass data. Only titanium is significantly out! It is clear that Cannizzaron knew that hydrogen, nitrogen, oxygen, chlorine, bromine & iodine existed as diatomic molecules."

Below is a list of the elements showing which ones were included by Cannizzaro and which one were ommitted (because they had not been discovered) or are strangely missing. Odd ommissions (to the modern eye) include: Lithium, Beryllium, Cobalt, Nickel, Palladium, Tungsten and Gold.

Discovery of Radioactivity

From The Nuclear Wallchart:

In 1896 Henri Becquerel was using naturally fluorescent minerals to study the properties of x-rays, which had been discovered in 1895 by Wilhelm Roentgen. He exposed potassium uranyl sulfate to sunlight and then placed it on photographic plates wrapped in black paper, believing that the uranium absorbed the sun’s energy and then emitted it as x-rays.

This hypothesis was disproved on the 26th-27th of February, when his experiment "failed" because it was overcast in Paris. For some reason, Becquerel decided to develop his photographic plates anyway. To his surprise, the images were strong and clear, proving that the uranium emitted radiation without an external source of energy such as the sun. Becquerel had discovered radioactivity.

Becquerel showed that the radiation he discovered could not be x-rays. X-rays are neutral and cannot be bent in a magnetic field. The new radiation was bent by the magnetic field so that the radiation must be charged and different than x-rays. When different radioactive substances were put in the magnetic field, they deflected in different directions or not at all, showing that there were three classes of radioactivity: negative, positive, and electrically neutral.

The term radioactivity was actually coined by Marie Curie, who together with her husband Pierre, began investigating the phenomenon recently discovered by Becquerel. The Curies extracted uranium from ore and to their surprise, found that the leftover ore showed more activity than the pure uranium. They concluded that the ore contained other radioactive elements. This led to the discoveries of the elements polonium and radium. It took four more years of processing tons of ore to isolate enough of each element to determine their chemical properties.

Ernest Rutherford, who did many experiments studying the properties of radioactive decay, named these alpha, beta, and gamma (α, β and γ) particles, and classified them by their ability to penetrate matter. Rutherford used an apparatus similar to Becquerel's. When the air from the chamber was removed, the alpha source made a spot on the photographic plate. When air was added, the spot disappeared. Thus, only a few centimeters of air were enough to stop the alpha radiation.

• α-particles carry more electric charge, are more massive, and move slowly compared to β and γ particles, they interact much more easily with matter.
• β-particles are much less massive and move faster, but are still electrically charged. A sheet of aluminum one millimeter thick or several meters of air will stop these electrons [and positrons].
• γ-rays carry no electric charge, they can penetrate large distances through materials before interacting–several centimeters of lead or a meter of concrete is needed to stop most γ-rays.

Henri Becquerel and Marie & Pierre Curie in their labs:

History of the Discovery of the Group 18 (erstwhile Group 0) Elements

John Marks has provided a concise history of the discovery of the Group 18 elements and the element name"Nitron/Radon".

Radioactivity was discovered by Becquerel in 1896 and the Curies noted transferred radioactivity rather like the induction of electric or magnetic charge. Radon was discovered in 1900, by Dorn in Halle; Rutherford discovered thoron in 1899; and Debierne discovered actinon in 1903. The time-line is:

• 1868 Lockyer observed the spectrum of helium in the solar corona
• 1894 Ramsay discovers argon
• 1895 Ramsay isolates helium
• 1898 Ramsay discovers krypton, neon & xenon
• 1899 Curie observes an emanation from radium
• 1899 Rutherford observes an emanation from thorium
• 1900 Dorn identifies radon
• 1902 Rutherford & Soddy characterize thoron
• 1903 Rutherford & Soddy isolate radon
• 1903 Debierne observes an emanation from actinium
• 1904 Ramsay names the isotopic emanations exactinio, exradio & exthorio and surmises they are one element, probably an inert gas
• 1908 Professor Sydney Young’s "Stoichiometry" has a periodic table shows niton, Z = 86
• 1909 Ramsay characterizes niton as a group 0 inert gas
• 1910 Cameron's "Radiochemistry" describes the radioactive displacement law
• 1912 The name "niton" accepted by the International Commission for Atomic Weights
• 1913 Soddy expounds theory of isotopes
• 1913 Rydberg's periodic table has Nt (86) for the last inert gas
• 1919 Irving Langmuir's PT has Nt as the last inert gas
• 1922 Niels Bohr’s PT has Nt (86) as the last inert gas
• 1923 GN Lewis’s PT has Nt as the last inert gas
• 1924 CRC’s Handbook of Chemistry and Physics has niton as the last member of Group 0

So niton (from Latin nitens = shining) was noticed by the Curies in 1899 as an emanation from radium. That same year Rutherford noted an identical emanation from thorium, and in 1903 Debierne discovered the same emanation from actinium. All three ('radon', 'thoron' and 'actinon') were identified as an element by Ramsay in 1904 and characterized by him in 1909.

Ramsay named the element niton after its most prominent property viz. that it glowed in the dark.

With the introduction of Soddy's isotopes, it became clear that: thoron was Nt-220, radon was Nt-222 & actinon was Nt-219.

There are natural traces of other isotopes (e.g. Nt-217, Nt-218) from beta disintegration of astatine. So "radon" was just one isotope of niton.

The foregoing history of niton is uncontroversial and the name niton, Nt, for Z = 86 dates at least from Professor Young´s textbook of stoichiometry in 1908.

In 1912, the name 'niton' was adopted by the International Commission for Atomic weights. Rydberg's PT of 1913 has Nt as the last inert gas, as does Irving Langmuir's PT of 1919, Niels Bohr's PT of 1922, GN Lewis's PT of 1923 and even the CRC's Handbook of Chemistry and Physics in 1924.

John Marks concludes:

"Niton, Nt, for Z = 86, was thus established by its discoverers and accepted by the chemistry (and physics) establishment. Radon, Rn, is an error perpetuated by IUPAC [amongst its many sins].

"Radon is an isotope. We do not refer to hydrogen as 'protium', so why are we referring to niton as 'radon'?"

Planck and E = hν

Planck, M. Über das Gesetz der Energieverteilung im Normalspektrum (On the law of energy distribution in the normal spectrum). Annalen der Physik, 4, 553–563 (1901). (Presented to the German Physical Society in Dec 1900).

Wikipedia

"In 1894, Planck turned his attention to the problem of black-body radiation which had been stated by Kirchhoff in 1859 as: 'How does the intensity of the electromagnetic radiation emitted by a black body (a perfect absorber, also known as a cavity radiator) depend on the frequency of the radiation (i.e., the colour of the light) and the temperature of the body?'

The central assumption of Planck’s new analysis, the Planck postulate, was that electromagnetic energy could be emitted only in quantized form; in other words, the energy could only be a multiple of an elementary unit:

E = hν

Where h is the Planck constant, also known as Planck's action quantum and ν (the Greek letter 'nu') is the frequency of the radiation."

Thomson and the Plum Pudding Model of the Atom

Thomson, J. J. On the Structure of the Atom. Philosophical Magazine, 7, 237–265 (1904). https://zenodo.org/records/1430726

Wikipedia:

"The view that the atoms of the elements consist of a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification, suggests, among other interesting mathematical problems, the one discussed in this paper, that of the motion of a ring of n negatively electrified particles placed inside a uniformly electrified sphere."

Rutherford and the Geiger–Marsden Gold Leaf Scattering Experiments

Geiger, H., & Marsden, E. On a Diffuse Reflection of the ?-Particles. Proceedings of the Royal Society A, 82, 495–500 (1909) and Rutherford, E. The Scattering of ? and ? Particles by Matter and the Structure of the Atom. Philosophical Magazine, 21, 669–688 (1911).

Wikipedia:

"The Rutherford scattering experiments were performed between 1906 and 1913 by Hans Geiger and Ernest Marsden under the direction of Ernest Rutherford at the Physical Laboratories of the University of Manchester.

"Experiments showed that every atom had a nucleus where all its positive charge and most of its mass is concentrated. This was deduced this after measuring how a beam of alpha particles is scattered when it strikes gold leaf (thin gold foil)."

Moseley's Periodic Law and Atomic Number Z

Moseley, H. G. J. The High-Frequency Spectra of the Elements. Philosophical Magazine, 26, 1024–1034 (1913).

Wikipedia:

"Moseley's law is an empirical law concerning the characteristic X-rays emitted by atoms. The law was discovered and published by the English physicist Henry Moseley in 1913–1914. Until Moseley's work, "atomic number" was merely an element's place in the periodic table and was not known to be associated with any measurable physical quantity.

"In brief, Moseley's law states that the square root of the frequency, ν, of the emitted X-ray is (approximately) proportional to the atomic number":

The Bohr Atom

Bohr, N. On the Constitution of Atoms and Molecules (Parts I–III). Philosophical Magazine, 26, 1–25; 476–502; 857–875 (1913).

Wikipedia:

"In the Bohr model (or the Rutherford–Bohr model) of the hydrogen atom (Z = 1), the negatively charged electron confined to an atomic shell encircles a small, positively charged atomic nucleus. When an electron jumps between orbits, is accompanied by an emitted or absorbed amount of electromagnetic energy (where E = hν). The orbits in which the electron may travel are shown as grey circles; their radius increases as n², where n is the principal quantum number. The 3 ? 2 transition produces the first line of the Balmer series, and for hydrogen (Z = 1) it results in a photon of wavelength 656 nm (red light).

"The Bohr atom consists of a small, dense atomic nucleus surrounded by orbiting electrons. It is analogous to the structure of the Solar System, but with attraction provided by electrostatic force rather than gravity, and with the electron energies quantised (assuming only discrete values). The Bohr model incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's discovery of the atom's nucleus, the model supplanted the plum pudding model of J. J. Thomson only to be replaced by the quantum atomic model in the 1920s.

"The Bohr model's key success lies in explaining the Rydberg formula for hydrogen's spectral emission lines. While the Rydberg formula had been known experimentally, it did not gain a theoretical basis until the Bohr model was introduced. Not only did the Bohr model explain the reasons for the structure of the Rydberg formula, it also provided a justification for the fundamental physical constants that make up the formula's empirical results."

Sommerfeld and the Azimuthal and Magnetic Quantum Numbers

Sommerfeld, A. Zur Quantentheorie der Spektrallinien. Annalen der Physik, 51, 1–94 (1916).

Wikipedia:

"Arnold Sommerfeld was a German theoretical physicist who pioneered developments in both atomic and quantum physics. He also educated and mentored many students for the new era of theoretical quantum physics.

"Sommerfeld introduced the second (azimuthal) and the third (magnetic) quantum numbers ℓ and m_ℓ. (He also introduced the fine-structure constant and pioneered X-ray wave theory.)

"In quantum mechanics, the azimuthal quantum number ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number, m_ℓ, and the spin quantum number m_s).

"Seven of Sommerfeld's doctoral students and postdoctoral supervisees: Werner Heisenberg, Wolfgang Pauli, Peter Debye, Hans Bethe, Linus Pauling, Isidor I. Rabi and Max von Laue went on to win Nobel Prizes in theoretical physics or chemistry. He also supervised at least 30 other famous physicists and chemists."

de Broglie and Wave–Particle Duality

de Broglie, L. Recherches sur la théorie des quanta. Annales de Physique, 3, 22–128 (1925). (Doctoral thesis, submitted 1924)

Wikipedia:

"Louis Victor Pierre Raymond, 7th Duc de Broglie was a French theoretical physicist and aristocrat known for his contributions to quantum theory. In his 1924 Ph.D. thesis, de Broglie postulated the wave nature of electrons and suggested that all matter has wave properties.

"This concept, now known as the de Broglie hypothesis, an example of wave–particle duality, and forms a central part of the theory of quantum mechanics. In 1929, de Broglie won the Nobel Prize in Physics, after the wave-like behaviour of matter was experimentally confirmed in 1927."

Pauli and The Exclusion Principle

Pauli, W. Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren. Zeitschrift für Physik, 31, 765–783 (1925).

Wikipedia:

"Wolfgang Pauli was an Austrian–Swiss theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics 'for the discovery of the Exclusion Principle, also called the Pauli Principle'. The discovery involved spin theory.

"The Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940.

"In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of all four of their quantum numbers, which are: n, the principal quantum number; ℓ, the azimuthal quantum number; m_ℓ, the magnetic quantum number; and m_s, the spin quantum number.

"If two electrons reside in the same orbital, then their values of n, ℓ, and m_ℓ are equal. In that case, the two values of m_s (spin) pair must be different. Since the only two possible values for the spin projection ms are +1/2 and –1/2, it follows that one electron must have m_s = +1/2 and one m_s = –1/2.

"To preserve the conservation of energy in beta decay, Pauli proposed the existence of a small neutral particle, dubbed the neutrino by Enrico Fermi, in 1930. Neutrinos were first detected in 1956. "

Heisenberg’s Matrix Mechanics and the Uncertainty Principle

Heisenberg, W. Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. (On the quantum-theoretical reinterpretation of kinematic and mechanical relationships.) Zeitschrift für Physik, 33, 879–893 (1925); Heisenberg, W. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. (On the intuitive content of quantum-theoretical kinematics and mechanics. "The Uncertainty Principle") Zeitschrift für Physik, 43, 172–198 (1927).

Wikipedia:

"Werner Karl Heisenberg was a German theoretical physicist, one of the main pioneers of the theory of quantum mechanics. Heisenberg published his Umdeutung paper in 1925, a major reinterpretation of old quantum theory.

"In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, his matrix formulation of quantum mechanics was substantially elaborated. He is also known for the uncertainty principle, which he published in 1927. He received the Nobel Prize in Physics in 1932 'for the creation of quantum mechanics'."

Below is a largely non-mathematical video that discusses the development of Heisenberg's matrix mechanics and then compares it to the Schrödinger wave equation analysis:

Schrödinger Wave Equation

Schrödinger, E. Quantisierung als Eigenwertproblem (Quantization as an eigenvalue problem) (Parts I–IV). Annalen der Physik, 79, 361–376; 489–527; 734–756; 80, 437–490 (1926).

Wikipedia:

"Erwin Schrödinger was an Austrian–Irish theoretical physicist who developed fundamental results in quantum theory. In particular, he is recognised for devising the Schrödinger equation, an equation that provides a way to calculate the wave function of a system and how it changes dynamically in time."

"A special case of the Schrödinger equation is the position-space Schrödinger equation for a single nonrelativistic particle in one dimension:

"The ψ is a wave function, a function that assigns a complex number to each point x at each time t. The parameter m is the mass of the particle, and V(x,t) is the potential energy function that represents the environment in which the particle exists. The constant i is the imaginary unit, and ħ is the reduced Planck constant, which has units of action (energy multiplied by time).

"Schrödinger coined the term 'quantum entanglement' in 1935. Schrödinger shared the 1933 Nobel Prize in Physics with Paul Dirac 'for the discovery of new productive forms of atomic theory.''

"The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterisation of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equation predicted bound states of the atom in agreement with experimental observations."

Three videos on the Schrödinger Wave Equation. (The middle one is very detailed.):

Born's Rule

Born, M. Zur Quantenmechanik der Stoßvorgänge. Zeitschrift für Physik, 37, 863–867 (1926).

Wikipedia:

"Max Born was a German–British theoretical physicist who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics, and supervised the work of a number of notable physicists in the 1920s and 1930s. He shared the 1954 Nobel Prize in Physics with Walther Bothe 'for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction.'

"The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that position. So is the wave function is ψ, the probability of finding the electron is |ψ|²."

A video explaining Born's Rule:

Schrödinger and The Hydrogen Atom

In Parts II and III of Schrödinger's 1926 papers: Annalen der Physik, 79 (1926), pp. 361–376 and Annalen der Physik, 80 (1926), pp. 437–490, the hydrogen atom is addressed.

Here Schrödinger:

• Separates the equation in spherical coordinates
• Solves the radial equation
• Derives hydrogen energy levels:

• Shows agreement with the Bohr spectrum

This is the first full wave-mechanical derivation of hydrogen.

There is an on-line English translation of Schrödinger's 1926 papers, published in 1928.

Fifth Solvay Conference on Physics

Wikipedia:

"The most famous conference was the fifth Solvay Conference on Physics, which was held from 24 to 29 October 1927. The subject was Electrons and Photons and the world's most notable physicists met to discuss the newly formulated quantum theory. The leading figures were Albert Einstein and Niels Bohr. Seventeen of the 29 attendees were or became Nobel Prize winners, including Marie Skłodowska-Curie who, alone among them, had won Nobel Prizes in two separate scientific disciplines. The anti-German prejudice that had prevented Einstein and others from attending the Solvay conferences held after the First World War had melted away. Essentially all of those names who had contributed to the recent development of the quantum theory were at this Solvay Conference, including Bohr, Born, de Broglie, Dirac, Heisenberg, Pauli, Planck, Lorentz, Compton, Ehrenfest, and Schrödinger. Heisenberg commented:

"Through the possibility of exchange between the representatives of different lines of research, this conference has contributed extraordinarily to the clarification of the physical foundations of the quantum theory. It forms, so to speak, the outward completion of the quantum theory."

"The photo taken of this conference's participants is sometimes entitled 'The Most Intelligent Photo Ever Taken', for its depiction of the world's leading physicists gathered together in one shot."

A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. De Donder, E. Schrödinger, J.E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin;
P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr;
I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch. E. Guye, C.T.R. Wilson, O.W. Richardson
Fifth conference participants, 1927. Institut International de Physique Solvay in Leopold Park.

Dirac Equation

Dirac, P. A. M. (1928). "The Quantum Theory of the Electron". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 117 (778): 610–624. PDF of paper.

Wikipedia:

"The Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-?1/2? massive particles, called Dirac particles, such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity and was the first theory to fully account for special relativity in the context of quantum mechanics. The equation is validated by its rigorous accounting of the observed fine structure of the hydrogen spectrum and has become vital in the building of the Standard Model pf particle physics.

"The equation also implied the existence of a new form of matter, antimatter, previously unsuspected and unobserved. The existence of antimatter was experimentally confirmed several years later. It also provided a theoretical justification for the introduction of several component wave functions in Pauli's phenomenological theory of spin. The wave functions in the Dirac theory are vectors of four complex numbers (known as bispinors), two of which resemble the Pauli wavefunction in the non-relativistic limit, in contrast to the Schrödinger equation, which described wave functions of only one complex value."

If you require deeper dive into quantum spin and the Dirac equation, these two linked videos by Physics Explained will be of interest. The videos discuss the history and the mathematics of the equation. The videos show that the Dirac formulation of the relativistic electron inevitably has four answers or solutions which correspond to the:

• Spin-up electron
• Spin-down electron
• Spin-up positron (anti-electron)
• Spin-down positron
• The result also shows that the spin must be +1/2 or –1/2.

Quantum Atoms

Dirac, P. A. M. The Principles of Quantum Mechanics. Oxford University Press (1st ed. 1930; 2nd ed. 1935). Wikipeda entry on this work.
von Neumann, J., Mathematische Grundlagen der Quantenmechanik (Mathematical Foundations of Quantum Mechanics), 1932, Springer, Berlin, Germany. Wikepedia entry on this work.

By the 1930s, the mathematics of quantum mechanics was mature, as exemplified by these two text books. Dirac explicitly develops methods for atoms, molecules, radiation, and many-particle systems. Von Neumann formulates a fully general mathematical framework applicable to arbitrarily complex systems (though with few concrete examples).

"The Principles of Quantum Mechanics is an influential monograph written by Paul Dirac and first published by Oxford University Press in 1930. In this book, Dirac presents quantum mechanics in a formal, logically consistent, and axiomatic fashion, making the book the first of its kind. It is based on matrices and operators rather than wave–particle duality. Its 82 sections contain 785 equations with no diagrams. Nor does it have an index, a bibliography, or a list of suggestions for further reading. The first half of the book lays down the foundations of quantum mechanics while the second half focuses on its applications. Dirac did not pursue a historical approach to the subject. Nor did he discuss at length the philosophy of quantum mechanics."

"Von Neumann formalised quantum mechanics using the concept of Hilbert spaces and linear operators. He acknowledged the previous work by Paul Dirac on the mathematical formalisation of quantum mechanics, but was skeptical of Dirac's use of delta functions. He wrote the book in an attempt to be even more mathematically rigorous than Dirac. It was von Neumann's last book in German, afterwards he started publishing in English."

To read Dirac's The Principles of Quantum Mechanics click this link.

Chadwick and the Discovery of the Neutron

Chadwick, J. Possible Existence of a Neutron. Nature, 129, 312 (1932).

Wikipedia:

"James Chadwick was a British experimental physicist who received the Nobel Prize in Physics in 1935 for his discovery of the neutron. In 1941, he wrote the final draft of the MAUD Report, which inspired the U.S. government to begin serious atomic bomb research efforts. He was the head of the British team that worked on the Manhattan Project during World War II.

"The discovery of the neutron and its properties was central to the extraordinary developments in atomic physics in the first half of the 20th century. Early in the century, Ernest Rutherford used alpha particle scattering to discover that an atom has its mass and electric charge concentrated in a tiny nucleus. By 1920, isotopes of chemical elements had been discovered, the atomic masses had been determined to be approximately integer multiples of the mass of the hydrogen atom, and the atomic number had been identified as the charge on the nucleus. Throughout the 1920s, the nucleus was viewed as composed of combinations of protons and electrons, the two elementary particles known at the time, but that model presented several experimental and theoretical contradictions.

"The essential nature of the atomic nucleus was established with the discovery of the neutron by James Chadwick in 1932 and the determination that it was a new elementary particle, distinct from the proton.

"The uncharged neutron was immediately exploited as a new means to probe nuclear structure, leading to such discoveries as the creation of new radioactive elements by neutron irradiation (1934) and the fission of uranium atoms by neutrons (1938). The discovery of fission led to the creation of both nuclear power and nuclear weapons by the end of World War II. Both the proton and the neutron were presumed to be elementary particles until the 1960s, when they were determined to be composite particles built from quarks. "

Seaborg's Periodic Table of 1945

From his Priestly Medal Address, The Periodic Table: Tortuous Path to Man-Made Elements printed in C&EN April 16, 1979 and reprinted in Modern Alchemy: Selected Papers of Glenn T. Seaborg (1994), page 181.

Seaborg describes how "the theory was advanced that [the] new elements heavier than than actinium might constitute a second series similar to the series of 'rare-earth' or 'lanthanide' elements":

Segrè Chart (Original)

Segrè, Emilio. Segrè Chart [Isotope Chart], technical drawing, April 1948;  Oak Ridge, Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc100789/: accessed February 17, 2026), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

Wikipedia:

"A table or chart of nuclides is a two-dimensional graph of isotopes of the chemical elements, in which one axis represents the number of neutrons (symbol N) and the other represents the number of protons (atomic number, symbol Z) in the atomic nucleus. Each point plotted on the graph thus represents a nuclide of a known or hypothetical element. This system of ordering nuclides can offer a greater insight into the characteristics of isotopes than the better-known periodic table, which shows only elements and not their isotopes. The chart of the nuclides is also known as the Segrè chart, after Italian physicist Emilio Segrè."

Click Image to Enlarge:

Elements Known in the Year 1950

Elements known in the year 1950, taken from this Wikipedia page:

© Mark R. Leach Ph.D. 1999 –

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