Category Archives: Physics

The World of Atom (Part XIII)

Reference: A Logical Approach to Theoretical Physics





The last aspect of investigation into the electron was the discovery of positron. The target of investigation then became the nucleus. This required the production of high energy particles that could penetrate the nucleus. This led to the invention of cyclotron. The discovery of neutron also provided an effective “missile” that could penetrate the nucleus. Investigation required the understanding the very substance and the force that held it was held together.


  1. The substance is palpable, and that palpability comes from force.
  2. The substance exists as a continuum, but it has a spectrum of thickness (viscosity).
  3. When this substance flows with uniform thickness it has wave characteristics.
  4. When that thickness varies with sudden and extreme gradients it acquires particle characteristics.
  5. An isolated particle may be visualized as a discrete solid center surrounded by a continuum of gradually thinning substance swirling around it. This would be the picture of the hydrogen atom.
  6. Any interaction with the surrounding continuum of substance shall produce sharp gradients and appearance of a particle. Such a particle is the electron with no solid center.
  7. Electron can have many energy levels and the change in energy levels is accompanied by the emission or absorption of a photon. Such energy level can be negative, a change from which is accompanied by a positron (an antiparticle).
  8. Different energy levels could be occupied by other electrons making the atomic structure more rigid. This simply means multiple continua of slightly different thicknesses surrounding the nucleus.
  9. Multiple electrons hold their relative configuration by continually exchanging photons among them.
  10. The center of a particle (the solid nucleus) may acquire greater complexity through accumulation as in the case of a Deuteron.
  11. Here too we have many energy levels in the nucleus and they may or may not be occupied by nucleons.
  12. Multiple nucleons in the nucleus hold their relative configuration by continually exchanging pions among them.


Chapter 72: The positive Electron – The First Particle of Antimatter – Carl D. Anderson (1905 – 1991)

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The Positive Electron. Dirac’s theory implies negative-energy states and the possibility of electrons emerging from these states along with anti-electrons (positrons). Dirac suggested that the chance of such pair being created would be small because it would require energy equivalent to at least twice the mass of electron. However enough energy is present in cosmic radiation to create such a pair as it passes through a sheet of matter. Carl Anderson’s discovery of such pair of particles in his cosmic ray photographs established the Dirac theory as one of the most reliable in physics. This has led to the concept of antimatter.

Chapter 73: The discovery of the Deuteron – Harold Clayton Urey (1893 – 1981)

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A Hydrogen Isotope of Mass 2 and its concentration. Fractional distillation of hydrogen to obtain a concentration of deuteron was accomplished by Harold Urey in 1932. This allowed the experimental investigation which resulted in the discovery of neutron soon afterwards.

Chapter 74: Discovery of the Neutron – James Chadwick (1891 – 1974)

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The Existence of a Neutron. Scientists faced great difficulty in accounting for the mass and charge of a nucleus in terms of the electron and proton only. Chadwick pictured the beryllium radiation as being not electromagnetic but rather as consisting of neutral particles with masses equal to the mass of the proton. He proved that these particles are highly penetrating because they have no charge and are thus not repelled by the electric fields surrounding nuclei. Neutron and proton are now considered as two different energy states of the same fundamental particle, the nucleon. 

Chapter 75: Fermi’s Contributions – Enrico Fermi (1901 – 1954)

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Quanta of a Field as Particles. Fermi-Dirac statistics add the restriction that electrons influence one another in such a way as to pre-empt or exclude identical motion in the same volume element (Pauli’s exclusion principle). Fermi did this to account for degeneracy. This was soon used to explain the properties of metals and to solve all kinds of solid-state problems. Fermi showed how various atomic problems can be treated statistically, to give results that are fairly accurate. Fermi demonstrated the existence of new radioactive elements produced by neutron irradiation. He developed a complete theory of β-decay and β-emission from the nucleus. His neutron research finally culminated in the first self-sustaining nuclear chain reaction on Dec 2, 1942.

Chapter 76: Artificial Nuclear Disintegration – John Cockcroft (1897 – 1967) and Ernest Walton (1903 – 1995)

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Experiments with High Velocity Positive Ions. Cockcroft and Walton were the first to construct an ion accelerator of sufficient energy to produce nuclear disintegrations.Gamow showed that α-particles, because of their wave nature, do indeed penetrate the Coulomb potential barrier at relatively low energies. Cockcroft became convinced that the wave properties of protons would allow them to enter light nuclei at low energies. Ernest Walton was then developing one of the first linear accelerators. Their collaboration in 1932 resulted in the first proton-induced artificial nuclear disintegration. The results showed that nuclei could be disrupted by particles of lower energy than previously supposed.

Chapter 77: The Electrostatic Generator – Robert Jemison Van De Graaff (1901 – 1967) 

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The Electrostatic Production of High Voltage for Nuclear Investigations. The Van de Graaff generator was developed as a particle accelerator for physics research; its high potential is used to accelerate subatomic particles to great speeds in an evacuated tube. It was the most powerful type of accelerator of the 1930s until the cyclotron was developed.

Chapter 78: The Cyclotron – Ernest O. Lawrence (1901 – 1958) and Milton S. Livingston (1905 – 1986)

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Production of High-Speed Ions. Lawrence introduced a new procedure: to accelerate ions to very high speeds in a series of steps, each of which would involve only a relatively small voltage. In a cyclotron, one must first have a magnetic field at right angles to the plane of the path of the ion and then an alternating electric field that changes its direction periodically in phase with motion of the ion.

Chapter 79: The Discovery of Induced Radioactivity – Jean F. Joliot (1900 – 1958) and Irene Curie Joliot (1897 – 1956)

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A New Type of Radioactivity. The Joliot-Curies showed in 1934 that when lighter elements, such as boron and aluminum, were bombarded with α-particles, the lighter elements continued to emit radiation even after the α−source was removed. They showed that this radiation consisted of positrons. The induced radioactivity appeared because an unstable nucleus had been created. This discovery set off similar research in physics laboratories around the world. 

Chapter 80: Prediction of the Meson – Hideki Yukawa (1907 – 1981)

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On the Interaction of Elementary Particles. Hideki Yukawa developed a quantum field theory of the nuclear forces. He quantized the nuclear force field in complete analogy with the electromagnetic radiation field. The interaction between two charged particles is described as arising from the mutual emission and absorption of photons. Yukawa postulated that a much heavier particle is emitted by the neutron and then absorbed by the proton that generates strong interactions between them and thus account for nuclear forces. Later pi mesons (pions) were discovered that have the property predicted by Yukawa.


The World of Atom (Part XII)

Reference: A Logical Approach to Theoretical Physics



Chapter 62: The Principle of Least Action – William Rowan Hamilton (1805 – 1865)
On a General Method of Expressing the Paths of Light, and of the Planets, by the Coefficients of a Characteristic Function. Hamilton’s mathematics was based on the analogy between the behavior of light of very short wavelength and the behavior of ordinary particles of matter. He demonstrated that the dynamical problem may be solved by considering the motion of a system as though it were a gradual unfolding of a series of states, each one derived from the preceding one by an infinitesimal transformation similar to what we have when a ray of light advances from one wave front to the next. 

Chapter 63: The Wavelengths of Particles – Prince Lois V. de Broglie (1892 – 1987)
The Undulatory Aspects of the Electron. At small scales, there is dualism in Nature between waves and corpuscles. The wavelength associated with a corpuscle is as concrete a physical quantity as its mass. The velocity of the corpuscle is equal to the group velocity of its associated wave. Planck showed that energy is connected to frequency, E = hv. It can also be shown that momentum is connected to wavelength, p = h/λ. This is a fundamental relation of the Theory.

Chapter 64: A Wave Equation for Particles – Erwin Schrodinger (1887 – 1961)
Derivation of the fundamental idea of wave mechanics from Hamilton’s analogy between ordinary mechanics and Geometrical Optics. At close range, the particle appears to be a wave motion represented mathematically by a continuous manifold of wave functions. Using this approach, Schrodinger could derive the arbitrary integers assigned to electron’s energy-levels in the Bohr’s Atomic model.

Chapter 65: Statistics and Waves – Max Born (1882 – 1970)
Wave Corpuscles. The waves do not represent physical vibrations but rather the unfolding of the probabilities of future events from a given initial state. The complex amplitudes of the waves obtained as solutions to Schrodinger’s wave equation can be interpreted better as the probability of finding the electron at a location.

Chapter 66: The Uncertainty Principle – Werner Karl Heisenberg (1901 – 1976)
Critique of the Physical Concepts of the Corpuscular Theory of Matter. Heisenberg discovered the foundation of quantum mechanics—the uncertainty principle.The uncertainty principle refers to a limit on the accuracy with which we can measure certain pairs of quantities simultaneously. Heisenberg introduced his square arrays or matrices, which depict the electron as existing simultaneously in all possible Bohr orbits.

Chapter 67: The Barrier around the Nucleus – George Gamow (1904 – 1968)
Quantum Theory of the Atomic Nucleus. While Gamow’s paper explains the spontaneous emission of  particles (alpha decay) from radioactive nuclei, it also validates Schrodinger’s wave equation inside the nucleus and demonstrates the correctness of Born’s concept that the Schrodinger wave function is the probability amplitude for finding a particle in a given small neighborhood of space.

Chapter 68: Electron Waves – Clinton J. Davisson (1881 – 1958) and George Paget Thomson (1892 – 1975)
Diffraction of Cathode Rays by a Thin Film. Davisson: Electrons reflect from crystalline surfaces. The relationship between the angle of maximum intensity, the speed of the electrons, and the lattice spacing in the crystal are the same as that for a wave. Thomson: The rings arising from diffraction show the wave properties of the electron. The radius of the rings is inversely proportional to the velocity of the electrons. These experiments provided evidence supporting the De Broglie equation.

Chapter 69: The Electron and Relativity – Paul Adrian Maurice Dirac (1902 – 1984) 
The Principle of Superposition. All one needs to know about the observable properties in order to understand their physics is the algebra that governs them (theory of operators). A system in quantum mechanics must be looked upon as simultaneously being in a whole set of states rather than in some particular state. The electron is forced in one of these states due to the perturbation of measurement. Dirac’s idea of states very brilliantly connected the Schrodinger wave function with the probability concept ascribed by Born.

Chapter 70: “Holes” in the Dirac Theory – J. Robert Oppenheimer (1904 – 1967) 
On the Theory of Electrons and Protons. Dirac’s theory predicts the existence of an infinite continuum of negative energy. Dirac proposed that all but few of these negative-energy states are filled with electrons with negative energy; negative-energy states that do not have electrons represent protons. Oppenheimer pointed out that this hole theory gave a different mass dependence and led to insurmountable difficulties. He proposed to retain the picture of the electron and the proton as two independent particles of opposite sign and dissimilar mass and to picture all of Dirac’s negative-energy states as filled. 

Chapter 71: Complementarity – Niels Bohr (1885 – 1962) 
Discussion with Einstein on Epistemological Problems in Atomic Physics. The discussion led to the Principle of Complementarity: There are always two complementary and mutually exclusive ways of looking at a physical phenomenon, depending on how we arrange our apparatus to measure the phenomenon. When we deal with an electron, we must use both the wave picture and the particle picture; one is complementary to the other in the sense that the more our apparatus is designed to look for the electron as a particle, the less the electron behaves like a wave and vice versa.



  1. The behavior of light of very short wavelength and the behavior of ordinary particles of matter are similar mathematically.
  2. The velocity of the corpuscle is equal to the group velocity of its associated wave.
  3. At close range, the particle appears to be a wave motion represented mathematically by a continuous manifold of wave functions.
  4. The EM wave is a wave of rising and falling inertial density. The electron wave is made up of inertial substance.
  5. The solutions to Schrodinger’s wave equation provide the probability of finding the electron at a location.
  6. A system in quantum mechanics must be looked upon as simultaneously being in a whole set of states rather than in some particular state. The electron is forced in one of these states due to the perturbation of measurement.
  7. The idea of Heisenberg’s uncertainty, Max Born’s probability, and Dirac’s superposition all point to the spread of a point in phase space.
  8. The quantum or an electron exists in its wave background much like a potential crystallization exists in a super-saturated solution.
  9. The wave function collapse is the crystallization of the particle from its super-saturated wave background.
  10. A subatomic particle is a high frequency pulse in a fluid-like continuum that materializes upon an interaction.


The Wave Function

ReferenceA Logical Approach to Theoretical Physics

In Schrodinger’s wave equation for the electron, the wave function (ψ) could represent the very substance of energy that thickens as frequency increases. Here the “center of mass” of the electron itself is no longer a point but dispersed. But the “center of mass” of the whole atom can be a point.

I do not see Quantum Mechanics as a radical break from the past. In the past a particle, such as, an atom, was perceived as a solid billiard ball whose internal structure was a black box. Quantum mechanics is simply an advance in science that is looking more closely at that black box. The mass of an atom is concentrated in the nucleus, except for some mass scattered around the nucleus in the form of the electrons. This shows that the mass “dilutes” into electromagnetic substance. The mathematics that is trying to explain this is complicated.

The mathematics of wave-particle duality of De Broglie and the Schrodinger’s equation is based on the analogy between the behavior of light of very short wavelength and the behavior of ordinary particles of matter. This means that matter could be an extension of the upper end of the electromagnetic spectrum.

The new discovery is that that the “center of mass” of a particle like electron cannot be determined precisely because it is dispersed. Classical Newtonian mechanics is based on precise point-like “center of mass.” But at very small scales, a “particle” seems to have a more diffused picture, and classical mechanics can no longer be used. At still smaller scales, we may find the nucleons to be diffused as well.

The location of a particle is determined by the location of its “center of mass”. If this location cannot be determined exactly, and is described in terms of probability, then the “center of mass” itself is dispersed. This gives the picture of a particle of variable energy density.

The Schrodinger’s equation treats electron as if it is a “wave” made of thick elastic fluid. This wave is not moving in some medium. It is the “medium” itself moving as a wave. It becomes “thicker” with higher amplitude. The amplitude is a measure of its thickness. The rising and falling “thickness” is made up of rising and falling frequency. The spectral line is the peak of this frequency. It is like a resonance; but this is a traveling “resonance”. The electron is an energy resonance moving around the nucleus of an atom.

In classical mechanics, the density of matter means the “concentration of atoms” in a certain volume. The density of individual atomic particle is determined by its mass number in the periodic table. The density of individual sub-atomic particle is then determined by its wave function. Beyond the density of the sub-atomic particle is the energy density of the electromagnetic quantum, which is based on simple frequency.


The World of Atom (Part XI)

Reference: A Logical Approach to Theoretical Physics



Chapter 54: Atomic Number – Henry G. J. Mosley (1887 – 1915)
The High-Frequency Spectra of the Elements. The structure and chemical behavior of an atom is determined by the charge on the nucleus rather than its mass. The charge on the nucleus is determined by the number of protons in the nucleus (atomic number).

Chapter 55: Quantum Theory of Radiation and Atomic Processes – Albert Einstein (1879 – 1955)
The Quantum Theory of Radiation. Einstein (1917) gave the nuclear atom a logically satisfying structure by deriving the Planck’s radiation formula from the Bohr Theory and stationary states. Einstein showed that radiation is a fully directed phenomenon because the momentum of a quantum must be taken into account. A remarkable aspect of this derivation is the appearance of the stimulated emission process (verified later by the development of Laser).

Chapter 56: The Compton Effect – Arthur H. Compton (1892 – 1962) 
A Quantum Theory of the Scattering of X-Rays by Light Elements. The X-ray beam, after it is scattered by electrons, suffers a definite reduction in frequency. Compton showed that energy of the photon, as given by its frequency, is reduced by the same amount that the kinetic energy of the recoil electron is increased. Thus, the photon is a momentum carrying corpuscle that can transfer its momentum in a given direction to the atom. The Compton effect also implies that the electron must be treated as a wave and not as a particle.

Chapter 57: Space Quantization – Otto Stern (1888 – 1969) Walter Gerlach (1889 – 1979)
Experimental Proof of Space Quantization in a Magnetic Field. The fine structure of spectral lines was explained by the quantization of the angular momentum, in addition to the quantization of electron orbits within the atom. Furthermore, there is “space quantization,” which is the concept that the component of the angular momentum vector along the z-direction can take only certain values.

Chapter 58: Electron Spin – Samuel A. Goudsmit (1902 – 1978) George E. Uhlenbeck (1900 – 1988)
Spinning Electrons and the Structure of Spectra. Electron was assumed to be like a golf ball and its spin was postulated to provide the fourth quantum number to explain the complexities of the atomic spectra, but electron can equally be a wave, with “electron spin” requiring a different explanation. Therefore, electron spin is essentially a mathematical parameter.

The four quantum numbers in atomic physics are: principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number. Together, they describe the unique quantum state of an electron.

The principal quantum number (n) indirectly describes the size of the electron orbital. It has the greatest effect on the energy of the electron. It was first designed to distinguish between different energy levels in the Bohr model of the atom. It is always assigned an integer value (e.g., n = 1, 2, 3…), but its value may never be 0. An orbital for which n = 2 is larger, for example, than an orbital for which n = 1. Energy must be absorbed in order for an electron to be excited from an orbital near the nucleus (n = 1) to get to an orbital further from the nucleus (n = 2).

The azimuthal quantum number (l) for an atomic orbital determines its orbital angular momentum and describes the shape of the orbital. 

The magnetic quantum number (ml): ml = -l, …, 0, …, +l. Specifies the orientation in space of an orbital of a given energy (n) and shape (l). This number divides the sub-shell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each sub-shell.

The spin quantum number (ms) describes the angular momentum of an electron. An electron spins around an axis and has both angular momentum and orbital angular momentum. Because angular momentum is a vector, the Spin Quantum Number (s) has both a magnitude (1/2) and direction (+ or -).

Chapter 59: The Exclusion Principle – Wolfgang Pauli (1900 – 1958) 
Exclusion Principle and Quantum Mechanics. The four quantum numbers were developed following the Bohr’s model to explain the atomic spectra and to establish consistency among the elements in the Periodic table. The Exclusion Principle has assisted greatly in postulating a structure for the atom. The atomic model is essentially based on a mathematical consistency.

Chapter 60: Secondary Radiation – Chandrasekhara Venkata Raman (1888 – 1970) 
A New Class of Spectra Due to Secondary Radiation. When light hits a molecule or an atom, it is scattered. The scattered light contains frequencies equal to, smaller than, and larger than the frequency of the primary light. That part of the incident frequency is absorbed which corresponds to the natural frequency of the molecule, and the rest is scattered, or the natural frequency is added to the incident frequency of the light that is scattered. This is the Raman Effect.

Chapter 61: Statistical Mechanics – S. N. Bose (1894 – 1974) 
Planck’s Law and Light Quantum Hypothesis. Bose applied quantum principle of discrete energy levels to Statistical mechanics. The quantum definition takes the identity of the particles into account. It leads to a distribution different from the Maxwell-Boltzmann distribution, and hence to a different equation of state for a perfect gas. Boyle’s law does not hold for such a gas and the departure from Boyle’s law becomes greater and greater as the temperature decreases.


The mathematical consistency provides insight into the structure of atoms that cannot be perceived otherwise.


The World of Atom (Part X)

ReferenceA Logical Approach to Theoretical Physics



Chapter 51: Interference Phenomena – Max von Laue (1879 – 1960) Walter Friedrich (1883 – 1968) Paul Knipping (1883 – 1935)
Interference phenomena for X-Rays. Ingenious idea of using the atoms forming the lattice structure of a crystal as a diffraction grating for X-rays of extremely short wavelength. From X-ray diffraction pattern, one can not only calculate the wavelength of the X-rays but also find out a great deal about the structure of the crystal.

Chapter 52: Bragg’s Law – William Henry Bragg (1862 – 1942) William Lawrence Bragg (1890 – 1971) 
The Reflection of X-Rays by Crystals. This research showed (1) that the X-ray emission spectrum of an element is characteristic of that element, and (2) that X-rays can be used as a powerful and precise means of crystal analysis.

Chapter 53: Atomic Number – Antonius van der Broek (1870 – 1926) 
The Number of Possible Elements and Mendeleev’s “Cubic” Periodic System. The number of the place each element occupies in the periodic table is proportional to the square root of the number of scattered -particles.


The short wavelength of X-rays provides greater insight into the structure of atoms.