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Reference: Boorse 1966: The World of Atom

PART XI – ATOMIC THEORY DEVELOPS

THE WORLD OF ATOM by Boorse

Chapter 54: Atomic Number (Henry G. J. Mosley 1887 – 1915)

It seemed to Mendeleev that the mass of an atom is the decisive physical parameter that determines its structure and chemical behavior. Mosley thought that if the electrons were moving in orbits according to the Bohr theory, the X-ray spectrum of a heavy element should exhibit a line structure similar to that of the hydrogen spectrum. The X-ray spectrum would change in a regular way according to charge on the nucleus (the atomic number) as one went from one heavy atom to the next if the Bohr-Rutherford model of the atom were correct.

As the charge increases, the electron orbits become more closely bound to the nucleus and we should expect the frequency of spectral lines to increase. This is precisely what Mosley found—the step-by-step change in the frequencies of two distinct lines as one progresses from the lighter to heavier elements. Mosley stated this relationship in a simple empirical formula, which he was able to match with the data. Mosley’s formula shows that the atomic number and not the atomic weight is the decisive quantity in the arrangement of the elements in the periodic table.

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 (m_l): m_l = -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 (m_s) 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. Within a given atom, no two electrons can have identical full sets of quantum numbers. 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.

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MAIN POINTS

1. The charge on the nucleus is represented by the atomic number.
2. Elements differ from each other by their atomic number and atomic weight.
3. As the charge increases, the electron orbits become more closely bound to the nucleus.
4. The atomic number and not the atomic weight is the decisive quantity in the arrangement of the elements in the periodic table.
5. The stationary orbits in Bohr’s model are consistent with Planck’s theory of Quantum.
6. The momentum of radiation makes it a directed phenomenon.
7. The photon is a momentum carrying corpuscle that can transfer its momentum in a given direction to the atom. 
8. The electron must be treated as a wave and not as a particle.
9. The quantization of the angular momentum explains the fine structure of spectral lines,
10. The electronic structure around the nucleus is defined by four different quantum numbers.
11. Within a given atom, no two electrons can have identical full sets of quantum numbers.
12. Lines in spectra occur also due to vibration phenomena other than absorption and emission.
13. More mathematical relationships are being worked out for the atomic domain.

THEORY
The structure of the atom is increasingly the result of mathematical consistency among experimental observations. The mathematical model defines the structure of the substance that is transitioning from mass of the nucleus into the surrounding vortex of energy.

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Reference: Boorse 1966: The World of Atom

PART IX – THE NUCLEAR ATOM

THE WORLD OF ATOM by Boorse

Chapter 43: Strange Results from α-Particle Scattering (Hans Geiger 1882 – 1945, Ernest Marsden 1889 – 1970)

The discovery of the electron in 1897 by J. J. Thompson meant that the atoms have a structure. Since the atom is electrically neutral it was assumed that small discrete electrons were embedded in a jelly like viscous sphere of positive electricity. Thompson made a study based on this model. He assumed that the angle of deviation suffered by the charged particle was always caused by a large number of collisions with many atoms. When Geiger and Marsden conducted their scattering experiments, they found that a thickness of 6 x 10^-5 cm of gold foil was sufficient to produce a deflection of 90 degrees or more. Rutherford contended that the large deviations observed experimentally must have been caused by single direct collisions, and he began looking for an alternative to explain the data.

Rutherford’s research gave us the nuclear atom, which is consistent with the “whirlpool” model of the atom.

Chapter 44: The Nuclear Atom (Ernest Rutherford 1871 – 1937)

Rutherford was impressed about some of the α-particles scattering back toward their source in the work of Geiger. To him this could only mean one thing: there was an enormous force in the atom, that it would take one hundred electron charges on the gold nucleus to give the observed result. He then proceeded to analyze the theory of single collisions on the basis of a model of the atom that is radically different from the Thomson model. Rutherford was particularly interested in the question, “How close to the nucleus can an alpha particle approach?” He got this answer from his theory and the measurements of the scattered α-particles. The answer, 3 x 10^-10 cm., showed him how small and compact a nucleus is, and thus the nuclear atom was born. In this Rutherford model the positive electricity is not distributed over a large volume but instead is concentrated in a very small nucleus at the center of the atom. A model of this sort cannot be in static equilibrium, yet this kind of dynamical equilibrium was in serious contradiction with classical electrodynamics.

This contradiction with classical electrodynamics was resolved later.

Chapter 45: Atomic Structure (Niels Bohr 1885 – 1962)

Rutherford had a planetary model in mind for his nuclear atom, but he could not determine a precise orbit for the electron since the classical electrodynamic theory showed that electron would radiate energy and it must ultimately spiral into the nucleus. Bohr reasoned that if the electron can change its state of motion only in discrete steps it must then stay in a particular orbit until it emits or absorbs enough energy in one single process to go from one orbit to another. Bohr introduced Planck’s constant, imposing the condition that the electron must not radiate continuously but rather in the form of “distinctly separated emissions.” Bohr then introduced the concept of “stationary states” to describe the discrete orbits. With his assumptions Bohr obtained correct expression for the frequencies of the spectral lines in the Balmer series in the spectrum of hydrogen.

Classical electrodynamics assumes electron to be a mass particle with charge, which then makes it spiral into the nucleus. But the atom is stable, and the dynamics of an electron occur naturally. That means that the electron cannot be a mass particle with charge. It is a substance of a very different consistency, and that fact is responsible of its dynamics and charge. Quantum mechanics simply introduces this new dimension of consistency of substance that determines its energy of interaction. The geometry of orbits stratifies this consistency. Transitions among these stratifications of consistency generate the spectral lines.

Chapter 46: The Quantum Theory is Tested (James Franck 1882 – 1964, Gustav Hertz 1887 – 1975)

It was not clear from Bohr’s theory of atomic spectra alone whether the quantum theory could be applied to ordinary mechanical energy of motion, or whether it was limited to the emission and absorption of radiant energy. In 1914 James Franck collaborated with Gustav Hertz and completed basic experiments on the collision of electrons with atoms, which demonstrated that an atom could take on energy from collisions only in discrete amounts, in agreement with Bohr’s theory. These experiments demonstrated that a particle like an electron would transfer its energy in a collision only in multiples of a fundamental quantum. From this point it was clear that quantum theory would have to be taken into account in all processes.

In truth electrons are just as massless as radiant energy, the only difference is that electron’s consistency, and hence its inertia, is much higher than the consistency and inertia of radiant energy.

Chapter 47: The discovery of Isotopes (Frederick Soddy 1877 – 1956)

It was recognized that some atomic weights, such as chlorine, were by no stretch of imagination integral. There was speculation that the atoms of a given element might not be identical and that the atomic weight of an element might be the average of the weight of several unequally massive atoms having the same chemical properties. As experience with radioactivity increased, Frederick Soddy (1910) realized that the radioactive transformations produced atoms of the same chemical species but of different weights. We now recognize such chemically non-separable atoms as “isotopes.”

Chapter 48: The Positive Rays (J. J. Thomson 1856 – 1940)

The canal rays were discovered in 1886. They consisted of positively charged particles, but their composition was found to be very complex. The problem was to develop an experimental method to separate out the various particle components. In a lecture in 1913, J.J. Thomson described a simple device, involving electric and magnetic fields, that is the forerunner of the modern mass spectrometer. In this way a spectrum of the canal ray is obtained on a photographic plate. Each point on the spectrum represents a particular value of the speed and of the ratio of charge to mass. The parabola corresponding to hydrogen ions (protons) is the one that is deflected the most. Thomson was thus able to catalogue the atomic and molecular weights of the various elements and compounds in the tube.

Chapter 49: Transmutation of an Element (Ernest Rutherford 1871 – 1937)

After his basic analysis of the experiments on the scattering of α-particles by heavy nuclei, which finally led to the nuclear model of the atom and to Bohr’s theory of atomic spectra, Rutherford began a series of experiments in 1915 on the scattering of α-particles by light atoms. These experiments resulted in the first artificially induced nuclear transformation of an element in 1919. He discovered that α-particles, in passing through air, collided with nitrogen atoms and knocked protons out of these atoms. The importance of Rutherford’s results for the future of atomic physics was of a twofold nature. First, he demonstrated experimentally that nuclei of atoms contain individual protons. Second, his experiment showed that nuclei could be disrupted and changed into other nuclei; this was the first example of the artificial transmutation of chemical elements.

Chapter 50: The Diversity of Atoms (Francis William Aston 1877 – 1945)

J. J. Thomson’s positive ray apparatus opened the door in 1912 for investigations into elements for their isotopes. F.W. Aston assisted Thomson in finding the isotopes of Neon. In 1919 Aston developed a mass spectrograph as an improvement of Thomson’s parabola method. This spectrograph was used to analyze some fifty elements in the following six years, revealing the almost universal existence of isotopes. Mass spectrometers of increasing precision followed, and Aston found that neither the whole number rule nor Prout’s hypothesis could be substantiated. The addition of masses, equal to that of hydrogen, did not give the masses of the succeeding elements in the periodic table. The elemental masses as measured by the spectrograph showed a “mass defect” as compared to the sum of the masses of their free constituent particles. The greater was the mass defect the more stable was the nucleus.

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MAIN POINTS

1. Large deflection of α-particles from very thin gold foil gives rise to the idea of a nuclear atom.
2. The size of the nucleus is of the order of 10^-10 cm., compared to the size of the atom of 10^-8 cm.
3. The positive charge is concentrated in a very small nucleus at the center of the atom.
4. Nuclear atom cannot be in static equilibrium, and dynamical equilibrium contradicts classical electrodynamics.
5. This necessitates the postulate that electron can change its state of motion in discrete steps only.
6. This then leads to discrete orbits, and transitions from one such orbit to another give rise to a discrete spectrum.
7. This was confirmed by correct expression for the frequencies of the spectral lines for hydrogen.
8. It was further confirmed with atoms taking on energy from collisions only in discrete amounts.
9. The radioactive transformations produce atoms of the same chemical species but of different weights (isotopes).
10. Particles in a ray can be separated by their masses.
11. Nuclei of atoms contain individual protons.
12. Nuclei can be disrupted and changed into other nuclei (artificial transmutation).
13. The elemental masses show a “mass defect” as compared to the sum of the masses of their free constituent particles. 
14. The greater is the mass defect the more stable is the nucleus.

THEORY
The atom consists of a small massive nucleus surrounded by a large volume of rapidly revolving electrons. The  electrons have momentum but no mass. They form discrete stationary orbits around the nucleus that have variations in consistency and energy. Exchanges among these stationary orbits generate the spectral lines. The nucleus is made up of protons but there is a mass defect as protons combine. There are isotopes and artificial transmutation can be induced.

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Reference: Boorse 1966: The World of Atom

PART VII – NEW IDEAS AND NEW MEASUREMENTS

THE WORLD OF ATOM by Boorse

Chapter 37: The “Thomson” Atom (J. J. Thomson 1856 – 1940)

[From Wikipedia] The plum pudding model is one of several historical scientific models of the atom. First proposed by J. J. Thomson in 1904 soon after the discovery of the electron, but before the discovery of the atomic nucleus, the model tried to explain two properties of atoms then known: that electrons are negatively charged particles and that atoms have no net electric charge. The plum pudding model has electrons surrounded by a volume of positive charge, like negatively charged “plums” embedded in a positively charged “pudding”.

From the very beginning we have associated electrons with unit charges and point configurations within the atom. This gives the impression that electrons are particles, but we know that they do not have point mass. They simply have thick consistency and distributed inertia. The quantum numbers associated with electrons come from their whirlpool-like motion in the atom. The charge exists at the interface between the mass of the nucleus and the distributed inertia of surrounding electrons. The charge does not neutralize because it is part of a stable whirlpool-like configuration. Any attraction or repulsion exists because charges want to re-establish that whirlpool-like configuration.

Chapter 38: The Determination of Avogadro’s Number (Jean Perrin 1870 – 1942)

The Avogadro constant is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. The numeric value of the Avogadro constant expressed in reciprocal mole, a dimensionless number, is called the Avogadro number, sometimes denoted N or N₀, which is thus the number of particles that are contained in one mole, exactly 6.02214076×10²³.

The experimental setup works because there is incessant motion of the molecules that generates Brownian motion. This motion in the solution helps maintain a certain distribution of suspended particles according to their height. The incessant motion arises because of the difference in consistencies of the nucleus and the electrons. 

Chapter 39: The α-Particle and Helium (Ernest Rutherford 1871 – 1937)

Radioactivity of Uranium was discovered in 1896 by Henri Becquerel. In 1899, Ernest Rutherford discovered α and β rays from radioactive emissions. In 1900, Paul Villard discovered γ rays as a natural emission from radium. α rays were defined by Rutherford as those having the lowest penetration of ordinary objects. Rutherford’s work also included measurements of the ratio of an alpha particle’s mass to its charge, which led him to the hypothesis that alpha particles were doubly charged helium ions. In 1907, Ernest Rutherford and his student, Thomas Royds, finally proved using a simple and elegant experiment that alpha particles were indeed helium ions.

Alpha rays, indeed, consist of mass particles. They are bare helium nuclei; so they are called particles correctly.

Chapter 40: Atoms of Electricity (Robert Andrews Millikan 1868 – 1953)

Thomson’s experiments in 1897 measured the ratio of charge to mass, e/m, of the cathode ray particles. The necessity of determining the value of e was immediately clear to Thomson. In 1909, Millikan showed unambiguously that nature supplies electric charge only in one fixed size, that all charges, no matter where they may occur, are only multiples of this charge, and that electric charges of any other magnitude do not exist.

The unit charge is part of the atomic configuration. It does not exist outside this configuration. It is the minimum amount of charge that appears in an atomic interaction. Therefore, it relates to the consistency of the cathode rays.

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MAIN POINTS

1. The number of particles that are contained in one mole, is exactly 6.02214076×10²³.
2. The atom as a whole is neutral, so it must have positive charge too.
3. There are negative and positive ions.
4. The unit charge appears on ions and does not exist otherwise.
5. The charge carried on by an ion in gases is the same as the charge on the beta or cathode-ray particle.
6. The α-particles with positive charges are indeed ionized helium atoms.
7. The charge to mass ratio of electron is 2000 times greater than hydrogen ions.
8. The speed of electron is many thousand times higher than the speed of hydrogen ions.
9. The number of electrons in an atom is between half and whole of atomic weight units.
10. The electron arrangements may cause periodic properties of chemical elements.

THEORY
A neutral atom consists of both positive and negative charges in equal amounts. The charges in atom do not neutralize because they are part of a stable whirlpool-like configuration. A unit charge at the level of atom may be determined just like the unit mass. The electronic charge may be added or removed to produce negative and positive ions respectively.

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