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Mediterranean Journal of Basic and Applied Sciences

X Rays and Electron Diffraction & Interference and Diffraction for the electron by using the Fourier Approach and Wave Properties, The Variant Mass of the Electron at the atom & The Variant Mass for an Accelerated Charged Particle (Maxwell Radiation)

Giovanni Alcocer

Published Jan 1, 2021• 1 citation
Publisher

Abstract

The X rays Diffraction Experiment covers: theory, interaction of photons with the matter, sources of x rays, x rays tube, radioactivity, x rays detector, x rays diffraction process, crystals, miller indices and Bravais lattices, Bragg reflection on crystal, symmetry elements, point group of symmetry, fourteen bravais lattices, crystalline systems bravais, 32 crystalline punctual groups, stereogram of the 32 crystalline punctual groups, brillouin zone and the cubic system lattice, real space (direct lattices) and the reciprocal space (reciprocal lattices), the Laue experiment of x rays diffraction on crystal, experimental set up, scintillators and photomultipliers.Besides, it is researched the Electron Diffraction and the Diffraction and Interference for the electron by using the Fourier Approach and Wave Properties, Diffraction: Heisenberg's Uncertainty Principle, Uncertainty Principle of Heisenberg by applying wave properties, Interference: Double Slit Experiment, The Copenhagen Interpretation, Pilot wave interpretation and why the electron doesn´t radiate energy as a particle.For other hand, Albert Einstein wrote in a research article: "Does the inertia of a body depend on its energy content?" (Ist die Trägheit eines Körpers von seimen Energienhalt abhängig?):"If a body emits energy E in the form of radiation, its mass decreases by E/c 2 ".The fact that the energy that leaves from the body is converted into radiation energy makes no difference, so the more general conclusion is reached that the mass of a body is a measure of the content of its energy...It is not impossible that with bodies whose content of energy is highly variable (for example radio salts) the theory can be successfully tested.If the theory corresponds to the fact, radiation conducts inertia between the bodies that emit and absorb it 1 ".This is true for any type of radiation emitted (gravitational or electromagnetic energy) which produces a decrease in the mass of the body.Respect to the gravitational energy emission, it is demonstrated by theory, experiment and result the discovery formula which describe exactly the variant mass of a particle which emits gravitational energy which was demonstrated by myself at the article: The Fundament of the Mass and Effects of the Gravitation on a Particle and Light in the mass, time, distance, velocity, frequency, wavelength: Variant Mass for a Particle which emits Gravitational Energy for a particle orbiting a large Planet or Sun and for a Binary Star and Variant Frequency for the Light passing close a Gravitational Field from a Massive Object (Sun).The results of the mass formula are of great relevance for Gravitational Interactions.It is in accordance with the classic result for the emission of the total gravitational energy (bond total energy) for a particle orbiting a large Planet or Sun and for a Binary Star.At the atom, the electron only radiates this energy when it jumps from one orbit to another orbit at the atom.It is in accordance with the experimental results from the spectral lines of the atom.The difference is that in a gravitational field the particle or a planet around the sun can take any position at the space and any radius.But, the electron at the atom only can take restricted positions which are explained by quantum mechanics, and the electrons don´t emit radiation when they orbit around the nucleus.At this article, it is demonstrated the development formula for the variant mass of the electron at the atom which describe exactly the variant mass of the electron (charged particle) at the atom which emits electromagnetic energy from one stationary level to other.The results of the formula are compared with the ionization energy emission for the electron at the atom and the bound energy for the diatomic molecules.The results are in agreement with high accuracy.Besides, Maxwell's theory shows that electromagnetic waves are radiated whenever charges accelerate as for example for the electrón.Then, this electromagnetic radiation (photons) produces a decrease in the mass of the electron which is given by the formula of the Variant Mass for an Accelerated Charged Particle which was demonstrated by me at this research.Therefore, an additional objective of this article is to demonstrate by theory, calculations and results the discovered formula which describe exactly the variant mass of an accelerated charged particle.This charged particle emits electromagnetic radiation which is called the Maxwell Radiation.Also, the article analyzes and establishes about the effects of the variant mass on the particle.In addition, the formula is tested with the electromagnetic radiation emitted for an electron when leaves from the atom.Finally, it is obtained the formula for the power energy emitted for an Accelerated Charged Particle.

DOI
10.46382/mjbas.2021.5406

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The X rays Diffraction Experiment covers: theory, interaction of photons with the matter, sources of x rays, x rays tube, radioactivity, x rays detector, x rays diffraction process, crystals, miller indices and Bravais lattices, Bragg reflection on crystal, symmetry elements, point group of symmetry, fourteen bravais lattices, crystalline systems bravais, 32 crystalline punctual groups, stereogram of the 32 crystalline punctual groups, brillouin zone and the cubic system lattice, real space (direct lattices) and the reciprocal space (reciprocal lattices), the Laue experiment of x rays diffraction on crystal, experimental set up, scintillators and photomultipliers.Besides, it is researched the Electron Diffraction and the Diffraction and Interference for the electron by using the Fourier Approach and Wave Properties, Diffraction: Heisenberg's Uncertainty Principle, Uncertainty Principle of Heisenberg by applying wave properties, Interference: Double Slit Experiment, The Copenhagen Interpretation, Pilot wave interpretation and why the electron doesn´t radiate energy as a particle.For other hand, Albert Einstein wrote in a research article: "Does the inertia of a body depend on its energy content?" (Ist die Trägheit eines Körpers von seimen Energienhalt abhängig?):"If a body emits energy E in the form of radiation, its mass decreases by E/c 2 ".The fact that the energy that leaves from the body is converted into radiation energy makes no difference, so the more general conclusion is reached that the mass of a body is a measure of the content of its energy...It is not impossible that with bodies whose content of energy is highly variable (for example radio salts) the theory can be successfully tested.If the theory corresponds to the fact, radiation conducts inertia between the bodies that emit and absorb it 1 ".This is true for any type of radiation emitted (gravitational or electromagnetic energy) which produces a decrease in the mass of the body.Respect to the gravitational energy emission, it is demonstrated by theory, experiment and result the discovery formula which describe exactly the variant mass of a particle which emits gravitational energy which was demonstrated by myself at the article: The Fundament of the Mass and Effects of the Gravitation on a Particle and Light in the mass, time, distance, velocity, frequency, wavelength: Variant Mass for a Particle which emits Gravitational Energy for a particle orbiting a large Planet or Sun and for a Binary Star and Variant Frequency for the Light passing close a Gravitational Field from a Massive Object (Sun).The results of the mass formula are of great relevance for Gravitational Interactions.It is in accordance with the classic result for the emission of the total gravitational energy (bond total energy) for a particle orbiting a large Planet or Sun and for a Binary Star.At the atom, the electron only radiates this energy when it jumps from one orbit to another orbit at the atom.It is in accordance with the experimental results from the spectral lines of the atom.The difference is that in a gravitational field the particle or a planet around the sun can take any position at the space and any radius.But, the electron at the atom only can take restricted positions which are explained by quantum mechanics, and the electrons don´t emit radiation when they orbit around the nucleus.At this article, it is demonstrated the development formula for the variant mass of the electron at the atom which describe exactly the variant mass of the electron (charged particle) at the atom which emits electromagnetic energy from one stationary level to other.The results of the formula are compared with the ionization energy emission for the electron at the atom and the bound energy for the diatomic molecules.The results are in agreement with high accuracy.Besides, Maxwell's theory shows that electromagnetic waves are radiated whenever charges accelerate as for example for the electrón.Then, this electromagnetic radiation (photons) produces a decrease in the mass of the electron which is given by the formula of the Variant Mass for an Accelerated Charged Particle which was demonstrated by me at this research.Therefore, an additional objective of this article is to demonstrate by theory, calculations and results the discovered formula which describe exactly the variant mass of an accelerated charged particle.This charged particle emits electromagnetic radiation which is called the Maxwell Radiation.Also, the article analyzes and establishes about the effects of the variant mass on the particle.In addition, the formula is tested with the electromagnetic radiation emitted for an electron when leaves from the atom.Finally, it is obtained the formula for the power energy emitted for an Accelerated Charged Particle.
Experimental results: Ionization energy of the electrons at the atom.Bound of the Diatomic Molecules.From Bohr to Schröndiger.Deduction of the radius formula with the analogy of the atom with the blackbody research from Planck and harmonic oscillators.Why the electrons orbit around the nucleus with specific radius for the case of electron as particle.Why the electron doesn´t radiate energy at the stationary levels as a wave and as a particle.Diffraction and Interference for the electron by using the Fourier Approach and Wave Properties
It has already been noted (section 2.8) that high frequency electromagnetic radiation can exhibit particle-like behaviour. For example, in the sensitive type of detector known as a photomultiplier tube (described in Wehr and Richards, Physics of the Atom , 2nd edn, Addison-Wesley, section 10.5), a beam of low-intensity X-rays is detected as a sequence of isolated sharp pulses, such as would be produced by a stream of particles arriving at the detector. As was pointed out, it is not surprising that it is usually high-frequency radiation which travels in particle form; as shown in figure 2.39, a wave group of high-frequency radiation can be compressed into a very short time span. However, when we speak of a particle, we mean something more than an entity which arrives in a short time span. A particle has a definite size, or more exactly it has a well-defined energy and momentum. It was discovered around about 1900 that the same is true of an X-ray wave packet: all packets of a given frequency radiation carry the same energy and momentum. This revolutionary discovery means that we must treat the wave packets as particles on exactly the same footing as more familiar particles such as electrons. The electromagnetic particle is called a photon . There is a wealth of experimental evidence which may be used to define the properties of a photon. We shall be highly selective, however, and simply present two particularly clear-cut experiments, the photoelectric effect and Compton scattering, which enable one to define the energy and momentum of the photon in terms of the frequency and wave number of the corresponding wave. These experiments will be described in detail in section 4.1.
Abstract 1. M. L. de Broglie has introduced a theory of mechanics according to which a moving particle behaves as a group of waves whose velocity and wave-length are governed by the speed and mass of the particle. In fact if m0 is the mass for slow speed and v the speed of a freely moving particle, the wave-length is given by λ = h√1-v2/c2 / m0v, and the wave velocity V by V = c2/v, the group velocity being v, the velocity of the particle. Here c is the velocity of light and it will be seen that the wave velocity is greater than c. There is nothing impossible in this because the waves are regarded as purely geometrical —“phase waves”—not as carrying energy. Compare, in ordinary optical theory, the case of substances, such as sodium, for which the refractive index is less than unity. The above is for free space; in the presence of a field of force V varies, and the consequent bending of the waves by refraction corresponds, on the new theory, to the deviation of the path of the particle by the field of force, on the old. The consequences of this theory have been worked out by de Broglie, Schrödinger and others and applied to problems in spectroscopy where they have provided the solution of several outstanding difficulties left by the older theory of orbits. In view, however, of the extremely fundamental nature of the theory it is highly desirable that it should rest on more direct evidence, and, in particular, that it should be shown capable of predicting as well as of merely explaining. Dymond has obtained some remarkable results on the scattering of slow electrons in helium which are of the general nature to be expected in this theory, but our knowledge of the structure of helium, together with the mathematical difficulties of the problem have so far prevented any exact comparision of the theory with experiment. Davisson and Kunsman and Davisson and Germer have obtained results on the reflection of slow electrons from the surfaces of crystals, especially nickel, which show good qualitative agreement with the theory but a discrepancy of 30 per cent. in certain magnitudes. It is hoped that the experiments described in this paper will advance the matter a stage further. They are a development of some experiments of which a preliminary account appeared recently in ‘Nature.’
This chapter describes the dual nature of electron/de Broglie waves. de Broglie suggested that like light, an electron also behaves as both a particle and a wave. Based on this hypothesis, a relationship between wavelength of electrons (a particle) and momentum was developed. It opines that ‘wavelength of the particle is inversely proportional to momentum’. This is called the de Broglie relation. On the basis of the above facts, we have developed a relationship between wavelength and voltage applied and this relation may be stated as ‘the wavelength of a particle is inversely proportional to the square root of the voltage applied to the system’. This chapter also uses the Davisson and Germer experiment to show the wave nature of the particle, i.e., diffraction of electrons by crystal lattice. The experimental results were the same as found in the case of the diffraction of X-ray by crystals. This chapter also provides an idea on quantisation of angular momentum. It also discusses Heisenberg’s uncertainty principle, phase velocity, group velocity, and uncertainty relation between energy and time. The chapter comprises the experimental evidence of Heisenberg’s uncertainty principle, such as by diffraction of electrons through a slit and gamma ray microscope thought experiment, which is shows the physical significance of the uncertainty principle. Sufficient references, solved problems, and questions on concepts have been provided at the end of chapter.
PREFACE PART I: THE STRUCTURE OF MATTER 1. THE MICROSCOPIC WORLD: ATOMS AND MOLECULES 1.1 Development of the Atomic Theory: Relative Atomic Weights 1.2 Atomic Magnitudes 1.3 The Charge-to-Mass Ratio of the Electron: Thomson's Method 1.4 The Charge of the Electron: Millikan's Method 1.5 Mass Spectrometry 1.6 The Atomic Mass Scale and the Mole 1.7 The Periodic Table 2. ORIGINS OF THE QUANTUM THEORY OF MATTER 2.1 The Franck-Hertz Experiment 2.2 The Photoelectric Effect 2.3 X-rays and Matter 2.4 The Emission Spectra of Atoms 2.5 The Nuclear Atom 2.6 The Problem of Black-Body Radiation 2.7 The Concept of Action 2.8 The Harmonic Oscillator 2.9 Action Quantized: The Heat Capacity of Solids 2.10 Some Orders of Magnitude 2.11 Bohr's Model of the Atom Appendix 2A: Rutherford Scattering 3. MATTER WAVES IN SIMPLE SYSTEMS 3.1 The de Broglie Hypothesis 3.2 The Nature of Waves 3.3 Dispersion Relations and Wave Equations: The Free Particle 3.4 Operators 3.5 Eigenfunctions and Eigenvalues 3.6 The Particle in a One-Dimensional Box 3.7 The Indeterminacy or Uncertainty Principle 3.8 Expectation Values Summary of Postulates 3.9 Particles in Two- and Three-Dimensional Boxes 3.10 Particles in Circular Boxes 3.11 Particles in Spherical Boxes 3.12 The Rigid Rotor Appendix 3A: More on Circular Coordinates and the Circular Box 4. PARTICLES IN VARYING POTENTIAL FIELDS TRANSITIONS 4.1 Finite Potential Barriers 4.2 The Quantum Mechanical Harmonic Oscillator 4.3 The Hydrogen Atom 4.4 The Shapes of Orbitals 4.5 Transitions between Energy Levels 5. THE STRUCTURE OF ATOMS 5.1 Electron Spin Magnetic Phenomena 5.2 The Pauli Exclusion Principle the Aufbau Principle 5.3 Electronic Configurations of Atoms 5.4 Calculation of Atomic Structures 5.5 Atomic Structure and Periodic Behavior 5.6 Term Splitting and the Vector Model 5.7 Fine Structure and Spin-Orbit Interactions Appendix 5A: The Stern-Gerlach Experiment 6. THE CHEMICAL BOND IN THE SIMPLEST MOLECULES: H[2+ AND H[2 6.1 Bonding Forces between Atoms 6.2 The Simplest Molecule: The Hydrogen Molecule-Ion, H[2+ 6.3 H[2+: Molecular Orbitals and the LCAO Approximation 6.4 H[2+: Obtaining the Energy Curve 6.5 H[2+: Correlation of Orbitals Excited States 6.6 The H[2 Molecule: Simple MO Description 6.7 Symmetry Properties of Identical Particles 6.8 H[2: The Valence Bond Representation 6.9 H[2: Beyond the Simple MO and VB Approximations 6.10 H[2: Excited Electronic States Appendix 6A: Orthogonality Appendix 6B: Hermitian Operators 7. MORE ABOUT DIATOMIC MOLECULES 7.1 Vibrations of Diatomic Molecules 7.2 Rotations of Diatomic Molecules 7.3 Spectra of Diatomic Molecules 7.4 The Ionic Bond 7.5 Homonuclear Diatomic Molecules: Molecular Orbitals and Orbital Correlation 7.6 Homonuclear Diatomic Molecules: Aufbau Principle and Structure of First-Row Molecules 7.7 Introduction to Heteronuclear Diatomic Molecules: Electronegativity 7.8 Bonding in LiH: Crossing and Noncrossing Potential Curves 7.9 Other First-Row Diatomic Hydrides 7.10 Isoelectronic and Other Series Appendix 7A: Perturbation Theory 8. TRIATOMIC MOLECULES 8.1 Electronic Structure and Geometry in the Simplest Cases: H[3 and H[3+ 8.2 Dihydrides: Introduction to the Water Molecule 8.3 Hybrid Orbitals 8.4 Delocalized Orbitals in H[2O: The General MO Method 8.5 Bonding in More Complex Triatomic Molecules 8.6 Normal Coordinates and Modes of Vibration 8.7 A Solvable Example: The Vibrational Modes of CO[2 8.8 Transitions and Spectra of Polyatomic Molecules: Rotations and Vibrations 8.9 Transitions and Spectra of Polyatomic Molecules: Magnetic Transitions 8.10 Transitions and Spectra of Polyatomic Molecules: Electronic Transitions 9. LARGER POLYATOMIC MOLECULES 9.1 Small Molecules 9.2 Catenated Carbon Compounds Transferability 9.3 Other Extended Structures 9.4 Some Steric Effects 9.5 Complex Ions and Other Coordination Compounds: Simple Polyhedra 9.6 Chirality and Optical Rotation 9.7 Chiral and Other Complex Ions 9.8 Magnetic Properties of Complexes 9.9 Electronic Structure of Complexes Appendix 9A: Schmidt Orthogonalization 10. INTERMOLECULAR FORCES 10.1 Long-Range Forces: Interactions between Charge Distributions 10.2 Empirical Intermolecular Potentials 10.3 Weakly Associated Molecules 11. THE STRUCTURE OF SOLIDS 11.1 Some General Properties of Solids 11.2 Space Lattices and Crystal Symmetry 11.3 X-ray Diffraction from Crystals: The Bragg Model 11.4 The Laue Model 11.5 Determination of Crystal Structures 11.6 Techniques of Diffraction 11.7 Molecular Crystals 11.8 Structures of Ionic Crystals 11.9 Binding Energy of Ionic Crystals 11.10 Covalent Solids 11.11 The Free-Electron Theory of Metals 11.12 The Band Theory of Solids 11.13 Conductors, Insulators, and Semiconductors 11.14 Other Forms of Condensed Matter APPENDICES I. Systems of Units II. Partial Derivatives III. Glossary of Symbols IV. Searching the Scientific Literature INDEX
The author has worked with high-resolution transmission electron microscope for many years, which provides the most direct evidence of wave-particle duality. This relates to Crookes and J. J. Thomson's cathode rays tubes to determine that electron beams are of particle nature. This also relates to Röntgen's discovery that when an electron beam in the cathode rays tube strikes the glass wall, it produces X-rays with extremely high penetrating power. This behavior is consistent with Maxwell-Lorentz’s electrodynamics that electromagnetic waves must be produced whenever electricity carriers alter their velocity. The wave-particle duality proposed by de Broglie refers to accelerated electron beam, rather than single electron. De Broglie emphasized that the crystallographic diffraction pattern produced by his electron beam was completely consistent with the crystallographic diffraction pattern of von Laue by X-rays, therefore, he proposed that electrons possess wave-particle duality. This is actually the selected area electron diffraction pattern in transmission microscope. It is X-rays, not the waves of the electrons themselves to produce diffraction pattern. He extended this to the wave-particle duality of all matter and light. Schrödinger directly introduced de Broglie's electron beam behavior into electron wave in atoms. It was just at this stage that illogical reasoning occurred, making the quantum theory increasingly difficult to understand.