This article is taken from the manuscript prepared by the author for his address at the joint meeting of Section B of the American Association for the Advancement of Science and the American Physical Society on December 28, 1927, at Nashville, Tennessee. An account of this work giving fuller experimental details is given by Davisson and Germer in the December, 1927, issue of the Physical Review. These experiments are fundamental to some of the newer theories in physics. Until they were performed, it could be said that all experimental facts about the electron could be explained by regarding it as a particle of negative electricity. It now appears that in some way a “wave-length” is connected with the electron's behavior. The work thus shows an interesting contrast with the discovery of A. H. Compton that a ray of light (a light pulse) suffers a change of wave-length upon impact with an electron, the change of wave-length corresponding exactly to the momentum gained by the electron. Until Compton's work, all the known facts about light could be explained by thinking of light as a wave motion. The Compton effect seems to prove the existence of particles of light. Physics is thus faced with a double duality. Compton showed that light is in some sense both a wave motion and a stream of particles. Davisson and Germer have now shown that a beam of electrons is in some sense both a stream of particles and a wave motion. At the same time, theoretical advances have been made which seem to pave the way for an understanding of this curious situation. A general account of these new developments was given by K. K. Darrow in his series “Contemporary Advances in Physics” in the Bell System Technical Journal for October, 1927. Some remarks on the relation of the Davisson and Germer experiments to the new mechanics were given in this article, p. 692 et seq. — Editor.
This article is taken from the manuscript prepared by the author for his address at the joint meeting of Section B of the American Association for the Advancement of Science and the American Physical Society on December 28, 1927, at Nashville, Tennessee. An account of this work giving fuller experimental details is given by Davisson and Germer in the December, 1927, issue of the Physical Review. These experiments are fundamental to some of the newer theories in physics. Until they were performed, it could be said that all experimental facts about the electron could be explained by regarding it as a particle of negative electricity. It now appears that in some way a “wave-length” is connected with the electron's behavior. The work thus shows an interesting contrast with the discovery of A. H. Compton that a ray of light (a light pulse) suffers a change of wave-length upon impact with an electron, the change of wave-length corresponding exactly to the momentum gained by the electron. Until Compton's work, all the known facts about light could be explained by thinking of light as a wave motion. The Compton effect seems to prove the existence of particles of light. Physics is thus faced with a double duality. Compton showed that light is in some sense both a wave motion and a stream of particles. Davisson and Germer have now shown that a beam of electrons is in some sense both a stream of particles and a wave motion. At the same time, theoretical advances have been made which seem to pave the way for an understanding of this curious situation. A general account of these new developments was given by K. K. Darrow in his series “Contemporary Advances in Physics” in the Bell System Technical Journal for October, 1927. Some remarks on the relation of the Davisson and Germer experiments to the new mechanics were given in this article, p. 692 et seq. — Editor.
Among the secondary effects produced in an X-ray, or cathode ray tube, there is one which is of special interest to physicists because it seems to throw some light on the question as to the nature of an electron. It appears that when a pencil of cathode rays falls upon the surface of a metal crystal, some of the rays are reflected, or “scattered,” and that the intensity of the scattered rays is greatest in certain directions, so that on a photographic plate placed to receive them, a diffraction pattern is produced as with X rays. The experiment proves that electrons, which were till recently supposed to be merely “particles,” really consist (like X rays), of waves, or at any rate have waves associated with them. It is to these waves associated with electrons, or “electron waves” as they are called, that I propose to devote my remarks this evening. The effect was first observed experimentally in 1927, by Davisson and Germer, who reflected cathode rays from a nickel crystal and, using an electrical method of detection, found maxima of intensity in certain directions. From the positions of the maxima and the known spacing constants of nickel they were able to deduce the wave-length of the electron waves. Later in the same year Professor G. P. Thomson obtained similar effects by transmitting cathode rays through thin metal films and receiving them on a photographic plate.
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.’
Einstein assumed duality between radiation and particles. Experiments involving electrons and diffraction effects are described to illustrate such behaviors. Classical physics and Einstein’s findings unmistakably demonstrated that light possessed both wave and particle properties. The responses of electrons in electric and magnetic fields are evidence for their existence as charged particles. The relationship between particle- and wave-like behavior was given by de Broglie in 1924. The dual nature of electrons was demonstrated experimentally by Davisson and Germer, when studying the diffraction of a stream of electrons. The reflection or diffraction of a beam of electromagnetic radiation can be expected to change its intensity, but changes in its wavelength would not ordinarily be anticipated. Photons and electrons may be described in terms of waves, but this approach has inherent limitations. The greater the attempt that is made to study the nature or behavior of a photon or a particle, the greater will be the uncertainty or error of the measurements.
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.
Abstract The famed Davisson-Germer Experiments demonstrated the wave phenomenon of electrons similarly to X-Ray scattering from Sir Lawrence Bragg’s X-ray experimentations on crystals c. 1913. Their empirical deduction of electrons behaving as waves (i.e. oscillatory) ignores the possibility of an electron beam behaving harmonically upon elastic collision with a diffraction grating - represented by nickel crystal - in their experiment. However, it is well established in the electrical engineering science that crystals possess piezoelectric effects and are used ubiquitously in electronic circuit designs for causing stable harmonic oscillation responses to direct current voltages. In light of this, the current mathematical model proposes the Davisson-Germer results to be the effect of a nickel crystal oscillator circuit which amplifies a direct voltage source – the electron beam – causing the phenomenon of inductance from the resultant electrical feedback with the crystal atom’s electromagnetic field.
The fact that light has some of the properties of ordinary particles led Louis de Broglie, in 1924, to construct a theory on the proposition that photons are particles. In the theory of wave motions, there is in general a difference between the speed of waves of some uniquely defined frequency, and the speed of a localized pulse such as de Broglie proposed to associate with a moving particle. Most often, one wishes to know the de Broglie wavelength for particles of a given kinetic energy. C. J. Davisson and L. H. Germer deliberately used single crystals as targets, and proceeded to discover just the kind of behavior that de Broglie's hypothesis of particle waves predicted. The development of electron microscopy, with its use of extremely well collimated, highly monoenergetic electron beams, has led to some beautiful demonstrations of the wave properties of electrons in analogs of optical diffraction phenomena. The strong reflection is a wave-like phenomenon totally unexpected from the classical picture of electrons.