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.
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.’
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.
Abstract The new wave mechanics has been eminently successful in correlating and accounting for the large amount of experimental data on the periodic properties of the atom. The applications of the new theory to aperiodic phenomena, though not nearly so numerous, have been attended with no less success; indeed, it is in these experiments on free electrons, in which diffraction patterns similar to those produced by beams of X-rays and light are obtained, that the wave nature of electrons is so clearly and objectively demonstrated. Such diffraction effects have been obtained by a number of investigators by scattering beams of homogeneous electrons in crystals, thin films and by a ruled grating. Similar effects are obtained when electrons are scattered by complex molecules, owing to the symmetrically situated nuclei in the molecular structure, and when α-particles are scattered by helium owing to interference between the waves of the scattered incident particles and recoiling helium nuclei.
To members of the British Institute of Radiology the cathode ray is probably most familiar as the necessary antecedent of X rays. You are interested in them chiefly as a means to an end, but the cathode rays had a very real intrinsic interest in the nineties of last century. It was the study of the beam of light in a low-pressure discharge tube which led to the recognition of the existence of a universal constituent of matter—the electron—and I hope to show that the importance of cathode rays for the study of fundamental problems in physics is not yet exhausted. The cathode rays still form in many respects the most convenient way of studying the properties if electrons. Of recent years our views on the nature of these electrons have undergone a striking change, as a result of the brilliant inspiration of Prince Louis de Broglie, who has been rewarded with a Nobel Prize. He founded the theory which is now dominant in physics under the name of wave mechanics, and which is a general theory of the behaviour of any form of particle. According to this view all particles are associated with some form of wave, the properties of which determine much of the behaviour of the particle. This theory was originally devised by de Broglie from considerations based upon relativity.
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.
Abstract The work about to be described is a continuation of an investigation begun by one of us at Princeton, New Jersey, on the scattering of electrons by gas atoms. The conditions there were so chosen that only single collisions were taken into account, and it was possible to investigate not only the energy loss on collision, as in the Franck and Hertz experiments, but also the direction of the path of the electron after collision. By employing a magnetic analysis of the velocity of the electron after impact it was found possible to obtain information as to the probability of excitation of various stationary states of the atom considered, on collision with electrons of much higher velocities than could previously be used. The curves relating scattered intensity with angle of scattering were found to have sharp maxima, which were strongly suggestive of diffraction maxima, as might be expected if the motion of electrons is governed by the wave mechanics. But whereas the wave mechanics has been eminently successful in explaining the scattering results of Davisson and Germer with single metal crystals, and of Thomson and Rupp with thin metal foils the results of Dymond have been inexplicable on this basis. It may be said at once that we have been unable to find any trace of the sharp maxima found by him in I, which were apparently due to a secondary cause. Indeed, as has recently been pointed out by Elsasser, no interference effects can be expected, when the electron loses energy on collision, the case in which Dymond found maxima, for the frequencies of the electron before and after interaction with the atom are different and there can consequently be no coherence of the scattered waves.