The experiments by the author and L. H. Germer, by G. P. Thomson and by others from which the wave properties of electrons are adduced are briefly described. The agreement between the results of these experiments and the prediction of L. de Broglie is pointed out. The wave and corpuscular properties of electrons are compared with the similar properties of light quanta.
The experiments by the author and L. H. Germer, by G. P. Thomson and by others from which the wave properties of electrons are adduced are briefly described. The agreement between the results of these experiments and the prediction of L. de Broglie is pointed out. The wave and corpuscular properties of electrons are compared with the similar properties of light quanta.
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.’
Davisson and Germer performed an experiment, in which electrons were reflected from parallel layers of atoms in a crystal. The electrons showed interference, thus demonstrating the wave nature of the electron. Louis de Broglie postulated a wave model of the electron, in which an electron orbit was represented by a group of in-phase waves. The model predicted that the angular momentum of an electron could take on only a limited number of values, a concept that Neils Bohr had introduced some years earlier as an ad hoc assumption. In an electron microscope, electrons stream off a hot filament and are accelerated to high velocity by passing between two electrically charged plates. The electrons' wavelength is related to their velocity and it is easy to obtain electrons with wavelengths near 0.1 nm, which suggests the possibility of obtaining resolution of about the same magnitude.
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.
Light quanta The history of the corpuscular and wave controversy in optical theory is well known. At the end of the last century physicists had no doubt as to the wave character of light, and the acceptance of the wave theory meant the rejection of the corpuscular theory. The possibility of both being correct and helpful to one another had not been much thought about and still less explored. At about this time Planck's quantum theory appeared and was soon followed in 1905 by Einstein's theory of ‘light quanta’ to explain the photo-electric effect, for which the wave theory alone had utterly failed to account. Einstein assumed that radiation exists in discrete ‘quanta’ of energy hν , where ν is the frequency; thus a quantum is a separate thing, like a corpuscle, and has a frequency associated with it, like a wave. There was a blend of the two older theories involved. This idea has been generalised by the speculations of Louis de Broglie, who pointed out the important clue given by the theory of relativity, namely, that of the identity of mass and energy, so that the conservation of mass is therefore also the conservation of energy. This suggested to him that all forms of energy (including radiation) should have an atomic structure, like matter; and that the atoms of energy are grouped round certain singular points, forming electrons, light quanta, and the like.
This chapter discusses the conceptual foundations of quantum mechanics in the context of matter. Classical physics identified matter with particles and radiation with "waves." Although this description accounted for a large number of very important facts, it became apparent around the turn of the century that other phenomena, such as blackbody radiation and photoelectric effect, are satisfactorily explained only if radiation is described in terms of particles. Sometime later the hypothesis that, conversely, matter has wave properties was proposed by Louis de Broglie and was confirmed by the Davisson-Germer experiment of electron diffraction. In this experiment and similar ones, an electron beam was passed through a regular lattice (crystal), and subsequently showed the well-known diffraction patterns that are characteristic of waves. These results confirmed the theoretical predictions that a monoenergetic electron beam should be described by a plane wave and that the wave vector k of the wave should be related to the momentum p of an individual electron.