Nobel Lecture, June 7, 1938

Electronic Waves

Ever since last November, I have been wanting to express in person my gratitude to the generosity of Alfred Nobel, to whom I owe it that I am privileged to be here today, especially since illness prevented me from doing so at the proper time. The idealism which permeated his character led him to make his magnificent foundation for the benefit of a class of men with whose aims and viewpoint his own scientific instincts and ability had made him naturally sympathetic, but he was certainly at least as much concerned with helping science as a whole, as individual scientists. That his foundation has been as successful in the first as in the second, is due to the manner in which his wishes have been carried out. The Swedish people, under the leadership of the Royal Family, and through the medium of the Royal Academy of Sciences, have made the Nobel Prizes one of the chief causes of the growth of the prestige of science in the eyes of the world, which is a feature of our time. As a recipient of Nobel’s generosity I owe sincerest thanks to them as well as to him.

The goddess of learning is fabled to have sprung full-grown from the brain of Zeus, but it is seldom that a scientific conception is born in its final form, or owns a single parent. More often it is the product of a series of minds, each in turn modifying the ideas of those that came before, and providing material for those that come after. The electron is no exception.

Although Faraday does not seem to have realized it, his work on electrolysis, by showing the unitary character of the charges on atoms in solution, was the first step. Clerk Maxwell in 1873 used the phrase a “molecule of electricity” and von Helmholtz in 1881 speaking of Faraday’s work said “If we accept the hypothesis that elementary substances are composed of atoms, we cannot well avoid concluding that electricity also is divided into elementary portions which behave like atoms of electricity.” The hypothetical atom received a name in the same year when Johnstone Stoney of Dublin christened it “electron”, but so far the only property implied was an electron charge.

The last year of the nineteenth century saw the electron take a leading place amongst the conceptions of physics. It acquired not only mass but universality, it was not only electricity but an essential part of all matter. If among the many names associated with this advance I mention that of J.J. Thomson I hope you will forgive a natural pride. It is to the great work of Bohr that we owe the demonstration of the connection between electrons and Planck’s quantum which gave the electron a dynamics of its own. A few years later, Goudsmit and Uhlenbeck, following on an earlier suggestion by A.H. Compton showed that it was necessary to suppose that the electron had spin. Yet even with the properties of charge, mass, spin and a special mechanics to help it, the electron was unable to carry the burden of explaining the large and detailed mass of experimental data which had accumulated. L. de Broglie, working originally on a theory of radiation, produced as a kind of by-product the conception that any particle and in particular an electron, was associated with a system of waves. It is with these waves, formulated more precisely by Schrödinger, and modified by Dirac to cover the idea of spin, that the rest of my lecture will deal.

The first published experiments to confirm de Broglie’s theory were those of Davisson and Germer, but perhaps you will allow me to describe instead those to which my pupils and I were led by de Broglie’s epoch-making conception.

A narrow beam of cathode rays was transmitted through a thin film of matter. In the earliest experiment of the late Mr. Reid this film was of celluloid, in my own experiment of metal. In both, the thickness was of the order of 10^-6 cm. The scattered beam was received on a photographic plate normal to the beam, and when developed showed a pattern of rings, recalling optical halos and the Debye-Scherrer rings well known in the corresponding experiment with X-rays. An interference phenomenon is at once suggested. This would occur if each atom of the film scattered in phase a wavelet from an advancing wave associated with the electrons forming the cathode rays. Since the atoms in each small crystal of the metal are regularly spaced, the phases of the wavelets scattered in any fixed direction will have a definite relationship to one another. In some directions they will agree in phase and build up a strong scattered wave, in others they will destroy one another by interference. The strong waves are analogous to the beams of light diffracted by an optical grating. At the time, the arrangement of the atoms in celluloid was not known with certainty and only general conclusions could be drawn, but for the metals it had been determined previously by the use of X-rays. According to de Broglie’s theory the wavelength associated with an electron is h/mv which for the electrons used (cathode rays of 20 to 60,000 volts energy) comes out from 8 X 10^-9 to 5 X 10^-9 cm. I do not wish to trouble you with detailed figures and it will be enough to say that the patterns on the photographic plates agreed quantitatively, in all cases, with the distribution of strong scattered waves calculated by the method I have indicated. The agreement is good to the accuracy of the experiments which was about 1%. There is no adjustable constant, and the patterns reproduce not merely the general features of the X-ray patterns but details due to special arrangements of the crystals in the films which were known to occur from previous investigation by X-rays. Later work has amply confirmed this conclusion, and many thousands of photographs have been taken in my own and other laboratories without any disagreement with the theory being found. The accuracy has increased with the improvement of the apparatus, perhaps the most accurate work being that of v. Friesen of Uppsala who has used the method in a precision determination of e in which he reaches an accuracy of I in 1,000.

Before discussing the theoretical implications of these results there are two modifications of the experiments which should be mentioned. In the one, the electrons after passing through the film are subject to a uniform magnetic field which deflects them. It is found that the electrons whose impact on the plate forms the ring pattern are deflected equally with those which have passed through holes in the film. Thus the pattern is due to electrons which have preserved unchanged the property of being deflected by a magnet. This distinguishes the effect from anything produced by X-rays and shows that it is a true property of electrons. The other point is a practical one, to avoid the need for preparing the very thin films which are needed to transmit the electrons, an apparatus has been devised to work by reflection, the electrons striking the diffracting surface at a small glancing angle. It appears that in many cases the patterns so obtained are really due to electrons transmitted through small projections on the surface. In other cases, for example when the cleavage surface of a crystal is used, true reflection occurs from the Bragg planes.

The theory of de Broglie in the form given to it by Schrödinger is now known as wave mechanics and is the basis of atomic physics. It has been applied to a great variety of phenomena with success, but owing largely to mathematical difficulties there are not many cases in which an accurate comparison is possible between theory and experiment. The diffraction of fast electrons by crystals is by far the severest numerical test which has been made and it is therefore important to see just what conclusions the excellent agreement between theory and these experiments permits us to draw.

The calculations so far are identical with those in the corresponding case of the diffraction of X-rays. The only assumption made in determining the directions of the diffracted beams is that we have to deal with a train of wave of considerable depth and with a plane wave-front extending over a considerable number of atoms. The minimum extension of the wave system sideways and frontways can be found from the sharpness of the lines. Taking v. Friesen’s figures, it is at least 225 waves from back to front over a front of more than 200 Å each way.

But the real trouble comes when we consider the physical meaning of the waves. In fact, as we have seen, the electrons blacken the photographic plate at those places where the waves would be strong. Following Bohr, Born, and Schrödinger, we can express this by saying that the intensity of the waves at any place measures the probability of an electron manifesting itself there. This view is strengthened by measurements of the relative intensities of the rings, which agree well with calculations by Mott based on Schrödinger’s equation. Such a view, however successful as a formal statement is at variance with all ordinary ideas. Why should a particle appear only in certain places associated with a set of waves? Why should waves produce effects only through the medium of particles? For it must be emphasized that in these experiments each electron only sensitizes the photographic plate in one minute region, but in that region it has the same powers of penetration and photographic action as if it had never been diffracted. We cannot suppose that the energy is distributed throughout the waves as in a sound or water wave, the wave is only effective in the one place where the electron appears. The rest of it is a kind of phantom. Once the particle has appeared the wave disappears like a dream when the sleeper wakes. Yet the motion of the electron, unlike that of a Newtonian particle, is influenced by what happens over the whole front of the wave, as is shown by the effect of the size of the crystals on the sharpness of the patterns. The difference in point of view is fundamental, and we have to face a break with ordinary mechanical ideas. Particles have not a unique track, the energy in these waves is not continuously distributed, probability not determinism governs nature.

But while emphasizing this fundamental change in outlook, which I believe to represent an advance in physical conceptions, I should like to point out several ways in which the new phenomena fit the old framework better than is often realized. Take the case of the influence of the size of the crystals on the sharpness of the diffracted beams, which we have just mentioned. On the wave theory it is simply an example of the fact that a diffraction grating with only a few lines has a poor resolving power. Double the number of the lines and the sharpness of the diffracted beams is doubled also. However if there are already many lines, the angular change is small. But imagine a particle acted on by the material which forms the slits of the grating, and suppose the forces such as to deflect it into one of the diffracted beams. The forces due to the material round the slits near the one through which it passes will be the most important, an increase in the number of slits will affect the motion but the angular deflection due to adding successive slits will diminish as the numbers increase. The law is of a similar character, though no simple law of force would reproduce the wave effect quantitatively.

Similarly for the length of the wave train. If this were limited by a shutter moving so quickly as to let only a short wave train pass through, the wave theory would require that the velocity of the particle would be uncertain over a range increasing with the shortness of the wave train, and corresponding to the range of wavelengths shown by a Fourier analysis of the train. But the motion of the shutter might well be expected to alter the velocity of a particle passing through, just before it closed.

Again, on the new view it is purely a matter of chance in which of the diffracted beams of different orders an electron appears. If the phenomenon were expressed as the classical motion of a particle, this would have to depend on the initial motion of the particle, and there is no possibility of determining this initial motion without disturbing it hopelessly. There seems no reason why those who prefer it should not regard the diffraction of electrons as the motion of particles governed by laws which simulate the character of waves, but besides the rather artificial character of the law of motion, one has to ascribe importance to the detailed initial conditions of the motion which, as far as our present knowledge goes, are necessarily incapable of being determined. I am predisposed by nature in favour of the most mechanical explanations possible, but I feel that this view is rather clumsy and that it might be best, as it is certainly safer, to keep strictly to the facts and regard the wave equation as merely a way of predicting the result of experiments. Nevertheless, the view I have sketched is often a help in thinking of these problems. We are curiously near the position which Newton took over his theory of optics, long despised but now seen to be far nearer the truth than that of his rivals and successors.

“Those that are averse from assenting to any new Discoveries, but such as they can explain by an Hypothesis, may for the present suppose, that as Stones by falling upon water put the Water into an undulating Motion, and all Bodies by percussion excite vibrations in the Air: so the Rays of Light, by impinging on any refracting or reflecting Surface, excite vibrations in the refracting or reflecting Medium or Substance, much after the manner that vibrations are propagated in the Air for causing Sound, and move faster than the Rays so as to overtake them; and that when any Ray is in that part of the vibration which conspires with its Motion, it easily breaks through a refracting Surface, but when it is in the contrary part of the vibration which impedes its Motion, it is easily reflected; and, by consequence, that every Ray is successively disposed to be easily reflected, or easily transmitted, by every vibration which overtakes it. But whether this Hypothesis be true or false I do not here consider.”

Although the experiments in diffraction confirm so beautifully the de Broglie-Schrödinger wave theory, the position is less satisfactory as regards the extended theory due to Dirac. On this theory the electron possesses magnetic properties and the wave requires four quantities instead of one for its specification. This satisfies those needs of spectroscopy which led to the invention of the spinning electron. It suggests however that electronic waves could be polarized and that the polarized waves might interact with matter in an anisotropic manner. In fact detailed calculations by Mott indicate that if Dirac electrons of 140 kV energy are scattered twice through 90° by the nuclei of gold atoms the intensity of the scattered beam will differ by 16% according to whether the two scatterings are in the same or in opposite directions. Experiments by Dymond and by myself have established independently that no effect of this order of magnitude exists, when the scattering is done by gold foils. While there is a slight possibility that the circumnuclear electrons, or the organization of the atoms into crystals might effect the result, it seems very unlikely. Some of the theorists have arrived at results conflicting with Mott, but I understand that their work has been found to contain errors. At present there seems no explanation of this discrepancy which throws doubt on the validity of the Dirac equations in spite of their success in predicting the positive electron.

I should be sorry to leave you with the impression that electron diffraction was of interest only to those concerned with the fundamentals of physics. It has important practical applications to the study of surface effects. You know how X-ray diffraction has made it possible to determine the arrangement of the atoms in a great variety of solids and even liquids. X-rays are very penetrating, and any structure peculiar to the surface of a body will be likely to be overlooked, for its effect is swamped in that of the much greater mass of underlying material. Electrons only affect layers of a few atoms, or at most tens of atoms, in thickness, and so are eminently suited for the purpose. The position of the beams diffracted from a surface enables us, at least in many cases, to determine the arrangement of the atoms in the surface. Among the many cases which have already been studied I have only time to refer to one, the state of the surface of polished metals. Many years ago Sir George Beilby suggested that this resembled a supercooled liquid which had flowed under the stress of polishing. A series of experiments by electron diffraction carried out at the Imperial College in London has confirmed this conclusion. The most recent work due to Dr. Cochrane has shown that though this amorphous layer is stable at ordinary temperature as long as it remains fixed to the mass of the metal, it is unstable when removed, and recrystalizes after a few hours. Work by Professor Finch on these lines has led to valuable conclusions as to the wear on the surfaces of cylinders and pistons in petrol engines.

It is in keeping with the universal character of physical science that this single small branch of it should touch on the one hand on the fundamentals of scientific philosophy and on the other, questions of everyday life.