g.p. thomson experiment notes pdf

30.2 Discovery of the Parts of the Atom: Electrons and Nuclei

Learning objectives.

By the end of this section, you will be able to:

• Describe how electrons were discovered.
• Explain the Millikan oil drop experiment.
• Describe Rutherford’s gold foil experiment.
• Describe Rutherford’s planetary model of the atom.

Just as atoms are a substructure of matter, electrons and nuclei are substructures of the atom. The experiments that were used to discover electrons and nuclei reveal some of the basic properties of atoms and can be readily understood using ideas such as electrostatic and magnetic force, already covered in previous chapters.

Charges and Electromagnetic Forces

In previous discussions, we have noted that positive charge is associated with nuclei and negative charge with electrons. We have also covered many aspects of the electric and magnetic forces that affect charges. We will now explore the discovery of the electron and nucleus as substructures of the atom and examine their contributions to the properties of atoms.

The Electron

Gas discharge tubes, such as that shown in Figure 30.4 , consist of an evacuated glass tube containing two metal electrodes and a rarefied gas. When a high voltage is applied to the electrodes, the gas glows. These tubes were the precursors to today’s neon lights. They were first studied seriously by Heinrich Geissler, a German inventor and glassblower, starting in the 1860s. The English scientist William Crookes, among others, continued to study what for some time were called Crookes tubes, wherein electrons are freed from atoms and molecules in the rarefied gas inside the tube and are accelerated from the cathode (negative) to the anode (positive) by the high potential. These “ cathode rays ” collide with the gas atoms and molecules and excite them, resulting in the emission of electromagnetic (EM) radiation that makes the electrons’ path visible as a ray that spreads and fades as it moves away from the cathode.

Gas discharge tubes today are most commonly called cathode-ray tubes , because the rays originate at the cathode. Crookes showed that the electrons carry momentum (they can make a small paddle wheel rotate). He also found that their normally straight path is bent by a magnet in the direction expected for a negative charge moving away from the cathode. These were the first direct indications of electrons and their charge.

The English physicist J. J. Thomson (1856–1940) improved and expanded the scope of experiments with gas discharge tubes. (See Figure 30.5 and Figure 30.6 .) He verified the negative charge of the cathode rays with both magnetic and electric fields. Additionally, he collected the rays in a metal cup and found an excess of negative charge. Thomson was also able to measure the ratio of the charge of the electron to its mass, q e q e / m e / m e —an important step to finding the actual values of both q e q e and m e m e . Figure 30.7 shows a cathode-ray tube, which produces a narrow beam of electrons that passes through charging plates connected to a high-voltage power supply. An electric field E E is produced between the charging plates, and the cathode-ray tube is placed between the poles of a magnet so that the electric field E E is perpendicular to the magnetic field B B of the magnet. These fields, being perpendicular to each other, produce opposing forces on the electrons. As discussed for mass spectrometers in More Applications of Magnetism , if the net force due to the fields vanishes, then the velocity of the charged particle is v = E / B v = E / B . In this manner, Thomson determined the velocity of the electrons and then moved the beam up and down by adjusting the electric field.

To see how the amount of deflection is used to calculate q e / m e q e / m e , note that the deflection is proportional to the electric force on the electron:

But the vertical deflection is also related to the electron’s mass, since the electron’s acceleration is

The value of F F is not known, since q e q e was not yet known. Substituting the expression for electric force into the expression for acceleration yields

Gathering terms, we have

The deflection is analyzed to get a a , and E E is determined from the applied voltage and distance between the plates; thus, q e m e q e m e can be determined. With the velocity known, another measurement of q e m e q e m e can be obtained by bending the beam of electrons with the magnetic field. Since F mag = q e vB = m e a F mag = q e vB = m e a , we have q e / m e = a / vB q e / m e = a / vB . Consistent results are obtained using magnetic deflection.

What is so important about q e / m e q e / m e , the ratio of the electron’s charge to its mass? The value obtained is

This is a huge number, as Thomson realized, and it implies that the electron has a very small mass. It was known from electroplating that about 10 8 C/kg 10 8 C/kg is needed to plate a material, a factor of about 1000 less than the charge per kilogram of electrons. Thomson went on to do the same experiment for positively charged hydrogen ions (now known to be bare protons) and found a charge per kilogram about 1000 times smaller than that for the electron, implying that the proton is about 1000 times more massive than the electron. Today, we know more precisely that

where q p q p is the charge of the proton and m p m p is its mass. This ratio (to four significant figures) is 1836 times less charge per kilogram than for the electron. Since the charges of electrons and protons are equal in magnitude, this implies m p = 1836 m e m p = 1836 m e .

Thomson performed a variety of experiments using differing gases in discharge tubes and employing other methods, such as the photoelectric effect, for freeing electrons from atoms. He always found the same properties for the electron, proving it to be an independent particle. For his work, the important pieces of which he began to publish in 1897, Thomson was awarded the 1906 Nobel Prize in Physics. In retrospect, it is difficult to appreciate how astonishing it was to find that the atom has a substructure. Thomson himself said, “It was only when I was convinced that the experiment left no escape from it that I published my belief in the existence of bodies smaller than atoms.”

Thomson attempted to measure the charge of individual electrons, but his method could determine its charge only to the order of magnitude expected.

Since Faraday’s experiments with electroplating in the 1830s, it had been known that about 100,000 C per mole was needed to plate singly ionized ions. Dividing this by the number of ions per mole (that is, by Avogadro’s number), which was approximately known, the charge per ion was calculated to be about 1 . 6 × 10 − 19 C 1 . 6 × 10 − 19 C , close to the actual value.

An American physicist, Robert Millikan (1868–1953) (see Figure 30.8 ), decided to improve upon Thomson’s experiment for measuring q e q e and was eventually forced to try another approach, which is now a classic experiment performed by students. The Millikan oil drop experiment is shown in Figure 30.9 .

In the Millikan oil drop experiment, fine drops of oil are sprayed from an atomizer. Some of these are charged by the process and can then be suspended between metal plates by a voltage between the plates. In this situation, the weight of the drop is balanced by the electric force:

The electric field is produced by the applied voltage, hence, E = V / d E = V / d , and V V is adjusted to just balance the drop’s weight. The drops can be seen as points of reflected light using a microscope, but they are too small to directly measure their size and mass. The mass of the drop is determined by observing how fast it falls when the voltage is turned off. Since air resistance is very significant for these submicroscopic drops, the more massive drops fall faster than the less massive, and sophisticated sedimentation calculations can reveal their mass. Oil is used rather than water, because it does not readily evaporate, and so mass is nearly constant. Once the mass of the drop is known, the charge of the electron is given by rearranging the previous equation:

where d d is the separation of the plates and V V is the voltage that holds the drop motionless. (The same drop can be observed for several hours to see that it really is motionless.) By 1913 Millikan had measured the charge of the electron q e q e to an accuracy of 1%, and he improved this by a factor of 10 within a few years to a value of − 1 . 60 × 10 − 19 C − 1 . 60 × 10 − 19 C . He also observed that all charges were multiples of the basic electron charge and that sudden changes could occur in which electrons were added or removed from the drops. For this very fundamental direct measurement of q e q e and for his studies of the photoelectric effect, Millikan was awarded the 1923 Nobel Prize in Physics.

With the charge of the electron known and the charge-to-mass ratio known, the electron’s mass can be calculated. It is

Substituting known values yields

where the round-off errors have been corrected. The mass of the electron has been verified in many subsequent experiments and is now known to an accuracy of better than one part in one million. It is an incredibly small mass and remains the smallest known mass of any particle that has mass. (Some particles, such as photons, are massless and cannot be brought to rest, but travel at the speed of light.) A similar calculation gives the masses of other particles, including the proton. To three digits, the mass of the proton is now known to be

which is nearly identical to the mass of a hydrogen atom. What Thomson and Millikan had done was to prove the existence of one substructure of atoms, the electron, and further to show that it had only a tiny fraction of the mass of an atom. The nucleus of an atom contains most of its mass, and the nature of the nucleus was completely unanticipated.

Another important characteristic of quantum mechanics was also beginning to emerge. All electrons are identical to one another. The charge and mass of electrons are not average values; rather, they are unique values that all electrons have. This is true of other fundamental entities at the submicroscopic level. All protons are identical to one another, and so on.

The Nucleus

Here, we examine the first direct evidence of the size and mass of the nucleus. In later chapters, we will examine many other aspects of nuclear physics, but the basic information on nuclear size and mass is so important to understanding the atom that we consider it here.

Nuclear radioactivity was discovered in 1896, and it was soon the subject of intense study by a number of the best scientists in the world. Among them was New Zealander Lord Ernest Rutherford, who made numerous fundamental discoveries and earned the title of “father of nuclear physics.” Born in Nelson, Rutherford did his postgraduate studies at the Cavendish Laboratories in England before taking up a position at McGill University in Canada where he did the work that earned him a Nobel Prize in Chemistry in 1908. In the area of atomic and nuclear physics, there is much overlap between chemistry and physics, with physics providing the fundamental enabling theories. He returned to England in later years and had six future Nobel Prize winners as students. Rutherford used nuclear radiation to directly examine the size and mass of the atomic nucleus. The experiment he devised is shown in Figure 30.10 . A radioactive source that emits alpha radiation was placed in a lead container with a hole in one side to produce a beam of alpha particles, which are a type of ionizing radiation ejected by the nuclei of a radioactive source. A thin gold foil was placed in the beam, and the scattering of the alpha particles was observed by the glow they caused when they struck a phosphor screen.

Alpha particles were known to be the doubly charged positive nuclei of helium atoms that had kinetic energies on the order of 5 MeV 5 MeV when emitted in nuclear decay, which is the disintegration of the nucleus of an unstable nuclide by the spontaneous emission of charged particles. These particles interact with matter mostly via the Coulomb force, and the manner in which they scatter from nuclei can reveal nuclear size and mass. This is analogous to observing how a bowling ball is scattered by an object you cannot see directly. Because the alpha particle’s energy is so large compared with the typical energies associated with atoms ( MeV MeV versus eV eV ), you would expect the alpha particles to simply crash through a thin foil much like a supersonic bowling ball would crash through a few dozen rows of bowling pins. Thomson had envisioned the atom to be a small sphere in which equal amounts of positive and negative charge were distributed evenly. The incident massive alpha particles would suffer only small deflections in such a model. Instead, Rutherford and his collaborators found that alpha particles occasionally were scattered to large angles, some even back in the direction from which they came! Detailed analysis using conservation of momentum and energy—particularly of the small number that came straight back—implied that gold nuclei are very small compared with the size of a gold atom, contain almost all of the atom’s mass, and are tightly bound. Since the gold nucleus is several times more massive than the alpha particle, a head-on collision would scatter the alpha particle straight back toward the source. In addition, the smaller the nucleus, the fewer alpha particles that would hit one head on.

Although the results of the experiment were published by his colleagues in 1909, it took Rutherford two years to convince himself of their meaning. Like Thomson before him, Rutherford was reluctant to accept such radical results. Nature on a small scale is so unlike our classical world that even those at the forefront of discovery are sometimes surprised. Rutherford later wrote: “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backwards ... [meant] ... the greatest part of the mass of the atom was concentrated in a tiny nucleus.” In 1911, Rutherford published his analysis together with a proposed model of the atom. The size of the nucleus was determined to be about 10 − 15 m 10 − 15 m , or 100,000 times smaller than the atom. This implies a huge density, on the order of 10 15 g/cm 3 10 15 g/cm 3 , vastly unlike any macroscopic matter. Also implied is the existence of previously unknown nuclear forces to counteract the huge repulsive Coulomb forces among the positive charges in the nucleus. Huge forces would also be consistent with the large energies emitted in nuclear radiation.

The small size of the nucleus also implies that the atom is mostly empty inside. In fact, in Rutherford’s experiment, most alphas went straight through the gold foil with very little scattering, since electrons have such small masses and since the atom was mostly empty with nothing for the alpha to hit. There were already hints of this at the time Rutherford performed his experiments, since energetic electrons had been observed to penetrate thin foils more easily than expected. Figure 30.11 shows a schematic of the atoms in a thin foil with circles representing the size of the atoms (about 10 − 10 m 10 − 10 m ) and dots representing the nuclei. (The dots are not to scale—if they were, you would need a microscope to see them.) Most alpha particles miss the small nuclei and are only slightly scattered by electrons. Occasionally, (about once in 8000 times in Rutherford’s experiment), an alpha hits a nucleus head-on and is scattered straight backward.

Based on the size and mass of the nucleus revealed by his experiment, as well as the mass of electrons, Rutherford proposed the planetary model of the atom . The planetary model of the atom pictures low-mass electrons orbiting a large-mass nucleus. The sizes of the electron orbits are large compared with the size of the nucleus, with mostly vacuum inside the atom. This picture is analogous to how low-mass planets in our solar system orbit the large-mass Sun at distances large compared with the size of the sun. In the atom, the attractive Coulomb force is analogous to gravitation in the planetary system. (See Figure 30.12 .) Note that a model or mental picture is needed to explain experimental results, since the atom is too small to be directly observed with visible light.

Rutherford’s planetary model of the atom was crucial to understanding the characteristics of atoms, and their interactions and energies, as we shall see in the next few sections. Also, it was an indication of how different nature is from the familiar classical world on the small, quantum mechanical scale. The discovery of a substructure to all matter in the form of atoms and molecules was now being taken a step further to reveal a substructure of atoms that was simpler than the 92 elements then known. We have continued to search for deeper substructures, such as those inside the nucleus, with some success. In later chapters, we will follow this quest in the discussion of quarks and other elementary particles, and we will look at the direction the search seems now to be heading.

PhET Explorations

Rutherford scattering.

How did Rutherford figure out the structure of the atom without being able to see it? Simulate the famous experiment in which he disproved the Plum Pudding model of the atom by observing alpha particles bouncing off atoms and determining that they must have a small core.

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• J.J.. Thomson - Nobel Lecture: Electronic Waves

George Paget Thomson

Nobel lecture.

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.

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