Half the electron by A. C. Lynch

_I. _I. Tvzomson discoveved the electron a hundred yeavs ago, but he nevev quite accepted that the electron does not obey the classical laws of electromagnetism that he usedfor discovering it.

t is generally agreed that the electron was dis- covered by Professor Sir I Joseph Thomson (Fig. 1)

in 1897, but the statement is a strange one. He could not exhibit an electron, or show a photograph of one; all he could do was to describe its properties, or, as it turned out later, just half of them. A second oddity: there is no definite date for the dis- covery. He mentioned it at the end of a lecture he gave to the Royal Institution in April, but so briefly that some of the audience hardly noticed it, and some others thought it was just a leg-pull. He reported it more fully at the British Association meeting in September, and the report of that meeting is the first definite printed statement. The third oddity is that it was J. J. Thomson rather than anyone else who

Fig. 1 J. J. Thomson in 1902: from the portrait he liked best, a painting by Arthur Hacker (Courtesy of the University of Cambridge, Cavendish Laboratory,

Madingley Road, Cambridge, UK)

made the discovery J.J., as he was always known*, was a mathematical physicist in the great tradition of 19th- century Cambridge, a worthy member of the group that includes Kelvin, Clerk Maxwell, Stokes, and Rayleigh; he had been appointed as Professor, at the age of 28, in recognition of his mathematical abilities. As an experimenter, he was first-rate in devising experiments, not so good in carrying them out, and then brilliant in interpreting them. His work before 1897 included two attempts to measure the velocity of electromagnetic waves-although to him this was the measurement of the ratio between the electromagnetic and the electrostatic units. His first attempt in the 1880s was not good, but in 1890 he tried again with the help of a marvellous experimenter, G. E C. Searle, and together they obtained a result which stood unchallenged for many years. Another of his early

*In the 1890s there were at least four physicists named Professor Thomson or Thompson.

interests was eddy-currents in metal sheets, for which he deduced the formulae that are still in use, although not many people know that J.J. was the author of them. They make use of the hyperbolic trigonometric functions, which were so new then that J.J. had to include definitions of them in his text; it may have been the first practical application of these functions.

In about 1896 J.J. returned to an earlier interest of his: how was electricity con- ducted through gases? It had suddenly become a much easier subject to study, because in 1895 X-rays were discovered and found to make gases conduct. With a controllable source of con- ducting gas, experiments began to give reproducible results. It was the interpre- tation of these experiments

that enabled J.J. to describe the electron, and so ‘discover’ it, even although neither he nor anyone else had ever seen one.

When J.J. described his experiments, he did not put them in chronological order. They are easier to understand in the order which he used in 1903, when they appeared in book form. He began by describing what was already known about the flow of electricity in liquids. Faraday, fifty years earlier, had studied electrolysis, and shown that the mass of material evolved or deposited was exactly proportional to the electrical charge that had passed and to the atomic weight divided by the valency. These atomic weights and valencies were already well known from chemical work. At that time not everyone believed in molecules and atoms, but, for those who did, it was natural to believe that electricity was atomic too, one atom of electricity being associated with each valency bond. There was, however, no precise estimate of the charge carried by one atom of electricity.

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Fig. 2 Cloud-chamber photographs of vapour trails left by electrons. The straight track is of a fast-moving electron (having large energy). The winding tracks were left by slow-moving electrons, buffeted by atoms and by other electrons (Photograph by C. T. R. Wilson. Courtesy of the University of Cambridge, Cavendish Laboratory, Madingley Road, Cambridge, UK)

Measuring the charge of the electron

J.J.’s discovery rests on two main groups of experiments. One of them measured, for the first time, the electric charge carried by each atom. It depended on a new instrument, the cloud chamber, invented by C. T. R. Wilson, one of his colleagues at Cambridge. Wilson was a keen mountaineer; in Scotland he had often seen the appearance and disappearance of mountain mists, and as a physicist he devoted his entire career to the apparatus he invented for studying mists in damp air in controlled conditions in the lab. The key to it is that very small water drops are unstable; they evaporate unless they contain somethmg acting as a nucleus, perhaps a speck of dust. J.J. found that water-vapour after exposure to X-rays would condense into droplets as if there were nuclei for them to form on (Fig. 2). (Actually it was their electric charge that prevented the drops from evaporating.) He could then observe the cloud slowly settle. He could collect the water and weigh it, but he still did not know how many drops had been there. At this stage important help came from one of his research students, John Townsend, who knew that, forty years earlier, Sir George Stokes had found a formula for the rate of fall of a spherical object in a viscous fluid. Stokes was s t d living in Cambridge in 1897, and occasionally visiting the laboratory, but there i s no indication that he himself suggested that h s

formula might be useful. Townsend used it to find what size of water-drop would fall at the observed rate, whch was very slow, a few millimetres per minute. Then, fiom the size of the drops, and the amount of water collected when they had fallen, he knew how many drops there had been; and as the total electric charge on the cloud could be measured, he could calculate the charge on each drop. The experiment i s difficult and could not be exact, but it gave an answer whch we now know was right within a factor of 2. The charge was not very mfferent from that on a hydrogen atom in a liquid-quite possibly the two were equal.

Townsend appears to have ‘done all the practical work for the measurement of charge. He wrote letters from Cambridge to his former tutor in Dublin, G. E Fitzgerald (famous for the Fitzgerald-Lorentz contrac- tion). Some of them were published recently. From them we know that J.J. set Townsend to repeat the experiments with various ways of makmg the gas conducting at the start of the experiment-first with a Crookes tube, then with X-rays, then with ramoactive materials. They all gave the same results for the charge on each water-drop. Townsend’s letters somehow imply less enthusiasm than J.J.’s about the number of repetitions needed. The measurement of the charge constituted one of J.J.5 two crucial experiments.

Measuring the charge per unit mass

The other group of experiments was more compli- cated. It provided a value for the ratio of the electron’s charge to its mass. These experiments were done inside a Crookes tube, the ancestor of the modern cathode- ray tube; they were therefore done in a vacuum, not at near atmospheric pressure as the cloud-chamber work had been.

The discharge in the Crookes tube i s invisible except where it falls on the end of the tube, where it forms a glowing patch. Any obstruction in the tube throws a sharp shadow in that glow. All the old pictures of Crookes tubes show the tube with a Maltese cross mounted in it, and the sharpness of the shadow proved that the discharge travelled in a straight line. Was it a wave or a stream ofparticles? Hertz (who had been the first to demonstrate radio waves) said it must be a wave, because it was not deflected by an electric field, and for some years this was accepted as a fact. But when J.J. tried to repeat the experiment, he must have done it slightly differently. Evidently Hertz had started the discharge in the Crookes tube, and then tried to deflect it-the obvious plan. But J.J., in some of his experiments, started a very weak discharge, then switched on the deflecting field, and then increased the current in the Crookes tube. In these conditions, he saw 3 momentary deflection which lasted 3 second or so before the beam returned to the straight-through position. It turned out that the beam is deflected if the vacuum is good enough, but in a poor vacuum the beam generates a protecting screen around itself-a

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space-chirge. In Hertz’s work, the space-charge formed before he tried to deflect the beam, so he always failed to see the deflection. J.J. got the right answer if he (or his assistant) had worked hard enough at hs vacuum-pump; the beam was made up of moving charges. All t h s was preliminary to J.J.’s crucial experiment.

For the experiment which J.J. chose to describe as the most si&cant one, he had a Crookes tube made with a small hole in a plate so as to form a narrow beam, and a small metal cup to collect what came through. Just inside the tube there were electrodes to impose an electric field on the beam, and when they were energised they diverted the beam out of the cup. Also, just outside the tube, there were the poles of a magnet whch could also &vert the beam. If the electric and magnetic fields were suitably adjusted they could oppose each other exactly and the beam could again enter the cup (see Fig. 3) . From the ratio of the two fields when they are balanced like this, it is possible to calculate the ratio of charge to mass, usually written as e/m. It turned out to be about 70 &on coulombs per gram, far bigger than the 70 000 for hydrogen atoms in a liquid. Combining this result with that for the charge, found in the first experiment, the mass of the electron can be calculated. From J.J.’s experiments, not very accurate, it was about 1 /lo00 of the mass of a hydrogen atom. (The true figure is about 1/1840.)

Interpreting the experimental results

Although this was how J.J. chose to describe his work, he was hiding the fact that he did the second experiment first, or strictly spealung one of the less convincing earlier experiments that led h m to the main one. So now we can see hs problem and why he took so long to publish h s result. He had the 70-

million figure before he knew the electric charge per atom. How could he explain the result? Either the carriers were hydrogen atoms carrying a charge of a thousand times as big as those they carry in liquids, or the carriers had the same charge as the hydrogen ions in a liquid but only one thousandth of the mass. The suggestion of the large charge was not convincing; chemical molecules are usually formed with s m a l l numbers of atoms, such as the seven that make up HzSO4. Why should a compound of hydrogen with electricity have something like 1000 atoms of elec- tricity to one of hydrogen? So J.J. believed that he had found ‘corpuscles’ (whch simply means ‘little bodies’) having masses far smaller than that of the hydrogen

Fig. 3 The principle of the e/m experiment

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atom. Ths was literally incredble to most of hs contemporaries, who knew very well that atoms were indivisible and that the hydrogen atom was the smallest of them.

Notice that J.J. d d not call hs particles ‘electrons’ even though the name had already been invented by Johnstone Stoney of Dublin to describe the atom of electricity which was implied by Faraday’s work on liquids. There was an important distinction. J.J. had found that the carriers had mass, even though it was very small. But it could never have crossed Stoney’s mind that the electrical atom had mass at all. So J.J.’s corpuscles were not the objects that Stoney was hoping to find. J.J. kept to ‘corpuscle’ until 1921; by that time everybody agreed that the carriers had mass, and everybody else was c&ng them electrons, so J.J. did so too.

The electron’s role in the atom

J.J.’s first thoughts about the corpuscles being exactly the same whatever atom they were derived &om was that evidently all atoms were made up of eleccrons- about 1000 for a hydrogen atom, 12000 for a carbon atom, and so on. It was not the first time that a theory of t h s sort had been put forward. Prout, a chemist in the early 1800s, had noticed that many atomic weights were integral multiples of the weight of a hydrogen atom, and suggested that all atoms were built up of hydrogen. Ths was ‘Prout’s Hypothesis’. It was

abandoned when it became clear that some atomic weights were not integers-that of chlorine, for example, was 35.5. Now J.J. briefly revived Prout’s Hypothesis with large numbers of electrons instead of hydrogen. The main difficulty with this idea is to see why some numbers of electrons such as 1000 formed a stable body but other numbers did not.

J.J.’s next idea was that as the corpuscles carried a negative charge there must be a positive charge somewhere to balance it. He assumed that the negative charge was hghly concentrated, whereas the positive was spread out uniformly as a sort ofjelly with no particular structure. This is remembered nowadays rather disrespectfully as’his Currant Bun theory of the atom, the electrons being the currants.

Could t h s be a stable arrangement? J.J. knew of a demonstration by an American named Mayer who had already noticed the stabhty of rings of small magnets in an external field. The corresponding experiment with electric charges is not possible, but the condtions are substantially the same as for long magnets in a magnetic field. J.J. was so impressed by the experiment that he used to include it in his lectures, although by 1933 he merely showed the results on lantern slides. The sigmficant feature is that as each new unit is added, the number in an inmost ring increases up to five or s i x , and then a new ring forms inside it (see Fig. 4). J.J. thought that, in the Periodic Table of the elements, each step down &om one line to the next corresponded to the formation of a new ring. J.J. was stdl describing

Mayer’s experiment in 1933, even although everyone else had come to believe that it was the outside electrons, not the inside ones, that defined the chemical properties.

Other speculations

It looks as though J.J. was uneasy about the mass of the electron, so dXerent from that of the atom and contradicting the idea that the hydrogen atom had the smallest possible mass and could not be divided. He thought it might not be the ordinary sort of mass affected by gravitation, but something else. Remember that J.J. and a l l his contemporaries believed in an ether whch had mass (see the Panel on ‘The ether’). If an electric charge moved, the ether had to redistribute itself around the moving body, and so an electron, even if it had no mass of its own, would have to move the mass of ether surrounding it. (Compare a bubble in water, which appears

Fig. 4 magnets and the lines have been added to show that they form rings as claimed

Patterns produced in Mayer‘s experiment. The spots represent the floating

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to have Aass because if the bubble moves then some water has to move too.) From ths argument J.J. calculated what size an electron must be ifit had no true mass of its own. The answer was a diameter of metres. As the diameter of an atom in a solid was thought to be much larger (more like lo-’” m) this was a satisfjiing result, although it had to be abandoned later.

JJ.’s experiments had shown that the electrons in the Crookes tube were travelling very fast-round about a fifth of the velocity of light, far faster than anythng else had ever been known to move. It meant that the energy of the electrons was large, and he calculated what it would be if it could somehow be released from them: the energy from 1 gram of electrons would lift a d o n tons to a height of a few hundred yards. Perhaps it is easier to imagine lifting a large shp (for example, the Queen Ma~y) to a height of about five miles. J.J.5 estimate may be compared ulth the one that Einstein made a few years later from h s famous formula E = mc2; Einstein’s figure is the larger, but by a factor of only 100.

The really serious d6culty in the theory was: Are the electrons moving in regular orbits? Probably yes. Then why don’t they lose energy all the time by radntion? Classical electromagnetic theory shows that they must; and as this was the theory that JJ. had used to discover the electron in the first place, he could hardly reject it now. But J.J. was always resourcefh- perhaps too much so-in finding an escape &om dfficulties. He pointed out that if there are a number of electrons all following the same orbit, the radiation from them is greatly decreased. Some tentative calculations showed that the radation from s i x electrons in the same orbit might be less than that from a single one in the ratio 10”. This would allow electrons to lose energy slowly over a long time. J.J. did not extend h s study to twelve electrons (why not, I wonder?) but if he had, the factor would have become about and then the energy in the electrons could have lasted for about a d o n years. As Kelvin was convinced that the earth and the sun could not possibly have been created more than 100000 years ago, J.J. would then have had an explanation of why all the electrons have not yet vanished. Fortunately a very dfferent explanation was invented a few years later.

Bohr takes over the electron

This was as far as J.J. could get with his theory. He knew of course that it was incomplete. Subsequent develop- ments were on very different lines. In 1900, Planck published a new formula for the energy of the radiation &om a hot body It contained a mysterious constant whch was not understood, but whch certainly made the formula fit the experimental results. Five years later, Einstein (not yet famous for his relativity theory) published a theory of the photoelectric effect, and ths , too, had a constant in it to make the theory fit the experiments. To everybody’s surprise, the two

J.J.’s tenacious beliefs graduate, I attended J.J.’s lectures on

of electricity in gases’. A few JJ’s published lectures on (Yale, 1904), I reahsed that

seIhadheardin1933.H -1910 ideas for so lon

clues in the biographes of JJ. swer must be that he was a sceptic, not to believe the new theories, and that he had tact wrth advanced research from 1914 Alternatively we might say that he was all

to investgate several theories simul- n if they were incompatible; ths

may not have believed in any of gly. He was sad to beheve that the

r a theory was a good one was not true but whether it suggested some

s us thatJ.J. used to point out that there d number ofphysical constants &om

results can be put together, and ories can therefore lead to sirmlar like those of electron energies ons and &om Einstein’s. Ths es works well, but sometimes it

constants turned out to be equal. Planck hmselfwas unhappy about it; probably he was s d feeling uneasy about having had to introduce it at all. But now it seemed to be a general-purpose constant. An Enghsh mathematician, Nicholson, showed that it was of the right order of magnitude to describe the energy of an electron in orbit round a positive charge, if we could assume that the energy was not being constantly radiated away.

Then in 1908 the Danish physicist Niels Bohr took the decisive step: he put forward a theory that, on the atomic scale, charges in motion do not normally radlate. If they are disturbed, then-and only then- they may radlate energy, or perhaps absorb it; and they do so in little packets of radation which consist of one quantum each. The assumption was a brdhant success. Apply Bohr‘s theory and Planck’s constant to the hydrogen atom, and you can calculate the exact wavelengths of all the strongest lines in the spectrum of hydrogen glowing in an electric discharge. Bohr‘s atom was like a miniature version of the sun and the planets, except that it was held together by electrical attraction rather than gravity.

The next step in ideas about atomic structure came from Rutherford in 1911, when he fired alpha particles from radum at a metal foil. Alpha particles are positively charged and by atomic standards rather heavy projectiles, but most of them went straight through, apparently without damage to either themselves or the foils. Just a few-a few in many thousands-were

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deflected, some through quite large angles. Ths implied that there were some highly-concentrated positive charges located in the foils but that they were so far apart from each other that there were wide spaces between them through whch most of the alpha particles could pass S-eely. (It was the very low rate of direct hits that made Rutherford so sceptical about ever deriving energy &om nuclear reactions.) The separation between the charges was of course the distance between atoms in a solid, which was already known. But the small size of the positive nuclei, to allow sufficient open space between them, was a shock. Their diameters had to be of the order of m, roughly the same as the diameter J.J. had calculated for the electron. Orbiting electrons of the same size as the nuclei would not be inconceivable, but they are implausible.

The Rutherford-Bohr model of the atom with its non-radating orbits was one that J.J. would never have imagined possible. It denied an important result in classical theory, whch had been so successful in the design of electrical machinery and in so many laboratory experiments, including J.J.’s own. JJ. probably never directly contradicted Bohr’s own ideas, but he seems to have accepted them only as an alternative to h s own ideas of atomic structure in the lectures he was giving to undergraduates even as late as 1933, when I went to them (see the Panel on ‘J.J.3 tenacious beliefs’).

The other half of the electron

In the 1920s the old controversy about whether light consists of waves or particles came to an end with the answer that it was both at the same time. If light can be both waves and particles at the same time, why not electrons too? Indeed &action patterns between beams of electrons were observed in the late 1920s, and one of the observers was J.J.s own son, Professor Sir George Thomson. Now reconsider the electron orbits referred to above. If the electron is a set of waves forming a circle round the nucleus, it must consist of an integral number of waves; 3% waves could not join to form a circle. This offers a simple picture of why only certain orbits are possible, and why the electron must jump &om one to another without going by a continuous path in between. Ths dual nature of the electron is the explanation of the title of ths article. J.J. dwovered only half the electron; but it was arguably the more important haK

Even after a hundred years we know little about the electron; only its mass, its charge, and a property described as ‘spin’-it behaves as if it were spinning at a k e d rate. We have no photograph of one; the nearest we can get is a picture of where one has been in a cloud-chamber, where it produces vapour-trails exactly like those sometimes left by hgh-flying aircraft. A fast-moving electron leaves a straight trd, a slow one shows how it is pushed around by atomic nuclei and by other electrons (Fig. 2).

J.J.’s other great discovery

This was not the end of J.J.’s career as an experimental physicist. From about 1904 onwards, he investigated the carriers of positive electricity, whch proved to be atoms from whch one or more electrons had been temporarily lost. So far ths was not surprising. Experiments had become easier; the use of a photographic plate inside a vacuum chamber shows how the t e c h q u e had improved in ten years. In 1897 it had been half a day’s hard work to pump the system out, but in 1908 it could be done in a few minutes, so there was no objection to opening the chamber to change the plate and then re-establishing the vacuum.

When he examined the carriers in neon gas, he found there were particles having two Herent values of e/m, as ifit were a mixture of two dfferent gases. His colleague E W; Aston showed that neon existed in two forms, having atomic weights of 20 and 22, mixed to produce an average value of 20.2. Such variants, known as isotopes, were already known in rachoactive materials, but ths was the first mscovery of isotopes of stable atoms. Chlorine was another example, being a mixture of atomic weights 35 and 37 to produce an average of 35.5. Prout’s hypothesis was right after all: atomic weights were (nearly) integers, but the building blocks were the nuclei of hydrogen atoms rather than the complete atom. These now became known as ‘protons’. J.J. had made a second important advance in atomic physics.

In 1914 J.J. was dverted to the assessment of proposals for scien&c warfare, and then in 1918 he became Master of Trinity College, a full-time post which he Ned admirably. His former student Ernest (later Lord) Rutherford took over the Cavendsh Laboratory and made it even more famous than before. JJ. remained gently sceptical of the new developments in physics whch he h s e l f had set in motion; but he had shaken the subject out of its nineteenth-century torpor and laid the foundations for modern physics and for the electronic industries whch have transformed our everyday lives.

References

1 THOMSON, J. J.: ‘Recollections and reflections’ (Eiell, London, 1936)

2 Lord RAYLEIGH: ‘The life of Sir J. J. Thomson’ (University Press, Cambridge, 1942)

3 WEAIIIE, D.: ‘Young man in a hurry’, Physics Wovld, Sep- tember 1995, pp.28-30 (for Townsend’s letters to Fitzgerald)

4 THOMSON, G. €?: ‘J. J. Thomson and the Cavendish Laboratory’ (Nelson, London, 1964)

0 IEE: 1997

This article is based on the lecture given by the author at the IEE, Savoy Place on 12th March 1997.

Dr. Arnold Lynch is an Honorary Research Fellow in the Dept. of Electronic Engineering, University College, London; correspondence can be addressed to him at 8 Heath Drive, Potters Bar, Herts., EN6 lEH, UK. He is an IEE Fellow.

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