The Danish Peace Academy

SCIENCE AND SOCIETY

John Avery
H.C. Ørsted Institute, University of Copenhagen

Chapter 13 ATOMIC AND NUCLEAR PHYSICS

The discovery of electrons

In the late 1880’s and early a 1890’s, a feeling of satisfaction, perhaps even smugness, prevailed in the international community of physicists. It seemed to many that Maxwell’s electromagnetic equations, together with Newton’s equations of motion and gravitation, were the fundamental equations which could explain all the phenomena of nature.

Nothing remained for physicists to do (it was thought) except to apply these equations to particular problems and to deduce the consequences. The inductive side of physics was thought to be complete.

However, in the late 1890’s, a series of revolutionary discoveries shocked the physicists out of their feeling of complacency and showed them how little they really knew. The first of these shocks was the discovery of a subatomic particle, the electron. In Germany, Julius Plücker (1801-1868), and his friend, Heinrich Geisler (1814-1879), had discovered that an electric current could be passed through the gas remaining in an almost completely evacuated glass tube, if the pressure were low enough and the voltage high enough. When this happened, the gas glowed, and sometimes the glass sides of the tube near the cathode (the negative terminal) also glowed. Pl¨ucker found that the position of the glowing spots on the glass near the cathode could be changed by applying a magnetic field.

In England, Sir William Crookes (1832-1919) repeated and improved the experiments of Plücker and Geisler: He showed that the glow on the glass was produced by rays of some kind, streaming from the cathode; and he demonstrated that these “cathode rays” could cast shadows, that they could turn a small wheel placed in their path, and that they heated the glass where they struck it.

Sir William Crookes believed that the cathode rays were electrically charged particles of a new kind - perhaps even a “fourth state of matter”. His contemporaries laughed at these speculations; but a few years later a brilliant young physicist named J.J.Thomson (1856-1940), working at Cambridge University, entirely confirmed Crookes’ belief that the cathode rays were charged particles of a new kind.

Thomson, an extraordinarily talented young scientist, had been appointed full professor and head of the Cavendish Laboratory at Cambridge at the age of 27. His predecessors in this position had been James Clerk Maxwell and the distinguished physicist, Lord Rayleigh, so the post was quite an honor for a man as young as Thomson. However, his brilliant performance fully justified the expectations of the committee which elected him. Under Thomson’s direction, and later under the direction of his student, Ernest Rutherford, the Cavendish Laboratory became the world’s greatest center for atomic and subatomic research; and it maintained this position during the first part of the twentieth century.

J.J. Thomson’s first achievement was to demonstrate conclusively that the “cathode rays” observed by Pl¨ucker, Geisler and Crookes were negatively charged particles. He and his students also measured their ratio of charge to mass. If the charge was the same as that on an ordinary negative ionthen the mass of the particles was astonishingly small - almost two thousand times smaller than the mass of a hydrogen atom! Since the hydrogen atom is the lightest of all atoms, this indicated that the cathode rays were subatomic particles.

The charge which the cathode rays particles carried was recognized to be the fundamental unit of electrical charge, and they were given the name “electrons”. All charges observed in nature were found to be integral multiples of the charge on an electron. The discovery of the electron was the first clue that the atom, thought for so long to be eternal and indivisible, could actually be torn to pieces.

X-rays

In 1895, while the work leading to the discovery of the electron was still going on, a second revolutionary discovery was made. In the autumn of that year, Wilhelm Konrad Roentgen (1845-1923), the head of the department of physics at the University of W¨urtzburg in Bavaria, was working with a discharge tube, repeating some of the experiments of Crookes.

Roentgen was especially interested in the luminescence of certain materials when they were struck by cathode rays. He darkened the room, and turned on the high voltage. As the current surged across the tube, a flash of light came from an entirely different part of the room! To Roentgen’s astonishment, he found that a piece of paper which he had coated with barium platinocyanide was glowing brightly, even though it was so far away from the discharge tube that the cathode rays could not possibly reach it!

Roentgen turned off the tube, and the light from the coated paper disappeared. He turned on the tube again, and the bright glow on the screen reappeared. He carried the coated screen into the next room. Still it glowed! Again he turned off the tube, and again the screen stopped glowing. Roentgen realized that he had discovered something completely strange and new. Radiation of some kind was coming from his discharge tube, but the new kind of radiation could penetrate opaque matter!

Years later, when someone asked Roentgen what he thought when he discovered X-rays, he replied: “I didn’t think. I experimented!” During the next seven weeks he experimented like a madman; and when he finally announced his discovery in December, 1895, he was able to report all of the most important properties of X-rays, including their ability to ionize gases and the fact that they cannot be deflected by electric or magnetic fields. Roentgen correctly believed X-rays to be electromagnetic waves, just like light waves, but with very much shorter wavelength.

It turned out that X-rays were produced by electrons from the cathode of the discharge tube. These electrons were accelerated by the strong electric field as they passed across the tube from the cathode (the negative terminal) to the anode (the positive terminal). They struck the platinum anode with very high velocity, knocking electrons out of the inner parts of the platinum atoms. As the outer electrons fell inward to replace these lost inner electrons, electromagnetic waves of very high frequency were emitted.

On January 23, 1896, Roentgen gave the first public lecture on X-rays; and in this lecture he demonstrated to his audience that Xray photographs could be used for medical diagnosis. When Roentgen called for a volunteer from the audience, the 79 year old physiologist, Rudolf von K¨olliker stepped up to the platform, and an X-ray photograph was taken of the old man’s hand. The photograph, still in existence, shows the bones beautifully.

Wild enthusiasm for Roentgen’s discovery swept across Europe and America, and soon many laboratories were experimenting with X-rays.

The excitement about X-rays led indirectly to a third revolutionary discovery - radioactivity.

Radioactivity

On the 20th of January, 1896, only a month after Roentgen announced his discovery, an excited crowd of scientists gathered in Paris to hear the mathematical physicist Henri Poincar´e lecture on Roentgen’s Xrays. Among them was Henri Becquerel (1852-1908), a professor of physics working at the Paris Museum of Natural History and the ´Ecole Polytechnique. Becquerel, with his neatly clipped beard, looked the very picture of a 19th century French professor; and indeed, he came from a family of scientists. His grandfather had been a pioneer of electrochemistry, and his father had done research on fluorescence and phosphorescence.

Like his father, Henri Becquerel was studying fluorescence and phosphorescence; and for this reason he was especially excited by the news of Roentgen’s discovery. He wondered whether there might be X-rays among the rays emitted by fluorescent substances. Hurrying to his laboratory, Becquerel prepared an experiment to answer this question.

He wrapped a large number of photographic plates in black paper, so that ordinary light could not reach them. Then he carried the plates outdoors into the sunlight, and on each plate he placed a sample of a fluorescent compound from his collection. After several hours of exposure, he developed the plates. If X-rays were present in the fluorescent radiation, then the photographic plates should be darkened, even though they were wrapped in black paper.

When he developed the plates, he found, to his excitement, that although most of them were unaffected, one of the plates was darkened!

This was the plate on which he had placed the compound, potassium uranium sulfate. Experimenting further, Becquerel found other compounds which would darken the photographic plates - sodium uranium sulfate, ammonium uranium sulfate and uranium nitrate. All were compounds of uranium!

At the end of February, Becquerel made his first report to the French Academy of Sciences; and until the end of March, he brought a new report every week, describing new properties of the remarkable radiation from uranium compounds. Then the weather turned against him, and for many weeks, Paris was covered with thick clouds. Too impatient to wait for sunshine, Becquerel continued his experiments in cloudy weather, hoping that even without direct sunlight there would be some slight effect.

To his astonishment, the plates were blackened as much as before, although without direct sunlight the fluorescence of the uranium compounds was much diminished! Could it be that the mysterious penetrating radiation from the uranium compounds was independent of fluorescence? To answer this question, Becquerel next tried placing the uranium-containing compounds on photographic plates in a completely darkened room. Still the plates were blackened! The effect was completely independent of exposure to sunlight!

This was indeed something completely new and strange: The radiation seemed to come from the uranium atoms themselves, rather than from chemical changes in the compounds to which the atoms belonged.

If the energy of Becquerel’s rays did not come from sunlight, what was its source? Two of the most basic assumptions of classical science seemed to be challenged - the indivisibility of the atom and the conservation of energy.

Marie and Pierre Curie

Among Henri Becquerel’s colleagues in Paris were two dedicated and talented scientists, Marie and Pierre Curie. As a boy, Pierre Curie (1859-1906), the son of an intellectual Parisian doctor, had never been to school. His father had educated him privately, recognizing that his son’s original and unworldly mind was unsuited for an ordinary education. At the age of 16, Pierre Curie had become a Bachelor of Science, and at 18, he had a Master’s degree in physics. Together with his brother, Jacques, Pierre Curie had discovered the phenomenon of piezoelectricity - the electrical potential produced when certain crystals, such as quartz, are compressed. He had also discovered a law governing the temperature-dependence of magnetism, “Curie’s Law”. Although Pierre Curie had an international reputation as a physicist, his position as chief of the laboratory at the School of Physics and Chemistry of the City of Paris was miserably paid; and his modest, unworldly character prevented him from seeking a better position. He only wanted to be allowed to continue his research.

In 1896, when Becquerel announced his revolutionary discovery of radioactivity, Pierre Curie was newly married to a Polish girl, much younger than himself, but equally exceptional in character and ability. Marie Sklodowska Curie (1867-1934) had been born in Warsaw, in a Poland which did not officially exist, since it had been partitioned between Germany, Austria and Russia. Her father was a teacher of mathematics and physics and her mother was the principal of a girl’s school.

Marie Sklodowska’s family was a gifted one, with strong intellectual traditions; but it was difficult for her to obtain a higher education in Poland. Her mother died, and her father’s job was withdrawn by the government. Marie Sklodowska was forced to work in a humiliating position as a governess in a uncultured family, meanwhile struggling to educate herself by reading books of physics and mathematics. She had a romance with the son of a Polish landowning family; but in the end, he rejected her because of her inferior social position.

Marie Sklodowska transmuted her unhappiness and humiliation into a fanatical devotion to science. She once wrote to her brother: “You must believe yourself to be born with a gift for some particular thing; and you must achieve that thing, no matter what the cost.” Although she could not know it at the time, she was destined to become the greatest woman scientist in history.

Marie Sklodowska’s chance for a higher education came at last when her married sister, who was studying medicine in Paris, invited Marie to live with her there and to enroll in the Sorbonne. After living in Paris with her sister for a year while studying physics, Marie found her sister’s household too distracting for total concentration. She moved to a tiny, comfortless garret room, where she could be alone with her work.

Rejecting all social life, enduring freezing temperatures in winter, and sometimes fainting from hunger because she was too poor to afford proper food, Marie Sklodowska was nevertheless completely happy because at last she had the chance to study and to develop her potentialities. She graduated from the Sorbonne at the top of her class. Pierre Curie had decided never to marry. He intended to devote himself totally to science; but when he met Marie, he recognized in her a person with whom he could share his ideals and his devotion to his work. After some hesitation by Marie, to whom the idea of leaving Poland forever seemed like treason, they were married. They spent a happy honeymoon touring the countryside of France on a pair of bicycles.

The next step for the young Polish student, who had now become Madame Curie, was to begin research for a doctor’s degree; and she had to decide on a topic of research. The year was 1896, and news of Becquerel’s remarkable discovery had just burst upon the scientific world. Marie Curie decided to make Becquerel’s rays the topic of her thesis.

Using a sensitive electrometer invented by Pierre and Jacques Curie, she systematically examined all the elements to see whether any others besides uranium produced the strange penetrating rays. Almost at once, she made an important discovery: Thorium was also radioactive; but besides uranium and thorium, none of the other elements made the air of her ionization chamber’ conduct electricity, discharging the electrometer. Among the known elements, only uranium and thorium were radioactive.

Next, Marie Curie tested all the compounds and minerals in the collection at the School of Physics. One of the minerals in the collection was pitchblend, an ore from which uranium can be extracted. She of course expected this uranium-containing ore to be radioactive; but to her astonishment, her measurements showed that the pitchblende was much more radioactive than could be accounted for by its content of uranium and thorium!

Since both Marie Curie’s own work, and that of Becquerel, had shown radioactivity to be an atomic property, and since, among the known elements, the only two radioactive ones were uranium and thorium, she and her husband were forced to the inescapable conclusion that the pitchblende must contain small traces of a new, undiscovered, highly radioactive element, which had escaped notice in the chemical analysis of the ore.

At this point, Pierre Curie abandoned his own research and joined Marie in an attempt to find the unknown element which they believed must exist in pitchblende. By July, 1898, they had isolated a tiny amount of a new element, a hundred times more radioactive than uranium. They named it “polonium” after Marie’s native country.

By this time, however, they had discovered that the extra radioactivity of pitchblende came from not one, but at least two new elements. The second undiscovered element, however, was enormously radioactive, and present only in infinitesimal concentrations. They realized that, in order to isolate a weighable amount of it, they would have to begin with huge amounts of raw pitchblende ore.

The Curies wrote to the directors of the mines at St. Joachimsthal in Bohemia, where silver was extracted from pitchblende, and begged for a few tons of the residue left after the extraction process. When they received a positive reply, they spent their small savings to pay the transportation costs.

The only place the Curies could find to work with the pitchblende ore was an old shed with a leaky roof - a chillingly cold place in the winter. Remembering the four years which she and her husband spent in this shed, Marie Curie wrote:

“This period was, for my husband and myself, the heroic period of our common existence... It was in this miserable old shed that the best and happiest years of our lives were spent, entirely consecrated to work.

I sometimes passed the whole day stirring a boiling mass of material with an iron rod nearly as big as myself. In the evening, I was broken with fatigue... I came to treat as many as twenty kilograms of matter at a time, which had the effect of filling the shed with great jars full of precipitates and liquids. It was killing work to carry the receivers, to pour off the liquids and to stir for hours at a stretch the boiling matter in a smelting basin.”

Marie and Pierre Curie began by separating the ore into fractions by various chemical treatments. After each treatment, they tested the fractions by measuring their radioactivity. They could easily see which fraction contained the highly radioactive unknown element. The new element, which they named “radium”, had chemical properties almost identical to those of barium; and the Curies found that it was almost impossible to separate radium from barium by ordinary chemical means. In the end, they resorted to fractional crystalization, repeated several thousand times. At each step, the radium concentration of the active fraction was slightly enriched, and the radioactivity became progressively stronger. Finally it was two million times as great as the radioactivity of uranium. One evening, when Marie and Pierre Curie entered their laboratory without lighting the lamps, they saw that all their concentrated samples were glowing in the dark. After four years of backbreaking labor, the Curies isolated a small amount of pure radium and measured its atomic weight. This achievement, together with their other work on radioactivity, brought them the 1903 Nobel Prize in Physics (shared with Becquerel), as well as worldwide fame. Madame Curie, the first great woman scientist in history, became a symbol of what women could do. The surge of public enthusiasm, which had started with Roentgen’s discovery of X-rays, reached a climax with Madame Curie’s isolation of radium.

It had been discovered that radium was helpful in treating cancer; and Madame Curie was portrayed by newspapers of the period as a great humanitarian. Indeed, the motives which inspired Marie and Pierre Curie to their heroic labors were both humanitarian and idealistic.

They believed that only good could come from any increase in human knowledge. They did not know that radium is also a dangerous element, capable of causing cancer as well as curing it; and they could not forsee that research on radioactivity would eventually lead to nuclear weapons.

Rutherford’s model of the atom

In 1895, the year during which Roentgen made his revolutionary discovery of X-rays, a young New Zealander named Ernest Rutherford was digging potatoes on his father’s farm, when news reached him that he had won a scholarship for advanced study in England. Throwing down his spade, Rutherford said, “That’s the last potato I’ll dig!” He postponed his marriage plans and sailed for England, where he enrolled as a research student at Cambridge University. He began work at the Cavendish Laboratory, under the leadership of J.J. Thomson, the discoverer of the electron.

In New Zealand, Rutherford had done pioneering work on the detection of radio waves, and he probably would have continued this work at Cambridge, if it had not been for the excitement caused by the discoveries of Roentgen and Becquerel. Remembering this period of his life, Rutherford wrote:

“Few of you can realize the enormous sensation caused by the discovery of X-rays by Roentgen in 1895. It interested not only the scientific man, but also the man in the street, who was excited by the idea of seeing his own insides and his bones. Every laboratory in the world took out its old Crookes’ tubes to produce X-rays, and the Cavendish was no exception.”

J.J. Thomson, who was interested in studying ions (charged atoms or molecules) in gases, soon found that gaseous ions could be produced very conveniently by means of X-rays. Rutherford abandoned his research on radio waves, and joined Thomson in this work.

“When I entered the Cavendish Laboratory”, Rutherford remembered later, “I began to work on the ionization of gases by means of X-rays. After reading the paper of Becquerel, I was curious to know whether the ions produced by the radiation from uranium were of the same nature as those produced by X-rays; and in particular, I was interested because Becquerel thought that his radiation was somehow intermediate between light and X-rays.”

“I therefore proceeded to make a systematic examination of the radiation, and I found that it was of two types - one which produced intense ionization, and which was absorbed by a few centimeters of air, and the other, which produced less intense ionization, but was more penetrating. I called these alpha rays and beta rays respectively; and when, in 1898, Villard discovered a still more penetrating type of radiation, he called it gamma-radiation.”

Rutherford later showed that the alpha-rays were actually ionized helium atoms thrown out at enormous velocities by the decaying uranium, and that beta-rays were high-speed electrons. The gamma-rays turned out to be electromagnetic waves, just like light waves, but of extremely short wavelength.

Rutherford returned briefly to New Zealand to marry his sweetheart, Mary Newton; and then he went to Canada, where he had been offered a post as Professor of Physics at McGill University. In Canada, with the collaboration of the chemist, Frederick Soddy (1877-1956), Rutherford continued his experiments on radioactivity, and worked out a revolutionary theory of transmutation of the elements through radioactive decay.

During the middle ages, alchemists had tried to change lead and mercury into gold. Later, chemists had convinced themselves that it was impossible to change one element into another. Rutherford and Soddy now claimed that radioactive decay involves a whole series of transmutations, in which one element changes into another!

Returning to England as head of the physics department at Manchester University, Rutherford continued to experiment with alpha-particles. He was especially interested in the way they were deflected by thin metal foils. Rutherford and his assistant, Hans Geiger (1886-1945), found that most of the alpha-particles passed through a metal foil with only a very slight deflection, of the order of one degree.

In 1911, a young research student named Ernest Marsden joined the group, and Rutherford had to find a project for him. What happened next, in Rutherford’s own words, was as follows:

“One day, Geiger came to me and said, ‘Don’t you think that young Marsden, whom I’m training in radioactive methods, ought to begin a small research?’ Now I had thought that too, so I said, ‘Why not let him see if any alpha-particles can be scattered through a large angle?’

I may tell you in confidence that I did not believe that they would be, since we knew that the alpha-particle was a very fast, massive particle, with a great deal of energy; and you could show that if the scattering was due to the accumulated effect of a number of small scatterings, the chance of an alpha-particle’s being scattered backward was very small.”

“Then I remember two or three days later, Geiger coming to me in great excitement and saying, ‘We have been able to get some of the alpha-particles coming backwards’. It was quite the most incredible event that has ever happened to me in my life. 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 must be the result of a single collision, and when I made calculations, I found that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus.”

“It was then that I had the idea of an atom with a minute massive center carrying a charge. I worked out mathematically what laws the scattering should obey, and found that the number of particles scattered through a given angle should be proportional to the thickness of the scattering foil, the square of the nuclear charge, and inversely proportional to the fourth power of the velocity. These deductions were later verified by Geiger and Marsden in a series of beautiful experiments.”

Planck, Einstein and Bohr

According to the model proposed by Rutherford in 1911, every atom has an extremely tiny nucleus, which contains almost all of the mass of the atom. Around this tiny but massive nucleus, Rutherford visualized light, negatively-charged electrons circulating in orbits, like planets moving around the sun. Rutherford calculated that the diameter of the whole atom had to be several thousand times as large as the diameter of the nucleus.

Rutherford’s model of the atom explained beautifully the scattering experiments of Geiger and Marsden, but at the same time it presented a serious difficulty: According to Maxwell’s equations, the electrons circulating in their orbits around the nucleus ought to produce elec- tromagnetic waves. It could easily be calculated that the electrons in Rutherford’s atom ought to lose all their energy of motion to this radiation, and spiral in towards the nucleus. Thus, according to classical physics, Rutherford’s atom could not be stable. It had to collapse.

The paradox was solved by Niels Bohr (1885-1962), a gifted young theoretical physicist from Copenhagen who had come to Manchester to work with Rutherford. Bohr was not at all surprised by the failure of classical concepts when applied to Rutherford’s nuclear atom. Since he had been educated in Denmark, he was more familiar with the work of German physicists than were his English colleagues at Manchester. In particular, Bohr had studied the work of Max Planck (1858-1947) and Albert Einstein (1879-1955).

Just before the turn of the century, the German physicist, Max Planck, had been studying theoretically the electromagnetic radiation coming from a small hole in an oven. The hole radiated as though it were an ideally black body. This “black body radiation” was very puzzling to the physicists of the time, since classical physics failed to explain the frequency distribution of the radiation and its dependence on the temperature of the oven.

In 1901, Max Planck had discovered a formula which fitted beautifully with the experimental measurements of the frequency distribution of black body radiation; but in order to derive his formula, he had been forced to make a radical assumption which broke away completely from the concepts of classical physics.

Planck had been forced to assume that light (or, more generally, electromagnetic radiation of any kind) can only be emitted or absorbed in amounts of energy which Planck called “quanta”. The amount of energy in each of these “quanta” was equal to the frequency of the light multiplied by a constant, h, which came to be known as “Planck’s constant”.

This was indeed a strange assumption! It seemed to have been pulled out of thin air; and it had no relation whatever to anything that had been discovered previously in physics. The only possible justification for Planck’s quantum hypothesis was the brilliant success of his formula in explaining the puzzling frequency distribution of the black body radiation. Planck himself was greatly worried by his own radical break with classical concepts, and he spent many years trying unsuccessfully to relate his quantum hypothesis to classical physics.

In 1905, Albert Einstein published a paper in the Annalen der Physik in which he applied Planck’s quantum hypothesis to the photoelectric effect. (At that time, Einstein was 25 years old, completely unknown, and working as a clerk at the Swiss Patent Office.) The photoelectric effect was another puzzling phenomenon which could not in any way be explained by classical physics. The German physicist Lenard had discovered in 1903 that light with a frequency above a certain threshold could knock electrons out of the surface of a metal; but below the threshold frequency, nothing at all happened, no matter how long the light was allowed to shine.

Using Planck’s quantum hypothesis, Einstein offered the following explanation for the photoelectric effect: A certain minimum energy was needed to overcome the attractive forces which bound the electron to the metal surface. This energy was equal to the threshold frequency multiplied by Planck’s constant. Light with a frequency equal to or higher than the threshold frequency could tear an electron out of the metal; but the quantum of energy supplied by light of a lower frequency was insufficient to overcome the attractive forces.

Einstein later used Planck’s quantum formula to explain the lowtemperature behavior of the specific heats of crystals, another puzzling phenomenon which defied explanation by classical physics. These contributions by Einstein were important, since without this supporting evidence it could be maintained that Planck’s quantum hypothesis was an ad hoc assumption, introduced for the sole purpose of explaining black body radiation.

As a student, Niels Bohr had been profoundly impressed by the radical ideas of Planck and Einstein. In 1912, as he worked with Rutherford at Manchester, Bohr became convinced that the problem of saving Rutherford’s atom from collapse could only be solved by means of Planck’s quantum hypothesis.

Returning to Copenhagen, Bohr continued to struggle with the problem. In 1913, he found the solution: The electrons orbiting around the nucleus of an atom had “angular momentum”. Assuming circular orbits, the angular momentum was given by the product of the mass and velocity of the electron, multiplied by the radius of the orbit. Bohr introduced a quantum hypothesis similar to that of Planck:

He assumed that the angular momentum of an electron in an allowed orbit, (multiplied by 2 pi), had to be equal to an integral multiple of Planck’s constant. The lowest value of the integer, n=1, corresponded to the lowest allowed orbit. Thus, in Bohr’s model, the collapse of Rutherford’s atom was avoided.

Bohr calculated that the binding energies of the various allowed electron orbits in a hydrogen atom should be a constant divided by the square of the integer n; and he calculated the value of the constant to be 13.5 electron-Volts. This value fit exactly the observed ionization energy of hydrogen. After talking with the Danish spectroscopist, H.M. Hansen, Bohr realized with joy that by combining his formula for the allowed orbital energies with the Planck-Einstein formula relating energy to frequency, he could explain the mysterious line spectrum of hydrogen.

When Niels Bohr published all this in 1913, his paper produced agonized cries of “foul!” from the older generation of physicists. When Lord Rayleigh’s son asked him if he had seen Bohr’s paper, Rayleigh replied: “Yes, I have looked at it; but I saw that it was of no use to me. I do not say that discoveries may not be made in that sort of way. I think very likely they may be. But it does not suit me.” However, as more and more atomic spectra and properties were explained by extensions of Niels Bohr’s theories, it became clear that Planck, Einstein and Bohr had uncovered a whole new stratum of phenomena, previously unsuspected, but of deep and fundamental importance.

Atomic numbers

Bohr’s atomic theory soon received strong support from the experiments of one of the brightest of Rutherford’s bright young men - Henry Moseley (1887-1915). Moseley came from a distinguished scientific family. Not only his father, but also both his grandfathers, had been elected to the Royal Society. After studying at Oxford, where his father had once been a professor, Moseley found it difficult to decide where to do his postgraduate work. Two laboratories attracted him: the great J.J. Thomson’s Cavendish Laboratory at Cambridge, and Rutherford’s laboratory at Manchester. Finally, he decided on Manchester, because of the revolutionary discoveries of Rutherford, who two years earlier had won the 1908 Nobel Prize for Chemistry.

Rutherford’s laboratory was like no other in the world, except J.J. Thomson’s. In fact, Rutherford had learned much about how to run a laboratory from his old teacher, Thomson. Rutherford continued Thomson’s tradition of democratic informality and cheerfulness. Like Thomson, he had a gift for infecting his students with his own powerful scientific curiosity, and his enthusiastic enjoyment of research.

Thomson had also initiated a tradition for speed and ingenuity in the improvisation of experimental apparatus - the so-called “sealingwax and string” tradition - and Rutherford continued it. Niels Bohr, after working with Rutherford, was later to continue the tradition of informality and enthusiasm at the Institute for Theoretical Physics which Bohr founded in Copenhagen in 1920.

Most scientific laboratories of the time offered a great contrast to the informality, enthusiasm, teamwork and speed of the Thomson- Rutherford-Bohr tradition. E.E. da C. Andrade, who first worked in Lenard’s laboratory at Heidelberg, and later with Rutherford at Manchester, has given the following description of the contrast between the two groups:

“At the Heidelberg colloquium, Lenard took the chair, very much like a master with his class. He had the habit, if any aspect of his work was being treated by the speaker, of interrupting with, ‘And who did that first?’ The speaker would reply with a slight bow, ‘Herr Geheimrat, you did that first’, to which Lenard answered, ‘Yes, I did that first’.” “At the Manchester colloquium, which met on Friday afternoons, Rutherford was, as in all his relations with the research workers, the boisterous, enthusiastic, inspiring friend, undoubtedly the leader but in close community with the led, stimulating rather than commanding, ‘gingering up’, to use a favourite expression of his, his team.”

Although Rutherford occasionally swore at his “lads”, his affection for them was very real. He had no son of his own, and he became a sort of father to the brilliant young men in his laboratory. Their nickname for him was “Papa”. Such was the laboratory which Harry Moseley joined in 1910. At almost the same time, Moseley’s childhood friend, Charles Darwin (the grandson of the “right” Charles Darwin), also joined Rutherford’s team.

After working on a variety of problems in radioactivity which were given to him by Rutherford, Moseley asked whether he and Charles Darwin might be allowed to study the spectra of X-rays. At first, Rutherford said no, since no one at Manchester had any experience with X-rays; “and besides”, Rutherford added with a certain amount of bias, “all science is either radioactivity or else stamp-collecting”. However, after looking more carefully at what was being discovered about X-rays, Rutherford gave his consent. In 1912, a revolutionary discovery had been made by the Munich physicist, Max von Laue (1879- 1960): It had long been known that because of its wavelike nature, white light can be broken up into the colors of the spectrum by means of a “diffraction grating” - a series of parallel lines engraved very closely together on a glass plate.

For each wavelength of light, there are certain angles at which the new wavelets produced by the lines of the diffraction grating reinforce each other instead of cancelling. The angles of reinforcement are different for each wavelength, and thus the different colors are separated by the grating.

Max von Laue’s great idea was to do the same thing with X-rays, using a crystal as a diffraction grating. The regular lines of atoms in the crystal, von Laue reasoned, would act be fine enough to fit the tiny wavelength of the X-rays, believed to be less than one ten-millionth of a centimeter.

Von Laue’s experiment, performed in 1912, had succeeded beautifully, and his new technique had been taken up in England by a father and son team, William Henry Bragg (1862-1942) and William Lawrence Bragg (1890-1971). The Braggs had used X-ray diffraction not only to study the spectra of X-rays, but also to study the structure of crystals. Their techniques were later to become one of the most valuable research tools available for studying molecular structure. Having finally obtained Rutherford’s permission, Moseley and Darwin threw themselves into this exciting field of study. Remembering his work with Harry Moseley, Charles Darwin later wrote:

“Working with Moseley was one of the most strenuous exercises I have ever undertaken. He was, without exception, the hardest worker I have ever known... There were two rules for his work: First, when you started to set up the apparatus for an experiment, you must not stop until it was set up. Second, when the apparatus was set up, you must not stop work until the experiment was done. Obeying these rules implied a most irregular life, sometimes with all-night sessions; and indeed, one of Moseley’s experteses was the knowledge of where in Manchester one could get a meal at three in the morning.” After about a year, Charles Darwin left the experiments to work on the theoretical aspects of X-ray diffraction. (He was later knighted for his distinguished contributions to theoretical physics.) Moseley continued the experiments alone, systematically studying the X-ray spectra of all the elements in the periodic system.

Niels Bohr had shown that the binding energies of the allowed orbits in a hydrogen atom are equal to Rydberg’s constant , R (named after the distinguished Swedish spectroscopist, Johannes Robert Rydberg), divided by the square of an integral “quantum number”, n. He had also shown that for heavier elements, the constant, R, is equal to the square of the nuclear charge, Z, multiplied by a factor which is the same for all elements. The constant, R, could be observed in Moseley’s studies of X-ray spectra: Since X-rays are produced when electrons are knocked out of inner orbits and outer electrons fall in to replace them, Moseley could use the Planck-Einstein relationship between frequency and energy to find the energy difference between the orbits, and Bohr’s theory to relate this to R.

Moseley found complete agreement with Bohr’s theory. He also found that the nuclear charge, Z, increased regularly in integral steps as he went along the rows of the periodic table: Hydrogen had Z=1, helium Z=2, lithium Z=3, and so on up to uranium with Z=92. The 92 electrons of a uranium atom made it electrically neutral, exactly balancing the charge of the nucleus. The number of electrons of an element, and hence its chemical properties, Moseley found, were determined uniquely by its nuclear charge, which Moseley called the “atomic number”.

Moseley’s studies of the nuclear charges of the elements revealed that a few elements were missing. In 1922, Niels Bohr received the Nobel Prize for his quantum theory of the atom; and he was able to announce at the presentation ceremony that one of Moseley’s missing elements had been found at his institute. Moseley, however, was dead.

He was one of the ten million young men whose lives were needlessly thrown away in Europe’s most tragic blunder - the First World War.

A wave equation for matter

In 1926, the difficulties surrounding the “old quantum theory” of Max Planck, Albert Einstein and Niels Bohr were suddenly solved, and its true meaning was understood. Two years earlier, a French aristocrat, Prince Louis de Broglie, writing his doctoral dissertation at the Sorbonne in Paris, had proposed that very small particles, such as electrons, might exhibit wavelike properties. The ground state and higher excited states of the electron in Bohr’s model of the hydrogen atom would then be closely analogous to the fundamental tone and higher overtones of a violin string.

Erwin SchrödingerAlmost the only person to take de Broglie’s proposal seriously was Albert Einstein, who mentioned it in one of his papers. Because of Einstein’s interest, de Broglie’s matter-waves came to the attention of other physicists. The Austrian theoretician, Erwin Schrödinger, working at Zürich, searched for the underlying wave equation which de Broglie’s matter-waves obeyed.

Schrödinger’s gifts as a mathematician were so great that it did not take him long to solve the problem. The Schrödinger wave equation for matter is now considered to be more basic than Newton’s equations of motion. The wavelike properties of matter are not apparent to us in our daily lives because the wave-lengths are extremely small in comparison with the sizes of objects which we can perceive. However, for very small and light particles, such as electrons moving in their orbits around the nucleus of an atom, the wavelike behavior becomes important.

Schrödinger was able to show that Niels Bohr’s atomic theory, including Bohr’s seemingly arbitrary quantization of angular momentum, can be derived by solving the wave equation for the electrons moving in the attractive field of the nucleus. The allowed orbits of Bohr’s theory correspond in Schrödinger’s theory to harmonics, similar to the fundamental harmonic and higher overtones of an organ pipe or a violin string. (If Pythagoras had been living in 1926, he would have rejoiced to see the deepest mysteries of matter explained in terms of harmonics!)

Bohr himself believed that a complete atomic theory ought to be able to explain the chemical properties of the elements in Mendeléev’s periodic system. Bohr’s 1913 theory failed to pass this test, but the new de Broglie-Schr¨odinger theory succeeded! Through the work of Pauli, Heitler, London, Slater, Pauling, Hund, Mulliken, H¨uckel and others, who applied Schrödinger’s wave equation to the solution of chemical problems, it became apparent that the wave equation could indeed (in principle) explain all the chemical properties of matter.

Strangely, the problem of developing the fundamental quantum theory of matter was solved not once, but three times in 1926! At the University of Göttingen in Germany, Max Born (1882-1970) and his brilliant young students Werner Heisenberg and Pascal Jordan solved the problem in a completely different way, using matrix methods. At the same time, a theory similar to the “matrix mechanics” of Heisenberg, Born and Jordan was developed independently at Cambridge University by a 24 year old mathematical genius named Paul Adrien Maurice Dirac. At first, the Heisenberg-Born-Jordan-Dirac quantum theory seemed to be completely different from the Schr¨odinger theory; but soon the Göttingen mathematician David Hilbert (1862-1943) was able to show that the theories were really identical, although very differently expressed.

Chapter 14: RELATIVITY.

Suggestions for further reading

1. Alfred Romer (editor), The Discovery of Radioactivity and Transmutation, Dover, New York (1964).
2. Marie Curie, Pierre Curie, Dover, New York (1963).
3. Eve Curie, Madame Curie, Pocket Books Inc., New York (1958).
4. Joseph Needham andWalter Pagel (editors), Background to Modern Science, Cambridge University Press (1938).
5. R. Harre (editor), Scientific Thought 1900-1960, A Selective Survey, Clarendon Press, Oxford (1969).
6. J.B. Birks (editor), Rutherford at Manchester, Heywood and Company Ltd., London (1962).
7. Niels Bohr, On the Constitution of Atoms and Molecules, W.A. Benjamin Inc., New York (1963).
8. S. Rosenthal (editor), Niels Bohr, His Life and Work, North Holland (1967).
9. Ruth Moore, Niels Bohr, the Man and the Scientist, Hodder and Stoughten, London (1967).
10. Bernard Jaffe, Moseley and the Numbering of the Elements, Heinemann, London (1971).
11. E.A. Hylleraas, Remaniscences from Early Quantum Mechanics of Two-Electron Atoms, Reviews of Modern Physics, 35, 421 (1963).

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