His first six weeks in Manchester he spent following “an introductory course on the experimental methods of radioactive research,” with Geiger and Marsden among the instructors.267 He continued pursuing his independent studies in electron theory. He began a lifelong friendship with a young Hungarian aristocrat, George de Hevesy, a radiochemist with a long, sensitive face dominated by a towering nose. De Hevesy’s father was a court councillor, his mother a baroness; as a child he had hunted partridge in the private game park of the Austro-Hungarian emperor Franz Josef next to his grandfather’s estate. Now he was working to meet a challenge Rutherford had thrown at him one day to separate radioactive decay products from their parent substances. Out of that work he developed over the next several decades the science of using radioactive tracers in medical and biological research, one more useful offspring of Rutherford’s casual but fecund paternity.
Bohr learned about radiochemistry from de Hevesy.268 He began to see connections with his electron-theory work. His sudden burst of intuitions then was spectacular. He realized in the space of a few weeks that radioactive properties originated in the atomic nucleus but chemical properties depended primarily on the number and distribution of electrons. He realized—the idea was wild but happened to be true—that since the electrons determined the chemistry and the total positive charge of the nucleus determined the number of electrons, an element’s position on the periodic table of the elements was exactly the nuclear charge (or “atomic number”): hydrogen first with a nuclear charge of 1, then helium with a nuclear charge of 2 and so on up to uranium at 92.
De Hevesy remarked to him that the number of known radio elements already far outnumbered the available spaces on the periodic table and Bohr made more intuitive connections. Soddy had pointed out that the radio elements were generally not new elements, only variant physical forms of the natural elements (he would soon give them their modern name, isotopes). Bohr realized that the radio elements must have the same atomic number as the natural elements with which they were chemically identical. That enabled him to rough out what came to be called the radioactive displacement law: that when an element transmutes itself through radioactive decay it shifts its position on the periodic table two places to the left if it emits an alpha particle (a helium nucleus, atomic number 2), one place to the right if it emits a beta ray (an energetic electron, which leaves behind in the nucleus an extra positive charge).
Periodic table of the elements. The lanthanide series (“rare earths”), beginning with lanthanum (57), and the actinide series, which begins with actinium (89) and includes thorium (90) and uranium (92), are chemically similar. Other families of elements read vertically down the table—at the far right, for example, the noble gases: helium, neon, argon, krypton, xenon, radon.
All these first rough insights would be the work of other men’s years to anchor soundly in theory and experiment. Bohr ran them in to Rutherford. To his surprise, he found the discoverer of the nucleus cautious about his own discovery. “Rutherford . . . thought that the meagre evidence [so far obtained] about the nuclear atom was not certain enough to draw such consequences,” Bohr recalled.269 “And I said to him that I was sure that it would be the final proof of his atom.” If not convinced, Rutherford was at least impressed; when de Hevesy asked him a question about radiation one day Rutherford responded cheerfully, “Ask Bohr!”270
Rutherford was well prepared for surprises, then, when Bohr came to see him again in mid-June. Bohr told Harald what he was on to in a letter on June 19, after the meeting:
It could be that I’ve perhaps found out a little bit about the structure of atoms. You must not tell anyone anything about it, otherwise I certainly could not write you this soon. If I’m right, it would not be an indication of the nature of a possibility . . . but perhaps a little piece of reality. . . . You understand that I may yet be wrong, for it hasn’t been worked out fully yet (but I don’t think so); nor do I believe that Rutherford thinks it’s completely wild; he is the right kind of man and would never say that he was convinced of something that was not entirely worked out. You can imagine how anxious I am to finish quickly.271
Bohr had caught a first glimpse of how to stabilize the electrons that orbited with such theoretical instability around Rutherford’s nucleus. Rutherford sent him off to his rooms to work it out. Time was running short; he planned to marry Margrethe Nørland in Copenhagen on August 1. He wrote Harald on July 17 that he was “getting along fairly well; I believe I have found out a few things; but it is certainly taking more time to work them out than I was foolish enough to believe at first.272 I hope to have a little paper ready to show to Rutherford before I leave, so I’m busy, so busy; but the unbelievable heat here in Manchester doesn’t exactly help my diligence. How I look forward to talking to you!” By the following Wednesday, July 22, he had seen Rutherford, won further encouragement, and was making plans to meet Harald on the way home.273
Bohr married, a serene marriage with a strong, intelligent and beautiful woman that lasted a lifetime. He taught at the University of Copenhagen through the autumn term. The new model of the atom he was struggling to develop continued to tax him. On November 4 he wrote Rutherford that he expected “to be able to finish the paper in a few weeks.”274 A few weeks passed; with nothing finished he arranged to be relieved of his university teaching and retreated to the country with Margrethe. The old system worked; he produced “a very long paper on all these things.”275 Then an important new idea came to him and he broke up his original long paper and began rewriting it into three parts. “On the constitution of atoms and molecules,” so proudly and bravely titled—Part I mailed to Rutherford on March 6, 1913, Parts II and III finished and published before the end of the year—would change the course of twentieth-century physics. Bohr won the 1922 Nobel Prize in Physics for the work.
* * *
As far back as Bohr’s doctoral dissertation he had decided that some of the phenomena he was examining could not be explained by the mechanical laws of Newtonian physics. “One must assume that there are forces in nature of a kind completely different from the usual mechanical sort,” he wrote then.276 He knew where to look for these different forces: he looked to the work of Max Planck and Albert Einstein.
Planck was the German theoretician whom Leo Szilard would meet at the University of Berlin in 1921; born in 1858, Planck had taught at Berlin since 1889. In 1900 he had proposed a revolutionary idea to explain a persistent problem in mechanical physics, the so-called ultraviolet catastrophe. According to classical theory there should be an infinite amount of light (energy, radiation) inside a heated cavity such as a kiln. That was because classical theory, with its continuity of process, predicted that the particles in the heated walls of the cavity which vibrated to produce the light would vibrate to an infinite range of frequencies.
Obviously such was not the case. But what kept the energy in the cavity from running off infinitely into the far ultraviolet? Planck began his effort to find out in 1897 and pursued it for three hard years. Success came with a last-minute insight announced at a meeting of the Berlin Physical Society on October 19, 1900. Friends checked Planck’s new formula that very night against experimentally derived values. They reported its accuracy to him the next morning. “Later measurements, too,” Planck wrote proudly in 1947, at the end of his long life, “confirmed my radiation formula again and again—the finer the methods of measurement used, the more accurate the formula was found to be.”277
Planck solved the radiation problem by proposing that the vibrating particles can only radiate at certain energies. The permitted energies would be determined by a new number—“a universal constant,” he says, “which I called h. Since it had the dimension of action (energy X time), I gave it the name, elementary quantum of action.”278 (Quantum is the neuter form of the Latin word quantus, meaning “how great.”) Only those limited and finite energies could appear which were whole-number multiples of hv: of the frequency ν times Planck’s h. Planck
calculated h to be a very small number, close to the modern value of 6.63 × 10−27 erg-seconds. Universal h soon acquired its modern name: Planck’s constant.
Planck, a thoroughgoing conservative, had no taste for pursuing the radical consequences of his radiation formula. Someone else did: Albert Einstein. In a paper in 1905 that eventually won for him the Nobel Prize, Einstein connected Planck’s idea of limited, discontinuous energy levels to the problem of the photoelectric effect. Light shone on certain metals knocks electrons free; the effect is applied today in the solar panels that power spacecraft. But the energy of the electrons knocked free of the metal does not depend, as common sense would suggest, on the brightness of the light. It depends instead on the color of the light—on its frequency.
Einstein saw a quantum condition in this odd fact. He proposed the heretical possibility that light, which years of careful scientific experiment had demonstrated to travel in waves, actually traveled in small individual packets—particles—which he called “energy quanta.” Such photons (as they are called today), he wrote, have a distinctive energy hv and they transfer most of that energy to the electrons they strike on the surface of the metal. A brighter light thus releases more electrons but not more energetic electrons; the energy of the electrons released depends on hv and so on the frequency of the light. Thus Einstein advanced Planck’s quantum idea from the status of a convenient tool for calculation to that of a possible physical fact.
With these advances in understanding Bohr was able to confront the problem of the mechanical instability of Rutherford’s model of the atom. In July, at the time of the “little paper ready to show to Rutherford,” he already had his central idea. It was this: that since classical mechanics predicted that an atom like Rutherford’s, with a small, massive central nucleus surrounded by orbiting electrons, would be unstable, while in fact atoms are among the most stable of systems, classical mechanics was inadequate to describe such systems and would have to give way to a quantum approach. Planck had introduced quantum principles to save the laws of thermodynamics; Einstein had extended the quantum idea to light; Bohr now proposed to lodge quantum principles within the atom itself.
Through the autumn and early winter, back in Denmark, Bohr pursued the consequences of his idea. The difficulty with Rutherford’s atom was that nothing about its design justified its stability. If it happened to be an atom with several electrons, it would fly apart. Even if it were a hydrogen atom with only one (mechanically stable) electron, classical theory predicted that the electron would radiate light as it changed direction in its orbit around the nucleus and therefore, the system losing energy, would spiral into the nucleus and crash. The Rutherford atom, from the point of view of Newtonian mechanics—as a miniature solar system—ought to be impossibly large or impossibly small.
Bohr therefore proposed that there must be what he called “stationary states” in the atom: orbits the electrons could occupy without instability, without radiating light, without spiraling in and crashing. He worked the numbers of this model and found they agreed very well with all sorts of experimental values. Then at least he had a plausible model, one that explained in particular some of the phenomena of chemistry. But it was apparently arbitrary; it was not more obviously a real picture of the atom than other useful models such as J. J. Thomson’s plum pudding.
Help came then from an unlikely quarter. A professor of mathematics at King’s College, London, J. W. Nicholson, whom Bohr had met and thought a fool, published a series of papers proposing a quantized Saturnian model of the atom to explain the unusual spectrum of the corona of the sun. The papers were published in June in an astronomy journal; Bohr didn’t see them until December. He was quickly able to identify the inadequacies of Nicholson’s model, but not before he felt the challenge of other researchers breathing down his neck—and not without noticing Nicholson’s excursion into the jungle of spectral lines.
Oriented toward chemistry, communicating back and forth with George de Hevesy, Bohr had not thought of looking at spectroscopy for evidence to support his model of the atom. “The spectra was a very difficult problem,” he said in his last interview. “ . . . One thought that this is marvelous, but it is not possible to make progress there. Just as if you have the wing of a butterfly, then certainly it is very regular with the colors and so on, but nobody thought that one could get the basis of biology from the coloring of the wing of a butterfly.”279
Taking Nicholson’s hint, Bohr now turned to the wings of the spectral butterfly.
Spectroscopy was a well-developed field in 1912. The eighteenth-century Scottish physicist Thomas Melvill had first productively explored it. He mixed chemical salts with alcohol, lit the mixtures and studied the resulting light through a prism. Each different chemical produced characteristic patches of color. That suggested the possibility of using spectra for chemical analysis, to identify unknown substances. The prism spectroscope, invented in 1859, advanced the science. It used a narrow slit set in front of a prism to limit the patches of light to similarly narrow lines; these could be directed onto a ruled scale (and later onto strips of photographic film) to measure their spacing and calculate their wavelengths. Such characteristic patterns of lines came to be called line spectra. Every element had its own unique line spectrum. Helium was discovered in the chromosphere of the sun in 1868 as a series of unusual spectral lines twenty-three years before it was discovered mixed into uranium ore on earth. The line spectra had their uses.
But no one understood what produced the lines. At best, mathematicians and spectroscopists who liked to play with wavelength numbers were able to find beautiful harmonic regularities among sets of spectral lines. Johann Balmer, a nineteenth-century Swiss mathematical physicist, identified in 1885 one of the most basic harmonies, a formula for calculating the wavelengths of the spectral lines of hydrogen. These, collectively called the Balmer series, look like this:
Balmer series
It is not necessary to understand mathematics to appreciate the simplicity of the formula Balmer derived that predicts a line’s location on the spectral band to an accuracy of within one part in a thousand, a formula that has only one arbitrary number:
(the Greek letter λ, lambda, stands for the wavelength of the line; η takes the values 3, 4, 5 and so on for the various lines). Using his formula, Balmer was able to predict the wavelengths of lines to be expected for parts of the hydrogen spectrum not yet studied. They were found where he said they would be.
A Swedish spectroscopist, Johannes Rydberg, went Balmer one better and published in 1890 a general formula valid for a great many different line spectra. The Balmer formula then became a special case of the more general Rydberg equation, which was built around a number called the Rydberg constant. That number, subsequently derived by experiment and one of the most accurately known of all universal constants, takes the precise modern value of 109,677 cm−1.
Bohr would have known these formulae and numbers from undergraduate physics, especially since Christensen was an admirer of Rydberg and had thoroughly studied his work. But spectroscopy was far from Bohr’s field and he presumably had forgotten them. He sought out his old friend and classmate, Hans Hansen, a physicist and student of spectroscopy just returned from Göttingen. Hansen reviewed the regularity of line spectra with him. Bohr looked up the numbers. “As soon as I saw Balmer’s formula,” he said afterward, “the whole thing was immediately clear to me.”280
What was immediately clear was the relationship between his orbiting electrons and the lines of spectral light. Bohr proposed that an electron bound to a nucleus normally occupies a stable, basic orbit called a ground state. Add energy to the atom—heat it, for example—and the electron responds by jumping to a higher orbit, one of the more energetic stationary states farther away from the nucleus. Add more energy and the electron continues jumping to higher orbits. Cease adding energy—leave the atom alone—and the electrons jump back to their ground states, like this:
With each jump,
each electron emits a photon of characteristic energy. The jumps, and so the photon energies, are limited by Planck’s constant. Subtract the value of a lower-energy stationary state W2 from the value of a higher energy stationary state W1 and you get exactly the energy of the light as hv. So here was the physical mechanism of Planck’s cavity radiation.
From this elegant simplification, W1—W2 = hv, Bohr was able to derive the Balmer series. The lines of the Balmer series turn out to be exactly the energies of the photons that the hydrogen electron emits when it jumps down from orbit to orbit to its ground state.
Then, sensationally, with the simple formula
(where m is the mass of the electron, e the electron charge and h Planck’s constant—all fundamental numbers, not arbitrary numbers Bohr made up) Bohr produced Rydberg’s constant, calculating it within 7 percent of its experimentally measured value! “There is nothing in the world which impresses a physicist more,” an American physicist comments, “than a numerical agreement between experiment and theory, and I do not think that there can ever have been a numerical agreement more impressive than this one, as I can testify who remember its advent.”281
“On the constitution of atoms and molecules” was seminally important to physics. Besides proposing a useful model of the atom, it demonstrated that events that take place on the atomic scale are quantized: that just as matter exists as atoms and particles in a state of essential graininess, so also does process. Process is discontinuous and the “granule” of process—of electron motions within the atom, for example—is Planck’s constant. The older mechanistic physics was therefore imprecise; though a good approximation that worked for large-scale events, it failed to account for atomic subtleties.