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The Path to the Quantum Atom John Heilbron Describes the Route That Led Niels Bohr to Quantize Electron Orbits a Century Ago

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The Path to the Quantum Atom John Heilbron Describes the Route That Led Niels Bohr to Quantize Electron Orbits a Century Ago COMMENT QUANTUM ATOM Frank Wilczek GENOMICS Is personalized ECONOMICS On the complex FILM Charting the celebrates the mysterious medicine squeezing out web of interactions that exploitation of a fishery in electron p.31 public health? p.34 gives money meaning p.35 the pristine Ross Sea p.36 UHLENBECK COLLECTION/AMERICAN INST. OF PHYSICS/SPL INST. COLLECTION/AMERICAN UHLENBECK Niels Bohr and his wife Margrethe around 1930. The path to the quantum atom John Heilbron describes the route that led Niels Bohr to quantize electron orbits a century ago. n the autumn of 1911, the Danish from the Royal Danish Academy of Sciences so advanced that no one in Denmark could physicist Niels Bohr set sail for a post- in 1908, at the age of 23, for a theoretical and evaluate it fully. doctoral year in England inflamed with experimental study of water jets published Bohr went to the University of Cam- I“all my stupid wild courage”, as he expressed by the Royal Society of London. His doctoral bridge, UK, to work with Joseph John (J. J.) his state of mind in a letter to his fiancée, thesis on the electron theory of metals was Thomson, famous as the discoverer of the Margrethe Nørlund1. Bohr would need that electron and recipient of the Nobel Prize in courage on his route to his revolutionary THE QUANTUM ATOM Physics for 1906. For Bohr, Thomson was “a quantum atom of 1913. A Nature special issue genius who showed the way to everyone”. But Bohr had reason to think himself designed nature.com/bohr00 Thomson was too full of his own ideas to lis- for great things. He had won a gold medal ten to those of a foreigner whose English 6 JUNE 2013 | VOL 498 | NATURE | 27 © 2013 Macmillan Publishers Limited. All rights reserved COMMENT NUCLEAR MODEL In February 1912, Bohr went to the Victoria University of Manchester, UK, to arrange to work on radioactivity in Ernest Ruther- ford’s laboratory. He looked forward to it in his understated way: “My courage is ablaze, so wildly, so wildly”1. Rutherford satisfied his expectations: “a really first-rate man and extremely capable, in many ways more able BOHR ARCHIVE, COPENHAGEN NIELS than Thomson, even though perhaps he is not as gifted”1. Rutherford certainly surpassed Thomson as a research director. When Bohr arrived, several men in the laboratory were work- ing on implications of the nuclear model of the atom that Rutherford had introduced in 1911. To explain the unexpected reflection of α-particles from thin metal foils, detected by his research students, Rutherford had found it necessary to collect all the positive charge in Thomson’s spheres into a tiny kernel at the atom’s centre. Soon Bohr joined in via his natural route: criticism. In calculating the transfer of energy from an α-particle to atomic elec- trons, Rutherford’s theorist Charles Galton Darwin had not taken into account the reso- nance that occurs when the time of passage of the particle past the atom coincides with the natural frequency at which the perturbed electrons oscillate. In improving the calculations, Bohr dis- covered that some modes of oscillation of a ring of electrons in the plane of their orbit grow until they tear the atom apart. This mechanical instability could not be mended by deploying accepted physical concepts. Bohr’s thesis work had familiarized him with more general examples of failure in theo- ries of heat radiation and magnetism that allowed electrons all the freedom that statis- tical mechanics granted them. To his unique way of thinking, the nuclear model appealed to Bohr precisely because it expressed this failure so conspicuously. Niels Bohr (left) with Albert Einstein in 1925. The model had further advantages. It made a clear distinction between radioactive he had to struggle to understand. “They charged. In this picture, Thomson elucidated and chemical phenomena, which in Bohr’s say he would walk away from the king,” Niels the periodic properties of the elements, the view derived from the nucleus and the elec- wrote to his brother Harald, “which means formation of simple molecules, radioactivity, tronic structure, respectively. This inference more in England than in Denmark”1. the scattering of X-rays and β-particles, and was not as evident then as it is now. Even Even if Thomson had been interested, he the ratio between the weight of an atom and Rutherford had not yet grasped the distinc- would have had trouble perceiving that his the number of its electrons. tion, and assigned the origin of β- and γ-rays postdoc was a mature mathematical physi- Bohr spent much of his time at Cam- to extra-nuclear electrons. cist. Furthermore, Bohr’s speciality was criti- bridge attending talks and reading widely. Most importantly, the nuclear model, cism. In his thesis work, he had discovered He extolled Thomson’s lectures and found combined with Rutherford’s conception errors in Thomson’s papers, which he tried much to admire in the treatise Aether and of the α-particle as a bare nucleus, almost to bring to the professor’s attention. That was Matter (1900), in which Joseph Larmor, the thrust the concept of atomic number on not the right gambit. occupant of the chair of mathematics once physicists. They knew that the α-particle Thomson was preoccupied with devel- held by Isaac Newton, developed a world was a helium atom minus two electrons; its oping consequences of the model atom he system based on electrons conceived as nucleus must therefore have a charge of two, had proposed in 1903. Later inappropriately permanent twists in the ether. “When I read implying that hydrogen’s has a charge of one, and derisively nicknamed a ‘plum pudding’, something that is so good and grand as that,” lithium’s a charge of three, and so on. it consisted of concentric rings of electrons Bohr wrote to Margrethe1, “then I feel such His confidence replenished by Ruther- rotating through a resistanceless spheri- courage and desire to try whether I too could ford’s interest, Bohr drew up a memoran- cal space that acted as if it were positively accomplish a tiny bit.” dum in June or July 1912 to show how Max 28 | NATURE | VOL 498 | 6 JUNE 2013 © 2013 Macmillan Publishers Limited. All rights reserved COMMENT Planck’s idea that energy came in packets, or quanta, could extend the purview of the THE BALMER FORMULA nuclear model to the problems that Thomson had considered, and to fix the size of atoms. Bohr’s key to the microworld Although most of the memorandum was qualitative, in one essential point Bohr The Balmer formula expresses the nth state with the second term, –Rh/n2. The could be exact where Thomson could only frequencies of some lines in the spectrum first term would then be the negative of estimate. Rutherford’s scattering theory and of hydrogen in simple algebra: the energy for the second state (n = 2), and experiments required that, for helium, the the formula could be read to mean that a 2 2 atomic weight (4) was twice the number νn = R(1/2 – 1/n ) Balmer line originates in a jump of of electrons (2). Thomson could only say, a hydrogen electron from its nth to its after extensive theoretical and experimen- where νn is the nth Balmer line and second state. tal work on the scattering of X-rays and R is the universal Rydberg constant for To calculate R, Bohr equated the energy β-particles, that the number of electrons frequency, named in honour of the Swedish of the nth state, –Rh/n2, with the expression in an element was roughly three times its spectroscopist Johannes Rydberg, who he already had for the kinetic energy Tn of atomic weight. generalized Balmer’s formula to apply to an orbiting electron in his quantized model After these first easy gains, Niels wrote elements beyond hydrogen. of the nuclear atom: 2 4 2 2 to Harald, “Perhaps I have found out a lit- Following Max Planck’s radiation theory, Tn = 2π me /h n tle about the structure of atoms. If I should Niels Bohr converted the equation into where e and m are the charge and mass be right, it wouldn’t be a suggestion of the units of energy, by multiplying both sides of the electron. Equating the two energies, nature of a possibility (i.e., impossibility as by Planck’s constant, h. This allowed him Bohr had R in terms of the fundamental J. J. Thomson’s theory) but perhaps a little to identify the energy of the electron in its constants. bit of reality”1. Nonetheless, Bohr followed Thomson’s Lyman series lead in the other subjects he discussed with HYDROGEN SPECTRUM Rutherford: the periodic properties of the Electrons jumping between energy levels in a Balmer series hydrogen atom give o light at certain frequencies, Paschen series elements, determined by stability require- corresponding to the energy dierence (wavelengths ments imposed on their ring structures, and given in nanometres, nm). Bohr focused on the Balmer series of spectral lines, between the second 94 nm the binding of atoms into simple molecules, and higher energy levels. secured by exchanges of electrons. 95 nm To proceed with his calculations, Bohr laid down the ad-hoc postulate, conceived in 97 nm analogy to Planck’s radiation theory, that if the kinetic energy of each electron is propor- 103 nm tional to the frequency of its orbit, it would 486 nm neither radiate nor succumb to unstable 122 nm 656 nm 434 nm oscillations, and he guessed that the constant 410 nm of proportionality was a fraction of Planck’s h.
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