A memorandum that changed the world Jeremy Bernstein Citation: Am. J. Phys. 79, 440 (2011); doi: 10.1119/1.3533426 View online: http://dx.doi.org/10.1119/1.3533426 View Table of Contents: http://ajp.aapt.org/resource/1/AJPIAS/v79/i5 Published by the American Association of Physics Teachers Related Articles Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913–1925. Am. J. Phys. 81, 237 (2013) Chasing Venus: The Race to Measure the Heavens. Am. J. Phys. 81, 78 (2013) Klein's theorem and the proof of E0=mc2 Am. J. Phys. 80, 1067 (2012) Kariamanikkam Srinivasa Krishnan: His Life and Work. Am. J. Phys. 80, 1035 (2012) Ampère’s motor: Its history and the controversies surrounding its working mechanism Am. J. Phys. 80, 990 (2012) Additional information on Am. J. Phys. Journal Homepage: http://ajp.aapt.org/ Journal Information: http://ajp.aapt.org/about/about_the_journal Top downloads: http://ajp.aapt.org/most_downloaded Information for Authors: http://ajp.dickinson.edu/Contributors/contGenInfo.html Downloaded 22 Feb 2013 to 128.95.100.35. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission A memorandum that changed the world Jeremy Bernstein ͑Received 23 July 2010; accepted 15 October 2010͒ We present an analysis of both the content and the influence of the 1940 memoir by Otto Frisch and Rudolf Peierls that showed that nuclear weapons were possible. © 2011 American Association of Physics Teachers. ͓DOI: 10.1119/1.3533426͔ In the summer of 1939 Otto Frisch, who was in Copen- in the fission process. Ironically, the barium-krypton split hagen, received an invitation from Mark Oliphant, a profes- which Hahn and Strassmann found was a relatively unlikely sor of physics at Birmingham, to come to Birmingham for nuclear splitting. the summer to see if some arrangements might be made for In his autobiography, What Little I Remember,1 Frisch Frisch to emigrate to Birmingham. War came that fall and writes “In all this excitement we had missed the most impor- Frisch could not return safely to Denmark. He was given a tant point. It was Christian Møller, a Danish colleague, who lectureship that enabled him to stay. first suggested to me that the fission fragments ͑the two The previous Christmas he had gone to visit his aunt Lise freshly formed nuclei͒ might contain enough surplus energy Meitner in Kungalv in Sweden. She had just received a letter to each eject a neutron or two; each of these might cause from Otto Hahn, the radiochemist in Berlin with whom she another fission and generate more neutrons. By such a “chain had collaborated for many years before she was forced to flee reaction” the neutrons would multiply in uranium like rabbits Germany. Meitner and Hahn had been using neutron sources in a meadow! My immediate answer was that in that case no to bombard various elements including uranium. Hahn had uranium ore deposits could exist; they would have blown up continued the experiments with Fritz Strassmann, another long ago by the explosive multiplication of neutrons in them. chemist. They had found something they did not understand. However, I quickly saw that my argument was too naive; Instead of finding elements in the residual bombarded ura- ores contained lots of other elements which might swallow nium that had masses comparable to uranium, they found up the neutrons; and the seams were perhaps thin, and then barium, which was somewhere in the middle of the Periodic most of the neutrons would escape. So from Møller’s remark Table. They were stuck for an explanation and Hahn ap- the exciting vision arose that by assembling enough pure pealed to Meitner. She and Frisch went for an excursion in uranium ͑with appropriate care!͒ one might start a controlled the snowy woods—he on skis and she on foot. During that chain reaction and liberate nuclear energy on a scale that outing they realized that by using the liquid drop model of really mattered. Many others had the same thought, as I soon the heavy nuclei, what Hahn and Strassmann had done was found out. Of course the specter of a bomb—an uncontrolled to fission the uranium nucleus. One product was barium and chain reaction—was there as well; however, for awhile any- the other was krypton with possible neutrons in addition. how, it looked as though it need not frighten us. That com- They worked out the energies and realized that about 200 placency was based on an argument of Bohr, which was MeV would be released, a very large amount of energy com- subtle but appeared quite sound.”2 pared to any chemical reaction. The February 15, 1939 issue of the Physical Review con- Frisch returned to Copenhagen after this visit with his aunt tained a two page article by Bohr that changed everything.3 It ͑his aunt remained in Sweden͒ and told Bohr about what he had the unremarkable title “Resonance in uranium and tho- and Meitner had concluded. Bohr’s reaction was like a great rium disintegrations and the phenomenon of nuclear fission.” many other physicists when they heard about it—it was so The essential point came in the penultimate paragraph and obvious why had not they thought of it. As it happened Bohr might easily have been overlooked. Bohr noted that what was about to leave for the United States where he was going counts in the fission process is the formation of a compound to spend time at the Institute for Advanced Study which was nucleus after the incident neutron has been absorbed. For then located at Princeton University. He was accompanied by 238U, the common isotope, it is 239U, while for 235U, the rare his assistant Lèon Rosenfeld. On the Atlantic crossing Bohr isotope, it is 236U. The latter is an even-even nucleus, while had a blackboard setup in his cabin, and he and Rosenfeld the former is an even-odd nucleus and hence more loosely went over the theory. He had promised Frisch and Meitner bound. This difference in binding energies results in a differ- not to say anything until their paper appeared, but he had ence in the mass defect between the initial state of the neu- forgotten to tell Rosenfeld who went at once to Princeton and tron and one of the isotopes of uranium and the compound told everybody. nucleus. This difference for the uranium isotopes is about 1.7 Even in those preinternet days the news spread all over the Mev. The extra energy due to this mass defect goes into the country and abroad and fission experiments proliferated. excitation energy of the compound nucleus and is what is Among the first were those of Frisch, who was primarily an responsible for its fission. To make 238U fission we must experimentalist. He looked for ionization pulses, which were supply an energy of at least 1 MeV from the incident neutron produced by the charged fission fragments. Others found the while for 235U this energy is supplied by the mass defect and additional neutrons—on average a little over two—produced hence neutrons of any energy can cause fission. This energy 440 Am. J. Phys. 79 ͑5͒, May 2011 http://aapt.org/ajp © 2011 American Association of Physics Teachers 440 Downloaded 22 Feb 2013 to 128.95.100.35. Redistribution subject to AAPT license or copyright; see http://ajp.aapt.org/authors/copyright_permission threshold or lack of same is the difference between a “fis- ber of neutrons that escape just balances the number of neu- sionable” and a “fissile” nucleus. trons that are created. If we know this critical radius, we Frisch’s complacency and Bohr’s as well had to do with know the volume of the sphere and from the mass density we the realization that the dominant isotope could not make a then know the critical mass. At just this mass there is no self-sustaining chain reaction. Much of the spectrum of the self-sustaining chain reaction produced. We need a “super- emitted neutrons would be below the threshold energy for critical” mass. This idea was tested and confirmed in the fission. Thus, to make such a chain reaction would require Godiva experiments at Los Alamos.6 Frisch participated and the separation of isotopes on an industrial scale. Bohr ruled gave its name because bare masses were being used. In an this separation out because he said it would take the re- actual bomb the fissile sphere is surrounded by a heavy metal sources of an entire country. Actually, it took the resources of casing that reflects neutrons and thus enhances the fission three: Great Britain, the United States, and Canada. How- reactions. ever, up to this point no one had actually determined how The fission mean free path for the neutrons, the average much 235U was needed to make a “critical mass”—a mass distance between fissions, is roughly the order of magnitude above which the chain reaction would be self-sustaining. En- of the critical radius. The Peierls theory refines this estimate. / ␴ ter Rudolf Peierls. The mean free path for fission is by definition rf =1 n f. Peierls was born in Berlin in 1907 which made him three Here, n is the number density of the uranium nuclei in the ␴ years younger than Frisch who was born in Vienna. Both sphere and f is the fission cross section. Curiously, Peierls men were of Jewish ancestry. Peierls, who was a theorist, did not put in any numbers to estimate this mass. This esti- took his degree in Munich from Arnold Sommerfeld.