Mystery Error in Gamow’s Tompkins Reappears
John D. Hey
The review by Daniel M. Greenberger of Russell Stannard’s The New World of Mr. Tompkins (Physics Today, June 2000, page 57) intrigued me sufficiently that I obtained a copy of this revised and extended version of George Gamow’s (now dated) three classic works for the general reader. I agree with much of what Greenberger writes. Stannard has “done a remarkable job of preserving the mood and feeling of the original,” and I hope that at least some of the few small slips will be edited out before this commendable book is reprinted.One error, however, struck me rather forcibly. In the diagram on page 159, the professor is lecturing to his evening audience, which contains the (as usual) dozing Mr. Tompkins. A slide of the Bohr-Sommerfeld orbits for principal quantum numbers n = 2,3 has been projected onto the screen. Unfortunately, the orbits with highest azimuthal quantum number (orbital angular momentum quantum number l) are shown as ellipses with the highest eccentricity, while the s-orbits (l = 0) are shown as circles. This confusion of “penetrating” with “nonpenetrating” orbits is common, occasioned perhaps by the recollection that in the wave-mechanical picture, the s-orbitals are spherically symmetrical, albeit with the important property that their probability densities peak at the origin. This property is of vital importance, for example, for the Lamb shift and the Fermi contact interaction in hyperfine structure, quite apart from the fact that the quantum defects are therefore largest for the s-orbitals in many-electron atoms. For comparison purposes, excellent diagrams of these two distinctly different forms of representation may be found in reference 11. H. E. White, Introduction to Atomic Spectra, McGraw-Hill, New York, (1934), pp. 47–71..How did this unfortunate mistake occur in the new work? On turning to its predecessor, 2 2. G. Gamow, Mr. Tompkins in Paperback, Cambridge U. Press, (1965) pp. 132–133. one finds on page 132 a picture containing the same Bohr–Sommerfeld orbits and, in addition, the quantization rules in the “old quantum theory” and formulas for the energies. (A keen-eyed reader will spot that the electronic charge e is raised to the wrong power in two places.) Moreover, in this diagram by Gamow himself, the orbitals are labeled in exactly the same incorrect fashion: The s- and d-labels should be interchanged.This brought to mind the amusing account in Gamow’s delightful “informal autobiography” My World Line (I write from memory of a book read well over two decades ago), in which he describes his initial difficulties on arrival from Russia at the University in Göttingen, home of the “new quantum theory,” around 1928. The easier problems having already been solved, his contemporaries were then working on aspects of atomic theory requiring considerable dexterity in advanced special function theory, and the sort of heavy algebraic manipulation (“exerei”) that Gamow disliked, topology and group theory being more appealing to him. On a certain day, the frustrated young Gamow was sitting on a park bench, wondering what to do. His eye fell on the description by Ernest Rutherford, in the Philosophical Magazine that he happened to be carrying, of a now rather implausible idea invoked to explain the escape of alpha particles from the atomic nucleus. In a flash of inspiration, Gamow sketched out in his mind the correct explanation, involving “quantum tunneling” and the now famous “Gamow factor.” When one considers the author’s age of barely 24 years, the ensuing paper 3 3. G. Gamow, Z. Phys. 51, 204 (1928) https://doi.org/10.1007/BF01343196. makes an astonishing impression of both maturity and unusual clarity, attributes that of course lent themselves admirably in due course to writing the “Tompkins” books.Making a hypothesis of my own, I surmised that his inattention to detail regarding the electron orbitals was perhaps a consequence of this early predilection for nuclear, rather than atomic, physics. But no—on turning to my last source, 4 4. G. Gamow, Mr. Tompkins Explores the Atom, Cambridge U. Press, (1946), pp. 72–74. I found not only the best drawing of all three (again by Gamow), but the orbits correctly labeled! No doubt the professor himself could comment most aptly on this mutilation of his original over time.REFERENCESSection:ChooseTop of pageREFERENCES <<1. H. E. White, Introduction to Atomic Spectra, McGraw-Hill, New York, (1934), pp. 47–71. Google Scholar2. G. Gamow, Mr. Tompkins in Paperback, Cambridge U. Press, (1965) pp. 132–133. Google Scholar3. G. Gamow, Z. Phys. 51, 204 (1928) https://doi.org/10.1007/BF01343196. Google ScholarCrossref, CAS4. G. Gamow, Mr. Tompkins Explores the Atom, Cambridge U. Press, (1946), pp. 72–74. Google Scholar© 2001 American Institute of Physics.
Physics Today•May 1, 2001•1 citation