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Cambridge University Press eBooks

The Gay Tribe of Electrons

George Gamow, Roger Penrose

Published Mar 26, 1993• 2 citations
Publisher

Abstract

A few days later, while finishing his dinner, Mr Tompkins remembered that it was the night of the professor's lecture on the structure of the atom, which he had promised to attend. But he was so fed up with his father-in-law's interminable expositions that he decided to forget the lecture and spend a comfortable evening at home. However, just as he was getting settled with his book, Maud cut off this avenue of escape by looking at the clock and remarking, gently but firmly, that it was almost time for him to leave. So, half an hour later, he found himself on a hard wooden bench in the university auditorium together with a crowd of eager young students. ‘Ladies and gentlemen,’ began the professor, looking at them gravely over his spectacles, ‘In my last lecture I promised to give you more details concerning the internal structure of the atom, and to explain how the peculiar features of this structure account for its physical and chemical properties. You know, of course, that atoms are no longer considered as elementary indivisible constituent parts of matter, and that this role has passed now to much smaller particles such as electrons, protons, etc. ‘The idea of elementary constituent particles of matter, representing the last possible step in divisibility of material bodies, dates back to the ancient Greek philosopher DEMOCRITUS who lived in the fourth century B.C. Meditating about the hidden nature of things, Democritus came to the problem of the structure of matter and was faced with the question whether or not it can exist in infinitely small portions.

DOI
10.1017/cbo9781139644143.013

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The Gay Tribe of Electrons

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A few days later, while finishing his dinner, Mr Tompkins remembered that it was the night of the professor's lecture on the structure of the atom, which he had promised to attend. But he was so fed up with his father-in-law's interminable expositions that he decided to forget the lecture and spend a comfortable evening at home. However, just as he was getting settled with his book, Maud cut off this avenue of escape by looking at the clock and remarking, gently but firmly, that it was almost time for him to leave. So, half an hour later, he found himself on a hard wooden bench in the university auditorium together with a crowd of eager young students. ‘Ladies and gentlemen,’ began the professor, looking at them gravely over his spectacles, ‘In my last lecture I promised to give you more details concerning the internal structure of the atom, and to explain how the peculiar features of this structure account for its physical and chemical properties. You know, of course, that atoms are no longer considered as elementary indivisible constituent parts of matter, and that this role has passed now to much smaller particles such as electrons, protons, etc.’

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EVERY atom-model that is worthy of notice was designed in view of a certain limited group of facts. That is to say, every valuable atom-model is the invention of somebody who, being acquainted with certain of the ways in which matter behaves, set himself to the devising of atoms of which an assemblage should behave like matter in those ways. Of course, it would be a most wonderful achievement to conceive atoms, of which assemblages should behave like matter in all ways; but this is too exalted an ambition for this day and generation, no man of science bothers with it. Each atom-model of the present is partially valid, not universally; and nobody can rightly appreciate any one of them, unless he knows the facts for which it was designed. I might add that he should also know the relative importance, in the world and in life, of the facts for which it was designed. But this also is too exalted an ambition; we do not know much, if anything, about the relative importance of facts sub specie aternitatis, and can hardly refrain from regarding with an especial favour the facts which happen to have been successfully explained. At all events it is clear that every account of an atom-model should be preceded by an independent account of the things it is meant to explain. For the favorite atom of these days, the atom of Rutherford and Bohr, I have provided this preliminary account of the facts in the First Part of the article. Let me give a brief outline of the most important among them, before entering upon the task of constructing an atom-model to reproduce them.

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Mystery Error in Gamow’s Tompkins Reappears

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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
A few days later, while finishing his dinner, Mr Tompkins remembered that it was the night of the professor's lecture on the structure of the atom, which he had promised to attend. But he was so fed up with his father-in-law's interminable expositions that he decided to forget the lecture and spend a comfortable evening at home. However, just as he was getting settled with his book, Maud cut off this avenue of escape by looking at the clock and remarking, gently but firmly, that it was almost time for him to leave. So, half an hour later, he found himself on a hard wooden bench in the university auditorium together with a crowd of eager young students. ‘Ladies and gentlemen,’ began the professor, looking at them gravely over his spectacles, ‘In my last lecture I promised to give you more details concerning the internal structure of the atom, and to explain how the peculiar features of this structure account for its physical and chemical properties. You know, of course, that atoms are no longer considered as elementary indivisible constituent parts of matter, and that this role has passed now to much smaller particles such as electrons, protons, etc. ‘The idea of elementary constituent particles of matter, representing the last possible step in divisibility of material bodies, dates back to the ancient Greek philosopher DEMOCRITUS who lived in the fourth century B.C. Meditating about the hidden nature of things, Democritus came to the problem of the structure of matter and was faced with the question whether or not it can exist in infinitely small portions.
A few days later, while finishing his dinner, Mr Tompkins remembered that it was the night of the professor's lecture on the structure of the atom, which he had promised to attend. But he was so fed up with his father-in-law's interminable expositions that he decided to forget the lecture and spend a comfortable evening at home. However, just as he was getting settled with his book, Maud cut off this avenue of escape by looking at the clock and remarking, gently but firmly, that it was almost time for him to leave. So, half an hour later, he found himself on a hard wooden bench in the university auditorium together with a crowd of eager young students. ‘Ladies and gentlemen,’ began the professor, looking at them gravely over his spectacles, ‘In my last lecture I promised to give you more details concerning the internal structure of the atom, and to explain how the peculiar features of this structure account for its physical and chemical properties. You know, of course, that atoms are no longer considered as elementary indivisible constituent parts of matter, and that this role has passed now to much smaller particles such as electrons, protons, etc.’
The description of the physical and chemical properties of matter is a central issue that has occupied the minds of scientists since the age of the ancient Greeks. In their route to dissect matter down to what cannot be divided any further, they coined the term atom , the indivisible . Matter became then a collection of atoms. More than twenty centuries had to pass until the development of a more precise concept of atom, thanks, amongst others, to the systematic studies of Mendeleyev and the establishment in 1869 of the periodic table of the elements (Mendeleyev, 1869). The discovery of the electron in 1897 and the first modern model of the atomic structure by Sir Joseph Thomson were soon refined by his student, Sir Ernest Rutherford, who in 1910 showed that an atom was made of a positively charged small nucleus and a number of negatively charged electrons that neutralize the nuclear charge. Much in the spirit of planetary systems, and drawing from the analogy between gravitational and electrostatic interactions, scientists in the beginning of the twentieth century built an image of the atom that consisted of a number Z of electrons – of elementary charge – e – orbiting around the nucleus of charge Ze . A number of experimental observations, though, were incompatible with this idea of orbiting electrons. In particular, according to the successful electromagnetic theory, charged electrons in orbital (radially accelerated) motion should radiate energy, thus decelerating and eventually collapsing onto the nucleus. Clearly, such a picture would imply that matter is essentially unstable, in flagrant contradiction with our everyday experience of the very existence of matter.
​Richard Feynman, in his famous Lectures on Physics, toyed with the idea of all scientific knowledge being wiped out and facing the choice of passing one single idea down to future generations (Feynman et al. 1989). He believed it should be the hypothesis that all things are made of atoms. The idea that matter is built up from discrete fundamental units can be traced back to several ancient cultures (the word atom deriving from the Greek word atomos ‘cannot be divided’). It is only within the last century or so, however, that theories for atomic structure were developed to explain a series of phenomena observed throughout the 18th–19th Centuries. Many of these phenomena were optical, such as Melvill’s observation in 1752 that a mixture of sea salt and alcohol would burn with a yellow flame (see Figure 1) or Wollaston’s observation in 1802 that sunlight contains black lines in its spectrum (Cajori 1962). Further refinement and characterisation from people like Fraunhofer, Kirchoff, Bun-sen, Balmer, and Zeeman followed, but it was not until 1913, with the introduction of the Rutherford-Bohr atomic model, that a cornerstone was laid for what would become a quantum mechanical description of the atom.
EVERY atom-model that is worthy of notice was designed in view of a certain limited group of facts. That is to say, every valuable atom-model is the invention of somebody who, being acquainted with certain of the ways in which matter behaves, set himself to the devising of atoms of which an assemblage should behave like matter in those ways. Of course, it would be a most wonderful achievement to conceive atoms, of which assemblages should behave like matter in all ways; but this is too exalted an ambition for this day and generation, no man of science bothers with it. Each atom-model of the present is partially valid, not universally; and nobody can rightly appreciate any one of them, unless he knows the facts for which it was designed. I might add that he should also know the relative importance, in the world and in life, of the facts for which it was designed. But this also is too exalted an ambition; we do not know much, if anything, about the relative importance of facts sub specie aternitatis, and can hardly refrain from regarding with an especial favour the facts which happen to have been successfully explained. At all events it is clear that every account of an atom-model should be preceded by an independent account of the things it is meant to explain. For the favorite atom of these days, the atom of Rutherford and Bohr, I have provided this preliminary account of the facts in the First Part of the article. Let me give a brief outline of the most important among them, before entering upon the task of constructing an atom-model to reproduce them.
Be this as it may, it seems worth our while to try to examine the matter from various angles. A point of view that I have previously touched on in these lectures and that does suggest itself is this, that our present difficulties in physical science are bound up with the notorious conceptional intricacy inherent in the idea of the continuum. But this does not tell you much. How are they bound up? What precisely is the mutual relationship? If you envisage the development of physics in the last half-century, you get the impression that the discontinuous aspect of nature has been forced upon us very much against our will. We seemed to feel quite happy with the continuum. Max Planck was seriously frightened by the idea of a discontinuous exchange of energy, which he had introduced (1900) in order to explain the distribution of energy in black-body-radiation. He made strong efforts to weaken the hypothesis, and, if possible, to get away from it, but in vain. Twenty-five years later the inventors of wave mechanics indulged for some time in the fond hope that they had paved the way of return to a classical continuous description, but again the hope was deceptive.
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.