Michael Fowler, University of Virginia
The first attempt toconstruct a physical model of an atom was made by William Thomson (laterelevated to Lord Kelvin) in 1867. The most striking property of the atom wasits permanence. It was difficult to imagine any small solid entitythat could not be broken, given the right force, temperature or chemical reaction.In contemplating what kinds of physical systems exhibited permanence, Thomsonwas inspired by a paper Helmholtz had written in 1858 on vortices.This work had been translated into English by a Scotsman, Peter Tait, whoshowed Thomson some ingenious experiments with smoke rings to illustrateHelmholtz' ideas. The main point was that in an idealfluid, avortex line is always composed of the same particles, it remains unbroken,so it is ring-like. Vortices can also form interesting combinations—a good demonstration is provided by creating twovortex rings one right after the other going in the same direction. They cantrap each other, each going through the other in succession. This is probablywhat Tait showed Thomson, and it gave Thomson the idea that atoms might somehowbe vortices in the ether.
Of course, in a non-idealfluid like air, the vortices dissipate after a while, so Helmholtz'mathematical theorem about their permanence is only approximate. But Thomsonwas excited because the ether was thought an ideal fluid, sovortices in the ether might last forever! This was very aesthetically appealingto everybody—"Kirchhoff, a man of cold temperament, canbe roused to enthusiasm when speaking of it." (Pais,Inward Bound, page 177, source for this material). In fact, theinvestigations of vortices, trying to match their properties with those ofatoms, led to a much better understanding of the hydrodynamics of vortices—the constancy of the circulation around avortex, for example, is known as Kelvin's law. In 1882 another (unrelated) Thomson,J. J., won a prize for an essay on vortex atoms, and how they might interactchemically. After that, though, interest began to wane—Kelvin himself began to doubt that his modelreally had much to do with atoms, and when the electron was discovered by J. J.in 1897, and was clearly a component of all atoms, different kinds ofnon-vortex atomic models evolved.
It is fascinating tonote that the most exciting theory of fundamental particles at the presenttime, string theory, has a definite resemblance to Thomson'svortex atoms. One of the basic entities is the closed string, a little loop,which has fields flowing around it reminiscent of the swirl of ethereal fluidin Thomson's atom. And it's a very beautiful theory—Kirchhoff would have been enthusiastic!
In 1878, Alfred Mayer,at the University of Maryland, dreamed up a neat demonstration of how heimagined atoms might be arranged in molecules (Note:not electrons inatoms, that idea came a bit later). He took a few equally magnetized needlesand stuck them through corks so that they wouldfloat with their north polesall at the same height above the water, all repelling each other equally. He thenheld the south pole of a more powerful magnet some distance above the water, toattract the needles towards this central point. The idea was to see whatequilibrium patterns the needles would form for different numbers of needles. Hefound something remarkable—the needles liked to arrange themselves inshells. Three to five magnets just formed a triangle, square and pentagon in succession.but for six magnets, one went to the center and the others formed a pentagon(well, usually—seepictures). For more magnets, an outer shell began toform.
Kelvin's immediateresponse to Mayer's publication was that this should give some clues about thevortex atom. Apparently it didn't, but twenty-five years later it guided histhinking on a new model.
Kelvin, in 1903,proposed that the atom had the newly discovered electrons embedded somehow in asphere of uniform positive charge, this sphere being the full size of the atom.(Of course, the sphere itself must be held together by unknownnon-electrical forces—which is still true of the positive charge inour modern model of the atom.) This picture was taken up by J. J. Thomson too,and was dubbed the plum pudding model, after traditional English Christmasfare, a large round pudding (rich with suet) with raisins embedded in it. In1906, J. J. concluded from an analysis of the scattering of X-rays by gases andof absorption of beta-rays by solids, both of which he assumed were effected byelectrons, that the number of electrons in an atom was approximately equal tothe atomic number. This led to a picture of electron arrangements in an atomreminiscent of Mayer's magnets. Perhaps by analyzing possible modes of vibrationof electrons in these configurations, the spectra could be calculated.
The simplest case toconsider was clearly hydrogen, now assumed (correctly) to contain just oneelectron.
By "color" wemean here the spectral colors emitted when the atom is excited. In Thomson'splum pudding model, there is a clear relationship between the size ofthe pudding and the frequency at which the electron willoscillate, and hence presumably radiate, when excited. The two are relatedbecause the assumption is that the total positive charge—which is uniformly spread throughout the sphere—is just equal to the electron's negative charge.At rest in its lowest state, the electron just sits in the middle of thissphere of charge. When bumped somehow, it will oscillate about that point. Ifthe electron is at distance from the center, it will feel a restoring forcetowards the center equal to the attraction from that part of the positivecharge it is "outside" of—that is, the charge within a sphere ofradius x about the center. Therefore, the larger thewhole atom—the pudding—the more thinly spread the positive charge is,and the smaller the amount of charge within the small sphereof radius that is attracting the electron back towardsthe center. So, thebigger the atomis, theslower the electron'soscillation is, and the lower frequency the radiation emitted.
It is straightforward togive a quantitative estimate of the size of the atom based on the observation thatwhen excited it emits radiation in the visible range.
Let us assume that thepositively charged sphere has radius (this is then the size of the atom, which weknow is about 10-10 meters).
If the electron isdisplaced from the center of the atom in the -direction an amount it is attracted back by all the charge that isnow closer to the center than itself, that is, an amount of charge equalto (Recall is the total amount of charge on the sphere,and is the fraction of the sphere closer to thecenter than ) This charge acts as if it were a point chargeat the origin, so the inverse-square law gives a factor, and the equation of motion for theelectron is therefore:
Provided it stays withinthe sphere, the electron will execute simple harmonic motion with a frequency
Notice that, as wediscussed above, as the size of the atom increases the frequency goes down. Andwe know the frequency, at least approximately—it corresponds to visible light. Therefore, thismodel will predict a size of the atom, which we can compare with the size fromother predictions, such as Brownian motion (plus the assumption that in aliquid, the atoms are fairly close packed—they take up most of the room available).
If we take visiblelight, say with a frequency 4.1015 radians per second, wefind must be about 2.10-10 meters, alittle on the large side, but encouragingly close to the right answer for afirst attempt.
Sad to report, though,no real progress was made beyond this in predicting spectra using Thomson'spudding. Many attempts were made to findstable arrangements of electrons in atoms, not just hydrogen, using models likeMayer's magnets, and also having the electrons going around in circles. It washoped that if certain numbers of magnets formed a very stable arrangement, thatmight model a chemically nonreactive atom, etc.—but nobody succeeded in making any realpredictions along these lines, the models could not be connected with theproperties of real atoms.
Evidently, then, thetheorists were stuck—and the experimental challenge was to find someway to look inside an atom, and see how the electrons werearranged. This is what Rutherford did, as we shall discuss in the next lecture.He was very surprised by what he saw.