Rice UniversityPhysics 332THE FRANCK-HERTZ EXPERIMENTI. INTRODUCTION ................................................................ 2II. THEORETICAL CONSIDERATIONS....................................... 3III. MEASUREMENT AND ANALYSIS ....................................... 5Revised July 19912I. IntroductionBy the early part of the twentieth century it was clear that isolated atoms absorb and emitelectromagnetic radiation at characteristic frequencies. Bohr's atomic model suggested that thiswas due to an inherent quantization of the allowed energies of atomic electrons. Given theseideas, it is reasonable to ask if other modes of energy transfer would also exhibit quantization.This was the question posed, and answered, by James Franck and Gustav Hertz (not HeinrichHertz, of electromagnetic fame) in 1914.Franck and Hertz bombarded isolated atoms with electrons and showed that the electrons lostdiscrete amounts of energy characteristic of each element. Further, they were able to show thatelectron bombardment at an appropriate energy led to optical emission at the known spectralfrequency corresponding to that energy. Their results could be interpreted within the Bohr modelas demonstrating excitation of one of the discrete energy levels, followed by a transition back tothe ground state with emission of light. This is obviously a classic experiment, in the sense ofbeing of key importance, but the adjective is otherwise unfortunate in that the experimentprovided strong evidence against classical mechanics and in favor of the nascent quantummechanics.In our laboratory we will repeat Franck and Hertz's energy-loss observations, using mercury,and try to interpret the data in the context of modern atomic physics. We will not attempt thespectroscopic measurements, since the emissions are weak and in the extreme ultraviolet portionof the spectrum.3II. Theoretical considerationsIt is well known that electrons can be boiled out of a hot metal filament. By applying apositive potential between the filament and a nearby electrode one can give the electrons anydesired kinetic energy. If the electron subsequently hits a gas atom it may transfer energy to theatom. In this experiment we seek to measure that energy transfer. Because of the large massdifference between the electron and any atom, collisions which do not excite internal motions inthe atom result in very small changes in electron energy. The energy loss we observe, therefore,is essentially a measure of the energy changes internal to the atom.To a first approximation, the experiment can be understood by examining the idealizedsketch in Fig. 1. Electrons are accelerated toward a grid through a sealed bulb containing a smallamount of mercury. If the accelerating voltage is large enough, and there is no loss of energy incollisions, most electrons will pass through the grid and continue up the retarding gradient to thecollector electrode. The current meter measures this flow of electrons. Alternatively, electronswhich have made an inelastic collision and reach the grid with small kinetic energy will becaptured there, rather than at the collector. If we measure the collector current as a function ofgrid-filament voltage we can infer the probability of an inelastic collision as a function ofelectron energy.With this geometry and our assumption of quantized atomic energy levels we should expectto see several dips in the collector current as we increase the accelerating voltage. Ignoring theretarding potential for the moment, the first dip will occur when electrons reach the grid with justenough energy to excite a mercury atom. The next dip will occur at twice this voltage, since anelectron can then lose its energy midway from filament to grid and then be accelerated enough tocollide again near the grid. At still higher voltages there can be additional collisions leading to++Filament GridCollectorHggas1.2V0-40VIIeVFilamentGridCollectorFig. 1 The drawing on the left shows the geometry and voltages used for the Franck-Hertzexperiment. The graph shows the mechanical potential energy of an electron as a function ofposition within the tube. Note that both accelerating and retarding regions are present.4more dips. The important point is that the whole array of equally-spaced dips will be due to thelowest energy transition that the electron can excite. In this picture, the only effect of theretarding potential is to shift the whole pattern to higher voltages.If there were only one transition, this would be the whole story. Actually, though, mercury isa multi-electron atom with a complicated excitation spectrum and electron impact is a violentprocess. As a result there are several competing processes, and the energy loss observed may notreflect the energy difference between the ground state and the first excited state of atomicmercury. You should refer to the attached reprint for a complete discussion of this issue. Figures4 and 7 are particularly informative.Several non-atomic factors also complicate the simple picture. First, electron impact canionize the atom, as well as induce the intra-atomic transitions we have discussed so far. The freeelectron produced by the ionization event can then be accelerated and ionize another atom,eventually leading to creation of a conducting plasma in the tube. This causes a large increase inthe collector current and, for the Hg vapor, a visible blue glow in the tube. The exact acceleratingvoltage at which breakdown occurs depends on the tube geometry, gas density and electroncurrent, as well as the type of gas present. Once the gas has broken down the electrons are in aconducting medium and we can no longer interpret the collector current as a measure of thecollision probability.A more modest difficulty arises from other potentials in the apparatus. There is likely to be adifference in work function between the filament and collector plate. As you recall from thephotoelectric effect, the work function is the minimum energy required to move an electron froma metal to the vacuum. This potential energy must be supplied when the electron leaves thefilament and a similar energy is gained when the electron enters the collector. If the twopotentials are not the same, the voltage scale will be shifted by a constant amount, of the order of1-2 volts. Since there are temperature gradients in the apparatus, there can also be thermoelectricvoltage differences, amounting to a few tenths of a volt. Finally, the deliberately