The Franck-Hertz Experiment (1961)

many of you will remember having seen the Mercury Spectrum an intense blue green line a dark blue line and an extremely difficult to see deep violet line and appropriate precautions to guard your eyes against the ultraviolet which is also produced by the Mercury atoms with the help of photographic film we can see the ultraviolet part of the spectrum as well as the visible part of the spectrum let's for a moment concentrate our attention on the intense line way down at the Left End of the photograph this line is measured as having a wavelength of 537 angstroms this means as you know that all of the light coming there has this same wavelength and of course has the same frequency light coming from identical Mercury atoms but you have recently learned that light behaves as photons whose energy is proportional to the frequency therefore for all of the photons coming into the spectral line that we've talked about they will all have the same energy and and that energy can be calculated from the simple formula that e is equal to 1 2 3 9 7 too bad it's not 1 2 3 4 5 divided by the wavelength of the photon where if the wavelength is in angstroms the energy is in electron volts thus Mercury atoms which are contributing photons into the line of the Mercury Spectrum which we've been looking at Must ALL lose energy exactly equal to the photon energy which is another way of saying that mercury atoms when they emit photons can only lose energy in certain sized packages detailed and very careful analysis of many such line Spectra of this type added to the information that was gained from other experiments for example the photoelectric experiment LED physicists of the early 1900s to the conclusion that an atom can only take on certain discret energy values that is the internal motion of the atom can only take on certain energy conditions not just any energy whatever this postulate formed one of the basic principles upon which the atomic theory of Neil's bore was developed in in 1913 and was such an important postulate that James Fran and Gustaf heritz in the following year devised an experiment to test the postulate in a very simple and direct way it is the experiment of Frank and herritz which we wish to perform today the question that we wish to ask is this if it is true that mercury atoms can only take on certain discreet energy states then can we produce these energy states by other means which do not involve photons for example can we produce a collision between a Mercury atom and let's say an electron whose energy we know very accurately in just such a way that the Mercury atom will be caused to move from one energy State up to another energy State can we bump the Mercury atom with an electron giving it just enough energy to cause it to jump this particular special amount of energy now before we look at the actual experiment let's take a look at a large scale and admittedly rather crude analogy I'd like to represent the Mercury atom with this dry ice disc which you already know and I would like to represent an electron with a pingpong ball in this model the ratio of masses is only about 1,000 to1 while in the real Atomic situation the Mercury atom has a mass almost a half million times the mass of the electron but that'll be all right I think for the effect that I want to show another thing should be said concerning the velocities of the particles you know that both particles are going to be in motion the Mercury atom will have the thermal motion of its surroundings and we can show that for uh temperatures just above room temperature the Mercury atom should have a speed of about 2 250 m/s while the electron if it's perhaps a one electron volt electron will have a speed nearly a million m/s and so from its point of view the Mercury atom is essentially standing still now let's watch this Collision as I send in a one electron volt electron against a Mercury atom I see that the electron comes away with almost the energy that it had when it went into the Collision I know this is true because the Mercury atom does not seem to acquire any appreciable amount of energy and of course this is what we expect for elastic collisions with this Mass ratio but this is really not a very good model yet because you know that with elastic collisions you cannot transfer energy into the internal motion of the atom so let's change the model by adding this and this still isn't exactly the way I picture an atom but it's a somewhat better model than the last one we then will send in another one electron volt electron and this time we see that we can transfer some energy to the internal motion let's try it again and this time watch the electron it goes in with high speed and comes out very slowly it has indeed transferred almost all of its energy to the internal motion of the atom but there still is one thing wrong if an atom behaved like this then we would expect that we could transfer any amount of energy to the atom for example if I send in a slow electron I transfer only a small amount of energy to the internal motion if I send in a high-speed electron I transfer a large amount of energy to the internal motion and we have just postulated that atoms do not behave this way but rather that there are only certain siiz packages of energy which can be transferred into the internal motion we therefore expect that slow electrons will be involved in only elastic collisions and will therefore not change their energy but that if we speed an electron up to a proper value that we then will make an inelastic collision and deliver all of that energy to the internal motion of the atom now to make a model which would exhibit this would really be pretty difficult so let's just go back and take a look at our original setup we are going to use a special vacuum tube for this experiment which has as you see a rather complicated electrode structure and a Big Blob of mercury inside to study this electrode structure in detail I have another tube which I've disassembled and we will take a good close look at this you see in the middle a little cylindrical cathode which has a heater inside and then there is a control grid just a spiral of wire very very fine in diameter and on the outside of this structure fits an accelerating grid a cylindrical wire screen and concentric with this accelerating grid is a metal anode now I'll show you the function of these parts in a schematic drawing I'll I'll start with the cathode and a heater which will operate on a 6volt storage battery and boil electrons out of the cathode the control grid then will determine the amount of current which passes through the control grid and into the region between control grid and accelerating grid I can adjust the amount of acceleration given to the electrons by means of a variable voltage and I will measure the voltage which is used for the acceleration to give the electrons energy as they come across the Gap I will then require that those electrons passing through Grid 2 have an energy of at least one electron hold in order that they be counted any a current meter which is attached to the anode now let us go back and look at the tube we will measure the tube current as we change the accelerating voltage and I will read the accelerating voltage on this meter from 0 to 30 volts and the anode current on the electrometer I will use the middle scale from 0 up to two measured in units of 10us 5 amp as I increase accelerating voltage we see first of all no current and then with further increase the current begins to rise if I increase the voltage continuously and smoothly the current Also Rises smoothly and returns back smoothly to zero now we can introduce Mercury atoms into the path of the electrons by placing the tube in this oven and heating it to about 160 degrees Centigrade Mercury atoms will vaporize from the Mercury blob and diffuse throughout the tube I can show you this using stop frame photography so that you can see the process happening more rapidly as the Mercury Heats it vaporizes from The Blob diffuses up through the tube condenses on the cooler portions drips down and runs back into the blob now if Mercury atoms behave according to our proposed model what do we think will happen this time as we increase the accelerating voltage at first of course we will expect no current until the electrons have acquired enough energy to get up the potential energy Hill then as we increase the accelerating voltage further we will expect that the current will increase just as before however this time there are Mercury atoms present in the space between the grids and we will expect that electrons will be making collisions with these Mercury atoms however as we saw in the dry ice dis experiment those electrons will not lose any appreciable energy to the Mercury atoms as long as the collisions are elastic therefore even though they Bounce Around quite a bit when they do go through Grid 2 they will have just the same energy which they had if there were no Mercury atoms present now as we increase the accelerating voltage still further we will finally arrive at a condition in which the electrons have gained enough energy in passing between the two grids so that they can deliver a full and proper sized package of energy to the Mercury atoms if they collide with such Mercury atoms right here near Grid 2 then they will lose all of their energy to those Mercury atoms and will not have enough energy left to get up the potential energy Hill at this accelerating voltage we will then expect to see a considerable drop in anode current let's try it and see what happens first I must change the scale on my current meter in order to read anode current in units of 10- 8 Amp because with Mercury atoms in the tube the overall tube current is cut down considerably now then as we increase the accelerating voltage again no current at first and then the current begins to come just as before electrons are being accelerated between the grid more and more there something's happening a drop in current something suddenly happened to the electrons so that they couldn't get across to the anode and be counted this is exactly what we were predicting therefore our postulate and the line of reasoning that we used seems to be borne out by the experiment apparently electrons can deliver to the atom only a certain siiz package of energy but now you also noticed that the current was beginning to increase as I stopped increasing accelerating voltage let's continue with this and see what happens as I continue to increase accelerating voltage 12 volts another drop once more an increase another drop a big one further increase smoothly increasing accelerating voltage another drop fourth one a fifth one and now I'm up to the full Voltage uh which I can apply across these grids well now this really looks interesting I think we'd better go back and do it again and see what we can make out of this result this time I would like to use an automatic recording device which will plot the anode current as a function of accelerating voltage this will make a permanent record and then we can read off from the graph the energy values at which the current dips occur I will increase the accelerating voltage and you remember that initially we have no current flow so you can get an idea of the noise of the system here at the beginning as I further increase accelerating voltage the current begins to rise there now starts the first dip once more the current begins to rise another decrease a big one this time and then another increase you'll notice that each inch of the horizontal scale represents 5 volts the Peaks seem to be just about 5 volts apart let's see if this continues we're approaching the fifth rise there is another another dip and now we're up to the 30 volts which is the maximum that I want to put between the grids now let's measure the voltage distance between these Peaks I don't really want to use the first Peak because I don't know where the current starts to rise from zero and also there are some Vol extra voltages around in the circuit that aren't being measured by this voltmeter but the distance between the first and second Peak is 4.5 vol volts between the second and third Peak is about 4.8 volts between the third and the fourth Peaks is about 4.9 volts and between the fourth and fifth Peaks about 5.1 volts these average out to be somewhere in the neighborhood of 4 .9 volt all of them as you see spaced rather uniformly now what does this tell us why should they all be just 4.9 volts apart there are two possible explanations for this and really this experiment alone cannot choose between them the first answer might be that an a Mercury atom can absorb only packages of energy which have a multiple value of 4.9 for example 4.9 volt 9.8 Vol 14.7 volt Etc or the other explanation could be that the electrons themselves collide with Mercury atoms so frequently when they get up to around 5 electron volts that they are not able to rise above that value but rather deliver their five electron volts to the Mercury atom and then have to start over again uh several times between the grids let me show you on our schematic why the second choice seems very plausible first I'll put a piece of glass over the schematic you remember that we said that when electrons are able to accelerate and Achieve an energy of five electron volts by the time they reach grid two that they then can make inelastic collisions with Mercury atoms in the vicinity of Grid 2 deliver their five electron volts to the Mercury atom and then not have enough energy left to get up the potential Hill and be counted in the current meter therefore a current dip is observed if now I increase the accelerating voltage further the distance which an electron must travel in order to acquire the five electron volts becomes smaller and smaller until finally when the accelerating voltage is 10 volts the first an elastic collisions can occur here and the electrons can still gain five electron volts of energy before reaching Grid 2 can make second inelastic collisions in this vicinity and then again are not able to get up the potential Hill and be counted therefore a second dip results with further increases in accelerating voltage You observe of course that the position of the first in elastic Collision is here and a second inelastic collision can occur here a third inelastic collision here and once more the electrons are not counted in the current meter resulting in a third dip thus with this experiment we can say only that the smallest of the packages of energy which a Mercury atom can accept is of size 4.9 electron volts now does this bear any relationship to the size of the energy package which can be carried off by a photon well using our relationship between the energy of a photon and the wavelength of the light and putting in 2537 angstroms for the spectral line which we looked at earlier we find that the energy of the photon is 124 ided by 254 it is 4.9 electron volts exactly the same sized energy package an atom therefore seems to absorb energy of this amount by electron collision and loses es the same amount Back Again by Photon emission as with any good theory a number of possible new experiments suggest themselves for example can we actually see 4.9 electronvolt photons coming out of this apparatus when we perform the experiment that we've just done is it possible to deliver this energy package of 4.9 electron volts to the Mercury atom through collisions with particles other than electrons for example with photons and indeed because there are other spectral lines present in the Mercury Spectrum do we not expect that the Mercury atom can absorb other sized packages of energy than this single 4.9 electron volts and then most important of all is this a particular behavior of mercury atoms or do all atoms do this and we should test this now of course to do these experiments requires equipment somewhat different from this however these experiments have all been done and your text gives you references to some of this work the demonstration and interpretation of the inelastic impact of 4.9 volt electrons with Mercury atoms in the film has been so clear that no supplement by my S is necessary to this experiment however I may speak a moment about another experiment we made to study what the results of these inelastic impacts you know and it was mentioned before in the film that one would expect that if 4.9 volt electrons lose all the energy to excite light that the line to 537 would occur because the Quantum of this ultraviolet light has exactly the same energy than the kinetic energy of the 4.9 Vol electrons so we made an experiment with a simpler apparatus I have a reprint of that fish me here of that old paper which was difficult to find because it's in the library Always Somewhere nearly 50 years ago somewhere in the Artic uh and uh we can see see the apparatus consisting only of two electrodes a glowing wire and other electrod anode included in a quartz tube because ultraviolet light should come out and would not penetrate through glass this qu tube contained Mercury and we heated it to suitable pressure so that enough en elastic impact would occur and we put a potential difference between the two electrodes a little bit higher than the 4. 9 Vol if we put that before the spectrograph which we bought for that purpose then we see that indeed only one spectral line occurs and we have also in this picture one normal Spectrum taken with the same bulb using higher voltages so that electric discharge occurred you will see in the Spectrum also a continuous Spectrum in visible region which is stay light coming from the glowing wire but uh that's all one can see the Spectrum gives only the line 2537 and no other spectral line occurs and so we had really the result which one might expect indeed we had a result which was in best agreement with B's uh Theory which said that atoms or better the electronic system of atoms can exist only in different discrete States of energy and that light emission occurs if an atom was excited to a higher so-called condom State and reverts by light mission to the ground state the line 2537 is the transition before between the first excited state in the ground streate it might interest you that when we made the experiment that we did not know B Theory we have neither read it nor heard about we have not read it because we've been negligent to read the literature well enough and uh you know how that happens and if on the other hand we one would think that other people would have told us about it for instance we had a at that time in berin in which all the important Pap were discussed nobody discussed B the why not the reason is that about 50 years ago I was so convinced that nobody could that state of knowledge we had available at that time understand spectral line emission that if somebody published a paper about it would assume probably it is not right so we did not know it that we made the experiment and got the result with confirmed B's uh theory was because we hoped that if we find out where the borderline between elastic and inelastic impact lies where the minimum velocity of electrons to emit some uh light lying it only one line might appear but we did not know whether that would be so and we did not know whether at all an emission of an atom is of such a type that one line alone can be emitted and all the energy could be used for that one purpose the experiment gave it to us and we were surprised about it but we are not surprised after we read B's paper later after our publication and when we made these other kinds of experiment and many other people made experiment of that type which are all in best agreement with this basic concept of B Theory indeed this uh experiment is good proof all the experiments on elastic impact of this Theory and you know that this first paper of B is really the fundament of the whole development of modern physics the whole development of attempts to understand the structure of atoms and molecules and even of the nuclei in detail