On the Influence of Temperature Upon the Photo-Electric Effect Citation Nielsen, Jeus Rud (1924) On the Influence of Temperature Upon the Photo-Electric Effect. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KFRS-VG77. https://resolver.caltech.edu/CaltechETD:etd-06162004-155504 Abstract No Abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Physics Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Millikan, Robert Andrews Thesis Committee: Unknown, Unknown Defense Date: 1 March 1924 Record Number: CaltechETD:etd-06162004-155504 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-06162004-155504 DOI: 10.7907/KFRS-VG77 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 2622 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 17 Jun 2004 Last Modified: 03 Oct 2019 23:19 Thesis Files Preview PDF (Nielsen_jr_1924.pdf) - Final Version See Usage Policy. 801kB Repository Staff Only: item control page

.On the Influence of Temperature upon the Photo-electric Effect By J. Rud Nielsen A Thesis Submitted to the Faculty of the California Institute of Technology In Partial Fulfilment of the Requirements for the Degree of Dector of Philosephy March 1924 Summary. 1. Interpretation of the threshold frequency. A discussion is given of the conclusion, reached by Millikan, that in the photo-electric effect the energy of the Light is transferred to the free electrons of the metal as well as to the bound electrons, and the threshold fre- quency Y, is interpreted by the equation hy,= d, - &, » where $, is the work necessary to remove a free electron from the metal, and E, the average kinetic energy of a free electron in the metal. In cases where E, is not small compared with $¢ the theory leads to a lack of sharpness in the definition of y. The observed uniformity of stopping potentials is due, according to the theory, ta the smallness of the Peltier effect. 2. Temperature variation of the long wave-length limit, From Millikan's free electron theory and Richardson's thermodynamical theory of electron emission the following expression is derived for the variation of the long wave- length limit with temperature: 24°. #?e« , @ being the Thom- son coefficient. In most cases , should be practically independent of temperature. 5. Effect of prolonged heating on the phete-electric current from aluminum for 2537 A. A solid target was heated in vacuum by high frequency induction for many hours to near the melting point, but the photo-electric current remained strong. 4. Variation with temperature of the photo-electric current from aluminum for 2537 A. - After prolonged heating, the current was found to remain constant within 1/2 per cent as the target cooled from 400 to 100 C. This constancy is interpreted as fairly conclusive evidence that the shift of the long wave-length limit with change of temperature is less than 1 A. The limit was found to be at about 2700 A. Similar observations with a nickel target and 2412 A gave inconclusive results as in spite of heating to 1300 C and reduction of the oxide on the surface by heating in hydrogen, reproducible results were not obtained, (1) Introduction. The influence of temperature upon the photo-electric effect has been studied by a number of investigators“, all with negative results. The photo-effect was found independent of temperature within the experimental errors, In the earlier investigations monochromatic light was not used, and the errors of observation were large. Koppius recently determined the long wave-length limit of platinum, and found it independ ent of temperature to less than 1 A for the range 50 to 500 °C, Other experiments? » however, have shown that the apparent long wave-length limit of platinum is gradually decreased as the surface is being denuded of occluded gases by prolonged heating at higher and higher temperatures. The question as to whether or not the photo-electric sensitivity is an intrinsic and invariable property of metals has thus been raised again. In the present investigation the variation of the long wave-length limit to be expected from a theoretical standpoint is discussed, and an attempt has been made to determine the temperature variation upon surfaces freed from gases as well as possible by heating in vacuum. (2) 1, Interpretation of the long wave-length limit, In 1921 Millikan® found that the "stopping potential" i.e. the potential that must be applied in order to prevent the photo-electrons from reaching the receiver, is quite accurately the same for different emitting metals, provided the same receiver is used. From earlier experiments by Her- mann t a similar inference may be drawn, This peculiar fact led Millikan to the conclusion that the electrons which escape from a metal with the maximum velocity under the influence of light are the free electrons of the metal, On account of the great importance of this result for the inter- pretation of the photo-electric phenomena a brief discussion of it will be given. It will be shown that 4t furnishes an interpretation of the long wave-length limit and leads to definite conclusions as to the temperature variation. It is immaterial for the analysis here given whether we assume that the light energy is transferred directly to the free electrons of the metal or indirectly, as suggested by Epstein, through collisions of the second Kind. Millikan's conclugion is that the light energy hy is transferred | undiminished to electrons which are in the same state as those emitted as thermo-electrons. Very little is known about the conditions of the free electrons. We shall, therefore, make no special assumptions but use only two equations, (3) derived by 0. W. Richardson” from purely thermodynamical though not quite rigorous considerations. These equations are z = 324 - ec (1) " oY ad : oT « O' -F where p is the increase of energy which accompanies the transference of an electron fron the interior of a metal to a point outside, ¢ and d"being the values for two differ- ent metals; T denotes the absolute temperature, k Boltzmann's constant, e the charge of an electron, G the coefficient of the Thomson effect, and V the contact difference of pot- ential between the two metals. The term et may also be written eP, P being the Peltier coefficient. The terms eG av and eT yp are, in general, small compared with the other terms in the equations. As Bohr ® has pointed out, P and G are not identical with the coefficients found by experiments, but this fact is of little importance for the present considerations. The values found for the specific heats of metals and for the Thomson coefficients indicate that the average kinetic energy of the free electrons within the metal is, in general, much smaller than the equipartition value 3/2 kT. We will, therefore, disregard the fact that the kinetic “energy 4s not the same for all the free electrons. We will (4) denote by Ep the potential energy of a free electron, and by E, its average kinetic energy within the metal, and will place P=b+ds where $, is the gain in potential energy, and dp, the gain in kinetic energy accompanying the trans- ference of a free electron from the metal to the surrounding electron atmosphere. If the heat energy of the electron atmo- sphere be assumed to equal that of a moatomic gas, we have $, = 3/2 kT -E,. We are now prepared to give an interpretation of the term hy in the expressicn for the maximum kinetic energy of the photo-electrons, which was predicted by Einstein and verified by Millikan, viz. (V.- Vee hy-hy , (3) where V, $s difference of potential between emittor and receiver. If, denotes the stopping potential, and V, the contact following Einstein, we assume that. the energy hy of a light quantum is transformed to kinetic energy of a single electron, then the largest possible value of the kinetic energy of a photo-electron escaping from the metal must be E+ hy - Pp . The frequency y for which this is zero is the threshold frequency, and we have hy=@-E. (4) Instead of using this expression for hy Millikan’, placing hy = >, used a value which is 3/2 kT larger. This, however, did not influence his result because the value of (5) hy, for one metal was subtracted from that for another, Substituting for hy in (3), and subtracting the equations for two different metals, we get U ” f 4 i ” “(Wo- We +Ve=f-P@-F+ Ek, where V = Y- Vis the contact difference cf potential between the two metals. Now substituting the value for Ve obtained from (2), and remembering that > +E = 3/2 kT, we simplify the equation to -(v'- vi") + 720 = 0, (5) The last term in (5), from the values of the measured Peltier coefficients, is of the order of magnitude of 10 to 10*volts. Millikan's conclusion that the light energy is transferred to the free electrons of the metal leads, there- fore, to a simple explanation of the independence of the stopping potential upon the nature of the emittor. From (5), however, it will be seen that accurate measurements of stop- ping potentials should reveal slight differences approximate- ly equal to the Peltier coefficients, expressed in volts. It would be of great importance for the theery if determinations of'ibtopping potentials could be made so accurately as to allow a test of (5). | The expression (4) for hy is valid only when the differences in the kinetic energies of the free electrons May be disregarded. It will, therefore, not hold at high temperatures. Under such conditions, according to the free (6) electron theory, an appreciable lack of sharpness in the definition of the threshold frequency and the stopping pot- ential should occur. It seems impossible to explain the equality of stop- ping potentials for different metals by any other simple theory of the photo-electric effect. The assumption that the light energy is transferred to electrons bound in the atoms would imply, as shown by reasoning similar to that given abow that the electrons bound in atoms of different metals possess. the same energy. This is at variance with all we know about atomic structure. The assumption that the uniformity of stopping potentials is due to a uniform gas layer on all metals would lead also to a uniform threshold wave-length and to a uniform photo-electric sensitiveness, due corrections being made for differences in reflecting power, This is not in accord with observations. The hypothesis that light energy can be transferred entirely to a free electron may seem rather strange at a first glance. It may, therefore, be worth while to note that it may be arrived at by a natural generalization of the ideas by which the continuous absorption spectrum of hydrogen or | sodium is explained. It is assumed that when light of shorter wave-length than the limit of the absorption series is absorb- ed, the electron is knocked out with a kinetic energy equal to the difference between hy and the work necessary for ion- ization. But if this absorption process may take place however (7) loosely the electron be bond, it should also occur in the limiting case of the electron being free. 2. Temperature variation of the long wave-length limit. The influence of a change in temperature upon the threshold frequency y may be found immediately from the theory discussed above. Since p = p+ 3/2 kT - Boo the equation (1) may be written 2. — =~ 0S Stl Pp EO) but f, > B= hy, hence a(ky,) - -~-eg (6) oT or » 2As —_ Ae Ag > 7A. being the one wave-length limit. oO The temperature variation of the threshoid frequency or the long wave-length limit is thus proportional to the Thomson coefficient. Since the Thomson effect is always very small, the long wave-length limit should be practically independent of temperature. For aluminum Borelius and Gunne- son’ have found G = - 0,56 microvolts per cegree at 400K, while A,= 2700 A. Substituting these values we get ahs = 3.3.x 10 *A per degree, i.e. a shift in long wave-length limit of 1/10 A for a change in temperature of 300 degrees. For all the metals for which both G and A,are measured (6 a) @ives so small values for the temperature variation that, (8) with the accuracy with which photo-electric measurements are now being carried out, it should not be possible to detect the variation. For the alkali metals, however, a . Measurable variation may be expected since G is large, as indicated by the values found for the specific heats, and since A, is also large. | In the preceding only the long wave-length limit has been considered. No satisfactory theory has yet been given for the velocity distribution nor for the magnitude of the photo-electric saturation current. The reason for thés ' is partly the lack of a satisfactory substitute for the old electron theory of metals and partly the lack of reliable photo-electric data. We shall, therefore, not attempt to treat theoretically the effect of temperature upon the photo- electric current. 5. Experimental method and apparatus. A variation of the long wave-length limit has been searched for by observing the photo-electric saturation current at different temperatures of the emitting metal, - using a wave-length just below the long wave-length limit. Actual measurements would require observations with differ- ent wave-lengths. If photo-currents are found to be constant, it may be reasonably inferred that the long wave-length limit is independent of temperature. (9) Photo-electric targets of aluminum and nickel were heated in vacuum by high frequency induction. Two Western Electric 212-A tubes, in parallel, served as generators of the high frequency currents which were sent through the primary coil of thick copper tubing surrounding the photo- electric tube. The targets were solid cylinders of diameter 1.9 cm and length 2.0 or 1.2 cm. Puring the slow cooling of the target the saturation current was measured by the aid of a quadrant electrometer connected to the cylindrical receiver which partly enclosed the target. Fig. 1 shows the two types of photo-electric tubes used. Both were made of Pyrex glass. A quartz window was cemented on with a high temperature cement. The temperature of the seal was kept below 100°C by water cooling. In tube A, with which most of the experiments with aluminum were made, the target was fixed with respect te the receiver. When the target was heated the receiver would also be heated. In order to prevent the receiver, which was made of copper, from melting the heating of the target had to be applied intermittently, so as to let the thin copper cylinder cool for a short time between consecutive heatings. In tube B, which was used for nickel, the target was heated outside the receiver, which was also made of nickel, and then lifted up into the receiver by a simple magnetic device. The light reached the target through a slit in the top of the receiver. Both tubes had, to begin with, thermo-couples for measuring nm (10) . the temperature of the target. These, however, soon got out of order. In one case the junction moved out of the target at the first heating to the melting point; in another case a discharge took place from the coil outside the tube to the thermo-couple wire inside. Enough data were obtained, however, to permit an estimate of the temperature during the cooling. The only temperature used for the calibration of the thermo- couples was the melting point of aluminum. - The tubes could not be used very long or the glass would be heated to the seftening point by radiation from the target and by currents in the layer of metal deposited on the glass wall by evaporation of the target. A 220 volts quartz mercury lamp and a Hilger mono- chromatic illuminator were used for illumination. The lamp was enclosed in an asbestos box and run at a constant high- voltage, the voltage drop in the arc alone being about 120 volts. By means of a large quartz lens an image of the arc, of nearly natural size, was formed on one slit of the illum- inator and adjusted so that the middle coveréd the slit. The light then just filled the collimator lens. Under these circumstances the variations in the intensity of the illum- ination were found to be practically negligible. The photo- electric tube was set up vertically so that the quartz win- dow was only a few mm from the other slit of the illuminator, the slit in the receiver being large enough to let the (11) slightly divergent light to pass to the target. The pressure in the tube was in most cases so low that no reading could be obtained by a McLeod gauge even when the target was heated. 4. The cleaning up of the aluminum surface by heating, With alumimum the photo-wurrents were so large that they could be measured by the constant deflection obtained when the two pairs of quadrants were shunted with a large resistance consisting of a line of ink on a strip of paper. The sensitiveness of the electrometer was about 1500 hm per volt at a scale distance of 1m. In almost all the experi- ments with aluminum the line 2537 A was used. Heating of the target was found to have a great effect upon the photo-electric current. When aluminum has been ex- posed to air, or when it has been kept for a long time in a vacuum without being heated, the photo-current is small. A short heating, however, will preduce a considerable increase in the current; and as the heating is continued, and the temperature raised, the photo-current will reach a maximun, decrease, and then increase again until a value of 5 or 10 times the original is reached. Further heating to a temp- erature close enough to the melting point produces a decrease in the current. When the aluminum had been heated for a long time, and the melting point had been reached several times (12) during the intermittent heating, the photo-current had attain- ed a value of about one third of the highest value observed, and continued heating produced no furhher change of the photo-current. In -one case the following values of the current for 2537 A were obtained during the process of cleaning up, the target being heated several times between consecutive values: 6.4, 25.8, 24.0, 18.9, 20.8, 27,7, 43.0, 45.5, 18,5, 17,5. The effect ofthe cleaning up by heating upon the photo-current from aluminum is of the same general character as that found for platinum by other observers”. The fact that the photo-current remains strong after prolonged heating at the melting point is an evidence against a fundamental dependence of the photo-effect upon surface impurities. Obviously, the heating has not produced a complete cleaning up of the aluminum surface. Close to the melting point, how- ever, a breaking up of the surface occurs, so that it becomes granular. Whether the currents are due mostly to aluminum or to the oxide is unknown. The following observations may be of interest in the difficult problem of determining the nature of the surface impurities. When the photo-current was observed for a suffi- ciently long time after the heating an increase in the current was always observed. However, if the liquid air were removed from the charcoal tube between the photo-electric tube and (18a) MINUTES LNG@a u¥n90- 0 Loud 300 200 100 FIG 2 (13) the pumps, leaving liquid air only on a trap closer to the pumps, a considerable decrease in the current would immediate- ly set in, amounting to about 30 per cent of the initial value in two minutes and to 40 per cent in ten minutes. 5. Temperature variation with aluminum, As long as the aluminum was not. sufficiently cleaned up by heating a considerable variation of the photo-electric current was observed during the cooling. In all cases the photo-current was found to decrease at first. The current would generally decrease and then become almost constant; in some cases, however, an increase followed the decrease. A typical example is given in Fig. 2 Curve 1, the photo-currett being plotted against time of cooling.The first readings were taken two or three minutes after the thermionic current had become negligible, the temperature then being about 400°C. By the time the photo-current had become constant the temp- erature was about 150°C. The constancy of the current during the last part of the ccoling is remarkable. This may be better seen from Table I which gives all the readings taken during twenty minutes. The smallness of the variations gives an idea both of the constancy of the light intensity and of the accuracy with which the photo-currents could be measured. That the decrease observed in the beginning is not due simply to a dependence of the photo-current upon tempera- Time 110 min 112 112 113 114 115 116 117 118 119 (13a) Table I. Pheto-current Time (2537 A) 28.20 (cm) 120 min 28,18 121 28.15 122 28,14 123 28.11 124 28,13 125 28.12 126 28.45 127 28.15 128 28.14 129 Table II. Time Photo-current (2537 A) 0 min 17.2 (cm) 10 17.3 20 17.35 30 17,29 40 17.30 50 17.33 62 17.6 70 17.8 80 18,0 Photo-current (2537 A) 28.13 (cm) 28.12 28.15 28,10 28,13 28,15. 28,10 28.20 28.12 28.14 (14) ture is most clearly brought out by comparing Curve 1 with Curve 2, which was taken immediately after Curve 1, the target having been heated for three minutes to about 400 C between the two sets of readings. The longer the aluminum was heated, and the higher the temperature to which it was heated, the smaller amas the variation of the photo-current observed during the cooling. Curve 3 was obtained after the target had been kept red hot for 1 1/2 hour, the temperature never quite reaching the melting point. The total variation of the current is only about 3 per cent. However, in this case the aluminum was not yet cleaned up as much as possible. Table II gives the result of the last experiment made with aluminum. The target had now been heated several hours daily for twe months. It was very much deformed and displaced, and the next heating resulted in a break-down of the tube. Immediately before the readings were taken. the target was heated for one hour, the temperature being kept clese to the melting point which it reached several times. The electrometer zero was determined twe minutes before and two minutes after every reading, and corrections were made for a slow motion of the zero amounting to 1.4 em per hour. Almost no variation whatever of the photo-current is obserded during the first 50 minutes of the cooling. The increase at lower temperatures indicates that some surface film is being (15) formed. The experiments with aluminum have thus failed to detect any variation of photo-currents with temperature between 400°C and room temperature. In the temperature range 400°C to 200°C the photo-current obtained with 2537 A is -found constant within 1/2 per cent. From the constancy of the saturation current we may infer that the temperature variation of the threshold wave- length of aluminum is very small. An estimate of the change in long wave-length limit corresponding to a change in the current for 2537 A of 1/2 per cent may be obtained in the following way. The curve representing photo-current per unit intensity of illumination as a function of the wave-length will be nearly a straight line in the neighborhood of the long wave-length limit. If we assume that a small change in the limit simply produces a displacement of the curve paral. el to the wave-length axis, then a constancy of the current within 1/2 per cent means a shift of the limit of less than 1 A, the limit being about 150 A from the wave-length used. . No accurate determination of ths long wave-length limit was made. A rough determinaticn gave for aluminum cleaned up by heating the limit 2700 A, which is much lower than that found by Richardson and Compton§, (16) 6. Experiments with nickel. With nickel the results were not nearly as conclus- ive as with aluminum. The photo-currents were. so small that the steady deflection method could not be used. The currents were measured by the rate of charging up of the receiver connected with one pair of quadrants. In order to clean up the target it was heated to 1300-1400°C. The tube could not stand a heating to this temperature for a very Long time. Oxide on the surface was reduced by heating in hydrogen. The readings of the photo-current were started, as with aluminum, as soon as the thermionic current was negligible, which occurred at about 550°C. A constant current was never obtained. Fig. 3 shows two of the curves obtained with 2412 A. Before Curve 1 was taken the target had been heated for 15 minutes at 1300-1400°C Curve 2 was obtained right after Curve 1, the target having been heated for 40 minutes between the two sets of readings. Though the current varies considerably during the cooling, the fact that there is no large variation during the first very rapid cooling indicates that the variation is not due simply to a dependence upon temperature of the photo-electric effect. The long wave-length limit of nickel was roughly determined at 2500 A. (16a) FIG 3 MINUITES LGTUNAO-O LOUd 60 50 40 30 a0 10 (17) In conclusion, the writer wishes to express his great indebtedness to Frofessor R. A. Millikan who suggested the problem, and under whose direction the work was done. Bibliography. Lienhop, Ann. der Phys., 21, 281, 1906. Dember, Ann. der Phys., 20, 378, 1906; 23, 957, 1907. ‘Ladenburg, Verh. ad. D. Phys. Ges., 9, 165, 1907, Millikan and Winchester, Phil. Mag., 24, 188, 1907, Kunz, Phys. Rev., 29, 174, 1909. Koppius, Phys. Rev., 18, 443, 1921. Hallwache, Phys. Zeitschr., 21, 561, 1920. Sende and Simon, Ann. der Phys., 65, 697, 1921, Suhrmann, Ann, der Phys., 67, 43, 1922, Tucker, Phys. Rev., 22, 574, 1923. Millikan, Phys. Rev., 18, 236, 1921, Hermann, Verh. d. D. Phys. Ges., 14, 557, 573, 936, 1912, Richardson, The Emission of Electricity from Hot Bodies, London, 1916, pp. 32, 41. Bohr, Phil. Mag., 23, 984, 1912, (18) 7 Borelius and Gunneson, Ann. der Phys., 65, 520, 1921. 8 Hallwachs’ article in Handbuch d. Radiologie, edited by E. Marx, vol. 3.