The Photoelectric Effect: Lab Guide

The Photoelectric Effect MIT Department of Physics The objective of this experiment is to demonstrate the quantization of energy in electromagnetic waves and to determine Planck’s constant h. You will measure the maximum kinetic energy of electrons ejected by the photoelectric effect from an alkali metal surface as a function of frequency. A constant offset in energy is caused by the work function φ of the metal cathode, i.e. the minimum energy needed to eject an electron out of the specific metal. PREPARATORY QUESTIONS Please visit the Photoelectric chapter on the course website to review the background material for this experiment. Answer all questions found in the chapter. Work out the solutions in your laboratory notebook; submit your answers on the web site. [Note: Not available to OCW users.] I. HISTORICAL BACKGROUND A very accessible introduction to this material is in the American Institute of Physics’s A Look Inside the Atom. In 1887 [3], soon after discovering radio waves, Heinrich Hertz observed that when ultraviolet light from the sparks of his radio wave generator fell on the nega-tive electrode of his radio wave detector, they induced a flow of electricity in the gap between the electrodes. Pur-suing the phenomenon in detail, he discovered the photoelectric effect whereby light of sufficiently short wavelength causes the emission of charge from a metal sur-face. Philipp Lenard (1905 Nobel laureate) made im-proved measurements and demonstrated that the charge to mass ratio of the emitted charge was identical to that of the electrons which had recently been discovered by 1906 Nobel laureate J. J. Thomson in experiments with cathode rays. Crude though the early data were, the qualitative fact of the dependence of the critical cutoff voltage on the wavelength of light emerged with sufficient clarity to induce the young Albert Einstein, working as a patent examiner in the Swiss Patent Office in 1905, to link the effect with the recent idea, introduced by Planck in 1900, that matter radiates its energy in quanta of energy hν. He postulated that light delivers its energy to an absorber in quanta with energy hν. Thus, if it takes an amount of energy φ to lift an electron out of the surface and away from its image charge, then the residual kinetic energy K of the ejected electron is K = hν − φ. (1) The 1921 Nobel Prize was awarded to Albert Einstein for his discovery of “the law of photoelectric effect”. It was not until 1912 that the technical problems of making precision measurements of the photoelectric effect were overcome by 1928 Nobel laureate Sir Owen Wilans Richardson and K. T. Compton (former MIT president) to the point where the Einstein photoelectric equation could be tested to high accuracy and used in precise determinations of Planck’s constant h = 6.626 × 10−34 J·s = 4.135 × 10−15 eV·s. In this experiment you will measure the photoelectric current from an alkali metal surface as a function of a retarding potential that opposes the escape of the electrons from the surface. From the data you will be able to derive the value of Plank’s constant and the work function φ of the cathode material. II. EXPERIMENTAL SETUP The apparatus is depicted in Figure 1. Familiarize yourself with all of the components before turning anything on or making any signal connections. Open the photocell enclosure and observe the photocell itself, noting the height and orientation of the anode ring. Be sure that the photocell is properly aligned with your optical path. CENTER CONDUCTOR KEITHLEY ELECTROMETER Triax ("COM" on back) MERCURY LAMP FILTER WHEEL TRIAX SHIELDS LENS (OPTIONAL) PHOTOSURFACE (CATHODE) AGILENT POWER SUPPLY RING-WIRE ANODE + - PHOTODIODE FIG. 1. Experimental arrangement for measuring the photoelectric effect. The lens focuses the light to avoid hitting the anode ring. The Agilent variable DC Power supply provides the retarding voltage between the anode and the cathode. Pay close attention to the grounding connections between the electrometer and the power supply! If the power supply meter does not have sufficient resolution, try using an external digital voltmeter. Connect the phototube cathode to the Keithly electrometer (or similar model) operating as an ultra- Id: 005.photoelectric.tex,v 1.57 2013/08/26 01:14:54 spatrick Exp Id: 005.photoelectric.tex,v 1.57 2013/08/26 01:14:54 spatrick Exp 6 3 x 10 Spectral Output of Thermo−Oriel Hg Lamp Model #65130 Photons 2.5 2 1.5 1 0.5 0 3000 3500 3 4000 4500 5000 5500 6000 5500 6000 With 4360 Angstrom Band−pass Filter 6 x 10 Photons 2.5 2 1.5 1 0.5 0 3000 3500 4000 4500 5000 Wavelength (Angstroms) FIG. 2. Top Panel: Spectral output of the Thermo-Oriel 65130 Hg lamp after about 20 minutes warmup. Bottom Panel: Shows the lamp output after passing through the 4360 Å filter. sensitive ammeter. Note that the input connector to the electrometer requires a triaxial connector for double grounding and thus be certain that you insert a BNC– triax connector before connecting the BNC cable from the cathode. Turn on the power supply and reduce the retarding voltage to zero. II.1. Light Source The radiation source for this experiment is a highpower mercury discharge lamp Oriel 65130, or similar model. You should turn on the lamp as soon as you begin the lab to allow it to warm up. The spectral output of the lamp will change during the first 10 – 15 minutes. Once the lamp has stabilized, the spectral output is similar to that shown in Figure 2. The narrow band pass filters used to select individual mercury emission lines have a preferred orientation; point the highly-reflecting side (a silvery color) toward the lamp and the colored side towards the phototube cathode. Be careful not to place the filters too close to the lamp! The heat can bleach the color of the filters, leading to undefined behavior! Monitor the heat of the filters as you perform the experiment. 2 potassium is the source of the photo-ejected electrons in this experiment. It is not possible to precisely determine the work function for removing an electron, because the cathode surface interacts with the remaining gases in the photocell as a getter, so that the surface characteristics change a little from the ideal case. It is important to note that the electronic work function φ is a material constant which incorporates the different emission potentials of the cathode and anode. The former is a difficult quantity to estimate due to the manufacturing process which makes the cathode surface inhomogeneous. It is composed of a mixture of potassium, potassium oxide and oxidized silver. For this reason, you need to take care that the same area is always illuminated. The emission work function of the photoelectrons can vary locally! Caution: 1. The photocell consists of an evacuated glass bulb. It is fragile! 2. Do not subject the photo cell to mechanical stresses. 3. Protect the photocell from overheating. 4. Protect the photocell against excessive incident light. Use filters if necessary. III. PROCEDURE Illuminate the photocathode with light of the various spectral lines of mercury selected by the interference filters mounted on the filter wheel. You may want to start with the more energetic spectral lines. Typical photoelectric currents are 100–1000 pA. Rigorously convince yourself that the current you are measuring is a photoelectric current caused by the mercury lamp. With creative use of black tape and the open hole, one can correct for ambient light effects if necessary. Measure, tabulate, and plot the phototube current as a function of the the retarding voltage for each filter. Make sure to extend the measurements beyond I = 0 in order to measure the effects of “reverse” current. Repeat the series of measurements at least five times to obtain the data necessary for a reliable estimate of the random errors of measurement. You will need to develop on a strategy to guide your data taking. You must decide: 1. how many wavelength filters to measure, II.2. Photocell The cathode of the Leybold photocell is a very thin layer of potassium (φK = 2.3 eV) deposited onto an oxidized silver coating electrically connected to the cylindrical brass cap on top of the cell. The anode ring is made from platinum-rhodium alloy (φPt = 5.7 eV). The 2. the range and step sizes of applied retarding voltages to use, and 3. the number of repetitions of each voltage scan. Obviously, for each listed factor, more data is better, but your available resources — in the context of Junior Lab, time is your principle manageable resource — to execute the strategy are very limited. You are therefore faced Id: 005.photoelectric.tex,v 1.57 2013/08/26 01:14:54 spatrick Exp 3 frequency of the filter bandpass. According to Eqn. (1), this should go as V = FIG. 3. Case A: electrons will travel in a straight direction when emitted for Vretarding =0. Case B: electron trajectories are nonlinear for finite retarding voltages. not with the simple question of what strategy is best, but rather the more subtle question of which strategies are good enough. To evaluate how good a strategy is, you must decide the scientific goal of your experiment: what are you trying to measure, and to what precision? The following are practical problems with which you must contend: 1. Light striking the anode ring can produce photoelectrons that cause a reverse (negative) current in the electrometer and confuse the identification of the critical cutoff voltage. You may need to focus the light beam so that it passes cleanly through the ring without illuminating it. Experiment with the location of a lens to produce the sharpest image possible at the aperture to the photocell holder. 2. Proper grounding of the apparatus is essential to obtaining reliable data. When the grounding is proper, the electrometer readings should be unaffected by touching or moving your hand near the equipment. 3. Because you are measuring such small currents (the currents you obtain with no retarding voltage should be on the order of hundreds of picoamps), the ammeter will be prone to pick up induced currents from ambient magnetic fields and your induction of charges while moving near the apparatus. You can avoid such interference by keeping the connecting wires as short and direct as possible and free of loops. For instance, you might want to use a short piece of copper wire to ground the positive terminal of the power supply as shown in Figure 1. You may also find it useful to twist some of the cables together. ANALYSIS To analyze the data, first determine the cutoff value of the retarding voltage for each of the filters, and assess the random and systematic errors of each determination. Then, plot the cutoff voltages against the center (2) Taking into account the uncertainties in the cutoff determinations, use linear fitting methods to compute the best-fit values and uncertainties of h and φ from your plots. Estimate the systematic errors in your best-fit values. Discuss in detail how you have determined the cutoff voltage. If you can use two different methods, the differences in h and φ will give you a lower limit of the systematic errors. Note that the very notion of a well-defined cutoff voltage is implicitly dependent on describing the system by theoretical models which predict a sharp cutoff in the photocurrent. You may find that the data themselves do not support the notion of a sharp cutoff voltage as anything more than an approximation1 . However, you may find that this approximation is adequate enough for performing the analysis. See References [1] and [4] for discussions of physical effects in the apparatus which confound the identification of the cutoff voltage by virtue of being difficult to capture in a simple model. Suggestion: You can probably make more reliable determinations of the change in cutoff voltage from one wavelength to the next if you normalize your current data so that the zero-voltage values are all the same. Plots of normalized current versus retarding voltage will then show clearly the effect of photon energy on the cutoff voltage. One significant problem lies in the observation that the current decrease is not linear close to the cutoff voltage. Consider Figure 3 cases A and B for easy visualization. IV.1. Topics which may come up during oral exams 1. The wave-particle duality of photons and electrons. 2. The potential energy in eV of an electron as a function of distance from a smooth conducting plane. 3. Classically consider a metal atom (d = 0.3 nm) bathed in radiation of intensity 1 mW·m−2 . How long does it take to accumulate enough energy to overcome φ = 4 eV? How can you disprove the classical estimate? 4. Your measurement chain may or may not be sensitive to ambient light. Check to see if the current you are measuring is affected when you cover the experiment with black cloth. IV. h 1 ν − φ. e e 1 Of course, for any model of finite detail, there always exists the potential of a sufficiently precise future data set capable of undermining it. The model is still useful for describing less precise data sets, but there is no meaning in quoting measured values of notions defined in the model to a precision greater than that to which the model describes the data set. Id: 005.photoelectric.tex,v 1.57 2013/08/26 01:14:54 spatrick Exp V. STATISTICAL EXERCISE 4 and frequency, estimate the variance. What does it mean for measurements to be independent? 1. From your hopefully independent measurements of current I at each value of the retarding voltage Vr [1] A. Melissinos, Experiments in Modern Physics (Academic Press, 1966). [2] P. Baumeister and G. Pincus, Sci. Am. 223, 58 (1970). [3] H. Hertz, Annalen der Physik 267, 983 (1887). [4] L. A. DuBridge, Physical Review 43, 727 (1933). Appendix A: Equipment 1. Manufacturer Thermo Oriel Thermo Oriel Thor Labs Leybold 2. Equipment List Description Low-Pressure Hg Lamp Hg Line Filters Optical Components Photocell URL oriel.com oriel.com thorlabs.com leybold-didactic.de Baking out the anode ring Potassium can precipitate on the anode ring in very old photo cells in the course of storage at higher ambient temperatures or under illumination of the photocell at very high intensities, making it necessary to bake out the anode ring. Bake out the anode ring only if the measurement cannot be improved by any other means, as the potassium atoms baked out of the anode ring can precipitate over the entire photocell. When the process is performed improperly, the potassium layer of the photocathode can be overheated, releasing more potassium and can irreparably damage the device! Please do not attempt this procedure without first consulting a member of the technical staff! 3. Ultraviolet Safety Ultraviolet radiation (UVR) is emitted from low pressure mercury vapor. The mercury vapor emits UVR when an electrical discharge is passed through it. Most of the energy emitted is at a wavelength of 254 nm. This lies in the UVC portion of the spectrum (180–280 nm). In the case of fluorescent lighting, the 254 nm radiation is used to excite a phosphor which coats the inside of the glass envelope of the lamp. The phosphor will re-emit at visible wavelengths (different phosphors produce different colors), and any UVC which is not absorbed by the phosphor will be absorbed by the glass wall of the lamp. However, the mercury discharge will also emit at other wavelengths — notably at 365 nm, which lies in the UVA (315–400 nm). This UVA radiation may not be absorbed by the phosphor, and much of it will pass out through the lamp walls into the environment. For more information on UV radiation, see the Health Physics Society site at http://www.hps.org/ hpspublications/articles/uv.html