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Physics 19 – Photoelectric Effect Overview: In 1887, Heinrich Hertz discovered that when electromagnetic radiation shines on a clean, metal surface, electrons are emitted from the surface. This phenomenon is called the photoelectric effect. Not surprisingly, the number of electrons emitted per unit time (called the photocurrent) depends on the intensity (i.e. brightness) and frequency (i.e. color) of the light that shines on the metal surface. However, the details of the relationship were quite surprising to 19th century scientists. The photoelectric effect can be studied using an apparatus like the one shown on the right. It consists of an evacuated glass tube that contains two metal electrodes. The tube is connected to a power supply with a variable resistor that controls the potential difference V between the two electrodes. Light shines on one electrode which emits electrons - this electrode is called the cathode. The current due to the emitted electrons is measured by the galvanometer. The purpose of the variable resistor and power supply is to measure the energy of the electrons emitted from the metal plate. If there is no potential difference (and therefore no electric field), electrons will be able to travel across the evacuated tube and reach the other end. However, if the potential is applied so that there is an electric force opposing the motion of each electron, only electrons with sufficient energy will be able to cross the tube. By increasing the potential until there is no photocurrent (and measuring that potential), the maximum kinetic energy of electrons leaving the metal plate can be determined. Most undergraduate physics labs try to reproduce the original method outlined above, but unfortunately it is very difficult to achieve accurate results this way. The advantage of the historical approach is that it allows one to be certain that one is precisely measuring the peak kinetic energy of the electrons ejected from the cathode. For simplicity, we will call this quantity here “voltage of the electrons.” The historical experiments were conducted using mercury lamps and filters to produce monochromatic light at a few different frequencies. For this lab we are using more modern circuitry to allow us to make precise measurements without having to take great care to shield our experiment from outside sources of noise. When we wish to measure the voltage due to the electrons ejected from the cathode, we connect the anode to an op-amp which provides a very high impedance. The electrons then cannot flow freely, so they will build up on the anode until it produces a field sufficient to repel even the fastest electrons back to the cathode. This is analogous to the “stopping potential” in the historical experiment. We can thereby estimate the maximal electron kinetic energy coming off the cathode without applying an external potential. We are also using laser diodes to produce monochromatic light that has a much narrower range of frequencies than we can achieve using filters, and which also produce greater intensity of light. Page 1 Photoelectric Effect: 10/2014 ABG Equipment: The silver box you will be using contains the following circuit: Amplifier box Essentially it is an amplifying circuit and an isolation circuit side by side. When you connect the phototube to the voltage side, the circuit isolates the phototube in such a way that measurements can be taken without affecting the small number of electrons that one has to work with. When you connect the tube to the current side, the op-amp converts the tiny current that the tube produces into a voltage. For each microamp (µA) of current, the circuit will produce a voltage of 1 volt. You will be able to measure either the voltage of the ejected electrons, or the (photo-) current generated. You can measure both, but only one at a time. The leads from the phototube can be connected to either the voltage inputs or the current inputs of the amplifier. When connecting to one side of the amplifier, the corresponding switch on top of the box needs to be in the “on” position, and the respective other switch needs to be off. Box containing phototube Page 2 Photoelectric Effect: 10/2014 ABG Effective experimental setup for photocurrent measurement: Effective experimental setup for stopping voltage measurement: The outputs of the amp should always be attached to the voltage measurement inputs of the multi-meter. Multimeter When measuring voltage, the meter will display the voltage of the ejected electrons. When measuring current, the meter will display: Page 3 1 volt per microamp. Photoelectric Effect: 10/2014 ABG The phototube we are using is an RCA 929, which has a cathode made of SbCs3. In the photo you can see the curved cathode and the thin, straight anode. The black tape is to block light from hitting the anode, since we're trying to measure the properties of only the cathode. The accepted value for the work function of this cathode material is 2.85 x 10-19 joules. Phototube Spectral sensitivity of the cathode You will be using lasers as light sources, since they reliably produce monochromatic light. These lasers can be dangerous – do not turn them on without first installing the diffuser. Everyone should have taken the online laser safety tutorial before lab. Please read the procedures carefully, and wear the appropriate safety glasses while you are working with the lasers. Many of the lasers look like standard laser pointers (two of them are actually sold as laser pointers), but don't let that fool you into thinking they are harmless. Be very careful not to look into the beam, and not to point them in such a way that they may reflect off a shiny object into someone else's eyes. The lasers have the following values: Page 4 405 nm Violet, <5mW class IIIa 445 nm Blue, <100 mW class IIIb 532 nm Green, <5 mW class IIIa 589 nM Orange, <10 mW class IIIb 650 nm Red, <5 mW class IIIa 808 nm IR, 50 mW class IIIb Photoelectric Effect: 10/2014 ABG Note that the beam from the infrared laser is nearly invisible. Do not assume that it is off just because you don't see anything. In order to determine if the infrared beam is working and is aimed properly you can use a cell phone camera. The CCDs in digital cameras are sensitive to IR light; you don't need to snap a photo – just turn on your camera and look at the image on your display. This is a bit tricky – DO NOT put your face in line with the beam! Put your camera in the path of the beam and view the image from an angle (i.e. DO NOT put your face in the path of the beam, even with the camera between you and the laser). You may need to move the camera around a bit – the beam is narrow and it needs to go straight into the camera's lens. You may also be able to see a spot on a piece of paper by pointing the beam at the paper and viewing it with your camera. If you can't detect a beam from the IR laser, make sure the protective shutter on the front is open. There are three different color safety goggles for your use. You may need to remove them to be able to see the laser beam well enough to aim it, but please use them when possible – ALWAYS WEAR THEM WHEN USING THE IR LASER. Note that the color you need to wear is the inverse of the color laser you need protection from. The colors are as follows: Blue goggles are for the Orange and Red lasers Green goggles are for the IR laser Red goggles are for the Violet, Blue, Green lasers In order to diffuse the laser beams and spread their light over the cathode in the phototube you will use plastic diffusers that are mounted on the front of black tubes. Place the diffuser over the laser before turning the laser on. For the laser pointer style lasers, there is a holder that will allow you to lock the laser on. Clamp the laser into it using the black screw, and turn it on by tightening the white screw down onto the “on” button. For the orange lasers, there is a push button on the back end that toggles between on and off. Note that the orange lasers have a safety cover that screws into the front of the laser – you'll need to make sure it's been removed before you can use the laser. Safety covers Diffuser in place - orange laser Diffusers Diffuser in place, and holder Finally, there is a polarizer which will allow you to vary the intensity of the beam. Since laser light is naturally polarized, you can vary the strength of the beam from almost full intensity to almost zero intensity by placing a polarizer in the path of the beam and rotating the polarizer. While you are reaching in to rotate the polarizer, remove any bracelets, rings, watches, etc. that could reflect the beam out of its intended path. One final note: the phototubes can (ironically) be damaged by excessive exposure to light. Please make sure to replace the black screen on the phototube's box. Page 5 Polarizer Photoelectric Effect: 10/2014 ABG Procedure: There are four different measurements you'll be recording for each wavelength laser. It does not matter which order you take them in, but don't leave the laser illuminating the cathode for longer than necessary. The work function of the cathode will change with temperature – and laser light on its surface will warm it up slowly, thus altering your results. Room lights must be off during this procedure, and even your small desk lamp will need to be turned off – the phototube is very sensitive to small amounts of stray light. The four questions are: 1. What is the voltage produced by laser light of one wavelength on the cathode? 2. Does the voltage change with light intensity? 3. What is the current produced by the same wavelength laser? 4. Does the current change with light intensity? Think about this (ideally out loud with your lab partner). Why would either the voltage or current change with intensity? Why might it change with wavelength? Attach the phototube to the voltage inputs of the amp (marked “V”). Attach the voltage outputs of the amp to the voltage inputs of the multimeter. Turn on the multimeter. Place a laser in its holder. For the laser-pointer style lasers make sure to line them up so that the on button is directly below the white screw which will hold the button down later. Slide a diffuser over the front of the laser. Line the laser up roughly with the phototube, and remove the black slide from the front of the phototube's box. Turn on the voltage switch on the amplifier – DO NOT turn on both switches – this will lead to faulty results. Put on your protective goggles and turn on the laser. Make sure the light from the laser is falling squarely on the opening in the phototube's box. Record the voltage as measured by the meter. Place the polarizer between the laser and the phototube. Rotate the polarizer slowly. Does changing the intensity of the light affect the voltage reading on the meter? Page 6 Photoelectric Effect: 10/2014 ABG Turn off the laser and the amplifier. Remove the polarizer. Swap the amplifier input wire from voltage to current (marked “I”), and do the same with the output. It is only necessary to switch the red terminals – all the black terminals are ground, and are thus all attached together. Turn on the current side of the amplifier. Turn the laser back on. Record the current as indicated by the multimeter. Remember, every microamp of current will display as one volt on the meter – you will need to convert appropriately. Put the polarizer back into place and rotate it slowly. Does changing the intensity of the beam affect the amount of current produced? (For one of the frequencies you do this, please establish an entire data series where you note in a table photocurrent versus angle reading of the polarizer. When doing this, also establish the angle reading of the maximum so that in your analysis you can use Malus’ law to convert angle into fractional intensity. You need to do this only for one frequency, not for all.) Repeat the above steps for each laser. Once you are done turn off all your equipment – especially take care that all lasers are turned off. Replace the black slide over the opening in the phototube box. Now that you have a set of data, make a graph of frequency of light vs. kinetic energy of ejected electrons. Remember that your units may need converting for any of this to work (think eV, Joules, Hz). Verify that your final units are correct! Interpret the graph. Is there a relationship? If the graph is linear, find the slope, x-intercept and yintercept and interpret the physical meaning of each. Are the values what you expect? Explain. Does the work function you calculated match the accepted work function of the cathode? How closely does your value for h agree with accepted values? Can you come up with more than one explanation for the effects you observed? What are the implications for the nature of light? Debate this (that's the scientific process, after all). Discuss your thoughts in your written report. Follow up: At the turn of the 20th century when Hertz and others were doing their experiments on the photoelectric effect, the dominant theory of the nature of light was the wave theory. In this theory, light was postulated to consist of oscillating electric and magnetic fields which propagated in continuous waves. The energy in the wave was contained in the oscillating electric and magnetic fields and was thought to be spread uniformly over the entire wave. The energy content of the wave was characterized by its intensity, the amount of energy which flows per unit time through a unit area perpendicular to the wave direction. The wave theory had been very successful up to that point in explaining phenomena involving light, but when it was applied to the photoelectric effect it could not explain all of the major experimental results. For example, according to the wave theory, the ejection of an electron from the surface of a metal occurred because of the interaction between the electric field of the light wave and the electric charge of the electrons. The oscillating electric field acting on the charged electrons would set them into vibration with an amplitude proportional to the square root of the energy they absorbed from the field. When an electron had absorbed enough energy, it would be literally vibrated out of the metal. If the light beam had a high intensity, this would happen quickly; but if the light beam had a low intensity, Page 7 Photoelectric Effect: 10/2014 ABG it would take some time before the electron had accumulated enough energy to be ejected from the metal. For a low intensity light beam, there would be an appreciable time lag between when the beam first struck the metal and when the first electron was ejected. Experiment showed no such time lag. A second area of difficulty concerned the relationship between the energies of the ejected electrons and the intensity of the light. The average kinetic energy of any vibrating body is proportional to the square of its amplitude of vibration. According to the wave theory, the square of the amplitude of vibration is proportional to the square of the amplitude of the oscillating electric field which, in turn, is proportional to the intensity of the light. In other words, (avg. kin. eng.) (amp. of vib.)2 (amp. of elec. field)2 (intensity) . Thus, the kinetic energies of the ejected electrons should show some dependence on the intensity of the light. Experiment showed the kinetic energies of the ejected electrons to be independent of the intensity. In 1905 Albert Einstein explained the photoelectric effect using quantum ideas introduced a few years earlier by Planck in his theory of blackbody radiation. According to Einstein, the energy in a light beam was not spread out uniformly over a continuous wave, but rather was concentrated in bundles, quanta of energy (called photons), each having an energy hv where v is the frequency of the electromagnetic wave. A light beam then could be thought of as a beam of photons with the intensity being a measure of the photon density. It is a collision between a single photon and single electron which, provided the photon contains enough energy, results in an ejected electron. Upon collision the electron completely absorbs the energy of the photon. If this energy is greater than the energy needed to overcome the attractive force at the surface, then some electrons will be ejected from the metal. Energy conservation requires that the most energetic electrons have an energy Emax= hν-, where (called the work function) is a constant which depends on the composition of the emitting surface. With Einstein's theory we can easily overcome the difficulties encountered by the wave theory. Since an electron absorbs all the energy a photon has in its collision with the photon, there is no time delay between the exposure of the surface to light and the ejection of the first electrons. There is no slow accumulation of energy. Furthermore, since the intensity of the light is a measure of the photon density and not their energy, there should be no relationship between the intensity of the beam and the kinetic energy of the ejected electrons. Either the photon has enough energy to eject the electron or it doesn't. If it does not, then no electrons will be emitted no matter how intense the beam. Can you think of any holes in this argument? Page 8 Photoelectric Effect: 10/2014 ABG