The Photoelectric Effect 1 The Photoelectric Effect Overview: The photoelectric effect is the light-induced emission of electrons from an object, in this case from a metal electrode inside a vacuum tube. In this experiment you ll vary the intensity and the color of the light, measuring the energy of the emitted electrons. The results provide a clue to the quantum nature of light. Physics principles: Light quanta (photons) Voltage Equipment needed: Photoelectric effect assembly (tube with high-impedance 1:1 amplifier) Mercury vapor lamp with lens/grating assembly Alignment hardware Three filters: green, yellow, and variable neutral-density Digital multimeter with banana leads Theory When you shine light on a metal surface, conduction electrons in the metal can absorb energy from the light and come flying off the surface. This process is called the photoelectric effect. Although the effect itself is hardly surprising, the relation between the electrons kinetic energy and the intensity and wavelength of the light gives us an important clue to the quantum nature of light. To measure the electrons kinetic energy, we can use the arrangement shown in Figure 1. We put the metal surface (called the cathode) into a vacuum tube, faced with a second metal surface (the anode) that will catch some of the ejected electrons. As electrons leave the cathode and build up on the anode, the unbalanced charges on these electrodes create an electric field that opposes the motion of subsequently ejected electrons. The voltage between the two electrodes is the potential energy per unit charge acquired by the next electron that crosses from the cathode to the anode: V = U, or U = q V. (1) q But in order to gain potential energy, the electron must lose an equal amount of kinetic energy. Therefore, in order to cross the gap between the electrodes, the electron must start with a kinetic energy at least equal to q V otherwise it runs out of kinetic energy before it reaches the anode. In other words, the voltage V tells us how much kinetic energy an electron must start with in order to make it to the anode.
The Photoelectric Effect 2 ++++++++ Voltmeter Figure 1: When light illuminates the cathode in a phototube, electrons are ejected and build up on the anode. The voltage between the electrodes is a measure of the energy that the next electron needs to cross the gap. Instructions The vacuum tube containing the photocathode and anode is enclosed in a small rectangular box, to shield it from the room lights. Also in this box is an electrical circuit called a highimpedance 1:1 amplifier, which allows you to measure the voltage between the cathode and anode while allowing very little current to pass between them. You will illuminate the cathode with light from a mercury vapor tube. There is nothing particularly special about this light source, except that it is relatively inexpensive and its spectrum contains five different colors that span a useful range of wavelengths. A diffraction grating, mounted on the light fixture, separates the five colors from each other. Mounted along with the grating is a lens, which focuses the spectral lines at a convenient distance. Figure 2 shows the phototube assembly, mercury lamp, grating/lens assembly, and alignment hardware. Turn on the mercury lamp and let it warm up for a few minutes. Hold a piece of paper in front of the grating/lens assembly, and observe the spectral lines. The lines on one side should be somewhat brighter than on the other side. It s best to use the first-order lines on the brighter side. In order by wavelength, we ll refer to the lines as ultraviolet, violet, blue, green, and yellow. (Although the ultraviolet line is technically outside the visible range of wavelengths, you can still see it when it strikes most white surfaces because the surfaces fluoresce.) On the front of the phototube assembly is a cylindrical light shield. Roll this shield out of the way so you can look in and see a portion of the phototube with its white mask. Align the apparatus so the blue spectral line strikes the window on the phototube. Adjust the position of the grating/lens assembly to obtain the best focus, then roll the cylindrical shield back into place. Switch on the electrical circuit in the phototube assembly, and plug a digital voltmeter into the red and black terminals on the box. Turn the voltmeter on and set it to read voltages up to 2.0 V. The reading on the voltmeter should soon stabilize at around 1.4 V. If you obtain a significantly different reading, or if the reading does not stabilize, ask your instructor or lab aide to check your apparatus and alignment. Your voltmeter measures the voltage between the cathode and the anode in the phototube. Before going on to make more measurements, think about how this voltage is related to the kinetic energy of the electrons ejected from the cathode. Answer Questions 1 and 2.
The Photoelectric Effect 3 Figure 2: Equipment setup for studying the photoelectric effect. Voltage as a function of intensity You will first study how the measured voltage (or equivalently, the maximum kinetic energy of the electrons) changes as you vary the intensity of the light. Included with your equipment is a variable neutral-density filter that allows between 20% and 100% of the light to pass through, in increments of 20%. Place this filter in front of the opening on the phototube assembly, starting at the 100% intensity level (clear glass). The opening should still be illuminated with the blue spectral line. Press the red button on the phototube box to discharge the electrodes, then release the button and wait for the voltage reading to stabilize. Record the voltage, then repeat at intensity levels of 80%, 60%, 40%, and 20%. Enter your results in a computer spreadsheet, with the intensity level in the first column and the voltage reading in the second column. Repeat the preceding measurements using the green spectral line. For this line, you will obtain better results if you also cover the opening with the green filter, which blocks other colors of light that might make their way into the opening. Enter the voltage readings in a third column in your spreadsheet. Create a graph of voltage vs. intensity, showing the data sets from both colors of light. Print copies of the table and graph for each person, and attach them to your Report. Be sure to label your graph appropriately, including the colors of light that produced the two data sets. Answer Questions 3, 4, and 5.
The Photoelectric Effect 4 Voltage as a function of wavelength Next you will study how the measured voltage changes as you vary the wavelength of the light. Using the same procedure as before, but without the neutral-density filter, measure the steady-state voltage across the phototube for each of the five colors in the mercury spectrum. Use the green and yellow filters with the green and yellow lines, respectively. Create a second spreadsheet with your data, putting the wavelengths in the first column and the voltages in the third column. The wavelengths of the five lines are 365 nm (UV), 405 nm (violet), 436 nm (blue), 546 nm (green), and 578 nm (yellow). In the second column, compute the frequency (in Hz) that corresponds to each wavelength. Make a graph of voltage vs. frequency for your data, and print copies of the table and graph for each person. Using a ruler and pencil, draw the steepest and shallowest plausible straight lines through your graph, and measure their slopes and intercepts with the voltage axis. As a check, have Excel compute the slope and intercept as follows. Assuming that your data are in rows 4 though 8, type the formula =LINEST(C4:C8,B4:B8,TRUE,TRUE) in cell B11. Then highlight cells B11, B12, C11, and C12. Finally, hold down the cloverleaf key while hitting the enter key. Excel will then calculate the slope of the line and the intercept, putting the values in cells B11 and C11. The one-standard-deviation uncertainties in these quantities are underneath, in row 12. Write these calculated values in the margin of your printed graph, then answer the rest of the Questions in the Report. Be sure to attach your computer-printed tables and graphs from both parts of the experiment to your Report.
The Photoelectric Effect 5 Report: The Photoelectric Effect NAME PARTNERS DATE Be sure to attach both of your tables and graphs (voltage vs. intensity and voltage vs. frequency) to this Report. Question 1. When the phototube is illuminated by monochromatic light, the voltage reading quickly stabilizes to a constant value. What property of the ejected electrons is measured by this value? Explain. Question 2. Show that the maximum kinetic energy of the electrons, in ev, is numerically equal to the voltage reading, in volts.
The Photoelectric Effect 6 Question 3. How would you summarize your results for the dependence of the voltage on the intensity of the light? Question 4. Thinking of light as a continuous wave, would you expect the voltage to depend on intensity? Explain. Question 5. How can you account for your result using a particle model of light? Question 6. Is your graph of voltage vs. frequency consistent with a linear relation between these quantities? Explain briefly.
The Photoelectric Effect 7 Question 7. How can you account for this graph using a particle model of light? Question 8. If we interpret the vertical axis of this graph as the maximum electron kinetic energy in ev, then the slope is (by definition) Planck s constant, h. What is your measured value of h, with uncertainty? (Please express your answer both in ev s and in J s.) Question 9. The accepted value of Planck s constant is 4.14 10 15 ev s. Is your measured value consistent with the accepted value? Question 10. In Einstein s explanation of the photoelectric effect, each electron absorbs one light quantum (now called a photon ), whose energy is h times the frequency. Using your measured value of h, compute the photon energies (in ev) corresponding to each of the five colors of light used in this experiment. Question 11. If each electron in the cathode absorbs all the energy of one photon, what is the physical meaning of the negative intercept in your graph of voltage vs. frequency?