PHY 290 Lab 1: Photoelectric Effect PDF

1 LAB 1 PHOTOELECTRIC EFFECT (PHY290) APPARATUS Photodiode with amplifier Batteries to operate amplifier and provide reverse voltage Digital voltmeter to read reverse voltage Source of monochromatic light beams to irradiate photocathode Neutral filter to vary light intensity BACKGRO...

1 LAB 1 PHOTOELECTRIC EFFECT (PHY290) APPARATUS Photodiode with amplifier Batteries to operate amplifier and provide reverse voltage Digital voltmeter to read reverse voltage Source of monochromatic light beams to irradiate photocathode Neutral filter to vary light intensity BACKGROUND The experiment serves to demonstrate the photoelectric effect, for which Einstein was awarded a Nobel prize, and in the process determine Planck’s constant, ℎ. The photoelectric effect is the process whereby a photon of energy 𝐸=ℎ𝜈, incident on the surface of a conductor, transfers its energy to one of the electrons of an atom. If the energy is sufficient, the electron can not only escape from the material, but do so with a certain amount of kinetic energy. If the electron is in the highest available energy state within the conductor, the least amount of energy, 𝑊0, is needed to free it, and it will escape with the maximum kinetic energy. 𝑊0 is called the work function of the conducting material Figure 1: Schematic of the photo-electric effect experiment. A photon hits the conducting anode and knocks out an electron. All electrons that have sufficient kinetic energy to reach the cathode produce an electric current. The adjustable stopping voltage determines the minimal kinetic energy the electrons need.  2 If the conductor forms the anode of a phototube, as shown in Fig. 1, no electrons will reach the cathode if the potential difference (retarding potential) between the anode and cathode is adjusted to the minimum value necessary to stop the fastest electrons. The loss of kinetic energy is then balanced by the gain of potential energy, 𝑒𝑉𝑠, and the energy equation is given by ℎ𝜈 = 𝑒𝑉𝑠 + 𝑊0 (1) where 𝑉𝑠 is called the stopping potential. The threshold frequency, 𝜈0 , is the minimum photon frequency capable of eliciting the photoelectric effect. 𝑉𝑠 = (ℎ⁄𝑒)𝜈 − 𝑊0 ⁄𝑒 (2) Eq. (2) shows a linear relationship between the stopping potential 𝑉𝑠 and the light frequency 𝜈, with slope ℎ⁄𝑒 and vertical intercept -𝑊0⁄𝑒. If the value of the electron charge 𝑒 is known, then this equation provides a good method for determining Planck's constant ℎ. In this experiment, we will measure the stopping potential with modern electronics. THE MONOCHROMATIC LIGHT BEAMS This experiment requires the use of several different monochromatic light beams, which can be obtained from the spectral lines that make up the radiation produced by excited mercury atoms. The light is formed by an electrical discharge in a thin glass tube containing mercury vapor, and harmful ultraviolet components are filtered out by the glass envelope. Mercury light has five narrow spectral lines in the visible region — yellow, green, blue, violet, and ultraviolet — which can be separated spatially by the process of diffraction. For this purpose, we use a high-quality diffraction grating with 6000 lines per centimeter. The desired wavelength is selected with the aid of a collimator,  3 while the intensity can be varied with a set of neutral density filters. A color filter at the entrance of the photodiode is used to minimize room light. The equipment consists of a mercury vapor light housed in a sturdy metal box, which also holds the transformer for the high voltage. The transformer is fed by a 115-volt power source from an ordinary wall outlet. In order to prevent the possibility of getting an electric shock from the high voltage, do not remove the cover from the unit when it is plugged in. To facilitate mounting of the filters, the light box is equipped with rails on the front panel. The optical components include a fixed slit (called a light aperture) which is mounted over the output hole in the front cover of the light box. A lens focuses the aperture on the photodiode window. The diffraction grating is mounted on the same frame that holds the lens, which simplifies the setup somewhat. A “blazed” grating, which has a preferred orientation for maximal light transmission and is not fully symmetric, is used. Turn the grating around to verify that you have the optimal orientation.  4 The variable transmission filter consists of computer-generated patterns of dots and lines that vary the intensity of the incident light. The relative transmission percentages are 100%, 80%, 60%, 40%, and 20%. INITIAL SETUP 1. Your apparatus should be set up approximately like the figure above. Turn on the mercury lamp using the switch on the back of the light box. Swing the ℎ⁄𝑒 apparatus box around on its arm, and you should see at various positions, yellow green, and several blue spectral lines on its front reflective mask. Notice that on one side of the imaginary “front-on” perpendicular line from the mercury lamp, the spectral lines are brighter than the similar lines from the other side. This is because the grating is “blazed”. In you experiments, use the first order spectrum on the side with the brighter lines. 2. Make the following alignment checks. Ask you TA for assistance if necessary. a. Check the alignment of the mercury source and the aperture by looking at the light shining on the back of the grating. If necessary, adjust the back plate of the light-aperture assembly by loosening the two retaining screws and moving the plate to the left or right until the light shines directly on the center of the grating. b. With the bright colored lines on the front reflective mask, adjust the lens/grating assembly on the mercury lamp light box until the lines are focused as sharply as possible.  5 c. Roll the round light shield (between the white screen and the photodiode housing) out of the way to view the photodiode window inside the housing. The phototube has a small square window for light to enter. When a spectral line is centered on the front mask, it should also be centered on this window. If not, rotate the housing until the image of the aperture is centered on the window, and fasten the housing. Return the round shield back into position to block stray light. 3. Connect the digital voltmeter (DVM) to the “Output” terminals of the photodiode. Select the 2 V or 20 V range on the meter. 4. Press the “Push to Zero” button on the side panel of the photodiode housing to short out any accumulated charge on the electronics. Note that the output will shift in the absence of light on the photodiode. 5. Record the photodiode output voltage on the DVM. This voltage is a direct measure of the stopping potential. 6. Use the green and yellow filters for the green and yellow mercury light. These filters block higher frequencies and eliminate ambient room light. In higher diffraction orders, they also block the ultraviolet light that falls on top of the yellow and green lines.  6 PROCEDURE PART I: DEPENDENCE OF THE STOPPING POTENTIAL ON THE INTENSITY OF LIGHT 1. Adjust the angle of the photodiode-housing assembly so that the blue line falls on the window of the photodiode. 2. Install the round light shield. 3. Install the variable transmission filter on the collimator such that the light passes through the section marked 100%. Record the photodiode output voltage reading on the DVM. Also determine the approximate recharge time after the discharge button has been pressed and released. 4. Repeat steps 1 – 3 for the other four transmission percentages, as well as for the ultraviolet light. 5. Plot a graph of the stopping potential as a function of intensity. Color #1……………………….. % Transmission Stopping Potential 100 80 60 40 20 Color #2……………………….. % Transmission Stopping Potential 100 80 60 40 20 PROCEDURE PART II: DEPENDENCE OF THE STOPPING POTENTIAL ON THE FREQUENCY OF LIGHT You can see five colors in the mercury light spectrum. The diffraction grating has two usable orders for deflection on one side of the center. 1. Adjust the photodiode-housing assembly so that only one color from the first-order diffraction pattern on the left side of the center falls on the collimator. 2. For each color in the first order, record the photodiode output voltage reading on the DVM.  7 3. For each color in the first order on the right side of the center, record the photodiode output voltage reading on the DVM. 4. Plot a graph of the stopping potential as a function of frequency, and determine the slope and the y-intercept of the graph. From this data, calculate 𝑊0 and ℎ. Compare this value of ℎ with that provided in the “Background” section of this experiment. Color Wavelength Frequency Stopping Potential (nm) (×1014 Hz) (Volts) Yellow 578 5.18672 Green 546.074 5.48996 Blue 435.835 6.87858 Violet 404.656 7.40858 Ultraviolet 365.483 8.20264