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Lesson Plan: Photoelectric Effect By Jeff Bourne Northview High School The Problem: To understand how Einstein’s interpretation of the photoelectric effect recreated a particle-nature theory for light that had been discounted for almost 100 years before that time. Abstract: Students will use an Internet-based simulation of the photoelectric effect to collect frequency, stopping voltage, and intensity data which will be mathematically analyzed in order to demonstrate the particle nature of light. Students will understand that wave properties such as the energy being a function of the intensity do not apply to light. Upon completion of the virtual experiment, students will analyze results from a device which utilizes 4 different LED’s as wavelength sources. Alignment with Standards: 1. National Standards: AP College Board AP Physics B Standards: III. Electricity and Magnetism A. Electrostatics 2. Electric field and electric potential B. Conductors, capacitors, dielectrics IV. Waves and Optics A. Wave motion 1. Traveling Waves: students should understand the description of traveling waves, so they can b) apply the relation among wavelength, frequency, and velocity of a wave. B. Physics Optics 1. Interference and diffraction: students should understand the interference and diffraction of waves, so they can: b) apply the principles of interference and diffraction to waves that pass through a single or double slit or through a diffraction grating, so they can: (5)describe or identify the interference pattern formed by a diffraction grating and calculate the location of intensity maxima. V. Atomic and Nuclear Physics A. Atomic physics and quantum effects 1. Photons, the photoelectric effect, … a) Students should know the properties of photons, so they can: (1) relate the energy of a photon in joules or electron-volts to its wavelength or frequency. B) Students should understand the photoelectric effect, so they can: (1) Describe a typical photoelectric effect experiment, and explain what experimental observations provide evidence for the photon nature of light. (2) Describe qualitatively hohw the number of photoelectrons and their maximum kinetic energy depend on the wavelength and intensity of the light striking the surface, and account for this dependence in terms of a photon model of light. (4) Sketch or identify a graph of stopping potential versus frequency for a photoelectric-effect experiment, determine from such a graph the threshold frequency and work function, and calculate an approximate value of h/e. 2. State of Georgia Standards: Characteristics of Science SCSh1. Students will evaluate the importance of curiosity, honesty, openness, and skepticism in science. c. Explain the further understanding of scientific problems relies on the design and execution of new experiments which may reinforce or weaken opposing explanations. SCSh3. Students will identify and investigate problems scientifically. b. Develop procedures for solving scientific problems. c. Collect, organize and record appropriate data. d. Graphically compare and analyze data points and /or summary statistics e. Develop reasonable conclusions based on data collected. f. Evaluate whether conclusions are reasonable by reviewing the process and checking against other available information. SCSh4. Students will use tools and instruments for observing, measuring, and manipulating scientific equipment and materials. a. Develop and use systematic procedures for recording and organizing information. b. Use technology to produce tables and graphs SCSh6. Students will communicate scientific investigations and information clearly. a. Write clear, coherent laboratory reports related to scientific investigations. 3. State of Georgia Standards: Content SP4. Students will analyze the properties and applications of waves. a. Explain the processes that results in the production and energy transfer of electromagnetic waves SP5. Students will evaluate relationships between electrical and magnetic forces. a. describe the transformation of mechanical energy into electrical energy and the transmission of electrical energy. b. determine the relationship among potential difference, current, and resistance in a dc circuit. SP6. The student will describe the corrections to Newtonian physics given by quantum mechanics and relativity when matter is very small, moving fast compared to the speed of light, or very large. a. Explain matter as a particle and wave. Objectives: 1. The student will understand the importance of Einstein’s interpretation of this famous experiment. 2. The student will understand how this experiment provided evidence for the “particlelike” nature of light. 3. The student will utilize the scientific method appropriately in the lab design. 4. The student will correctly analyze and interpret graphs that are generated. Anticipated learner outcomes: 1. The student will be able to define the concept of the work function of a metal. 2. The student will be able to describe the process of metal electron excitation by the photon, and how that energy is divided into the work function and kinetic energy. 3. The student will be able to discuss the relationship between the intensity of the photons and the photocurrent. 4. The student will describe the relationship between the electric field created by the stopping voltage and the photocurrent produced. 5. The student will be able to discuss the significance of Planck’s constant from this experiment. Assessment/Rubric Lab Report : Photoelectric effect Teacher Name: Mr. bourne Student Name: CATEGORY Experimental Design ________________________________________ 4 3 2 1 Group successfully designed a lab with proper variables and controls The group may have switched variables or not controlled all parameters The group No serious effect included variables at controlling they shouldn't variables. have. Data Professional looking and accurate representation of the data in tables and/or graphs. Graphs and tables are labeled and titled. Accurate representation of the data in tables and/or graphs. Graphs and tables are labeled and titled. Accurate Data are not representation of shown OR are the data in written inaccurate. form, but no graphs or tables are presented. Scientific Concepts Report illustrates an accurate and thorough understanding of scientific concepts underlying the lab. Report illustrates an accurate understanding of most scientific concepts underlying the lab. Report illustrates a limited understanding of scientific concepts underlying the lab. Report illustrates inaccurate understanding of scientific concepts underlying the lab. Spelling, Punctuation and Grammar One or fewer errors in spelling, punctuation and grammar in the report. Two or three errors in spelling, punctuation and grammar in the report. Four errors in spelling, punctuation and grammar in the report. More than 4 errors in spelling, punctuation and grammar in the report. Components of the report All required All required elements are elements are present and present. additional elements that add to the report (e.g., thoughtful comments, graphics) have been added. One required Several required element is elements are missing, but missing. additional elements that add to the report (e.g., thoughtful comments, graphics) have been added. Calculations All calculations are shown and the results are correct and labeled appropriately. Some calculations are shown and the results are correct and labeled appropriately. Some calculations are shown and the results labeled appropriately. No calculations are shown OR results are inaccurate or mislabeled. Conclusion Conclusion includes whether the findings supported the hypothesis, possible sources of error, and what was learned from the experiment. Conclusion includes whether the findings supported the hypothesis and what was learned from the experiment. Conclusion includes what was learned from the experiment. No conclusion was included in the report OR shows little effort and reflection. Questions Correctly answered 4 questions Correctly answered 3 questions Correctly answered 2 questions Correctly answered 1 question Appearance/Organization Lab report is typed and uses headings and subheadings to visually organize the material. Lab report is neatly handwritten and uses headings and subheadings to visually organize the material. Lab report is neatly written or typed, but formatting does not help visually organize the material. Lab report is handwritten and looks sloppy with cross-outs, multiple erasures and/or tears and creases. Date Created: June 26, 2007 Background In 1887, H.R. Hertz worked on testing Maxwell’s theories dealing with electromagnetism. In this process he noticed that when particular metals were wired to an electroscope and then irradiated with ultraviolet light waves, the leaves of the electroscope would move apart. He concluded that when the ultraviolet light struck the metal plate the electrons on the plate were set free. Hertz, however, did not develop this idea much further as to explain why. Several years after Hertz’s nascent research on the photoelectric effect, Max Planck researched the radiation emitted by a blackbody (an object that is a perfect absorber of radiation). His interested was sparked by the Ultraviolet Catastrophe, which demonstrated the inaccuracies of classical calculations and experimental data. Classically, when incident light (thought of as composed of waves) strikes a surface, the energy of the emitted electrons should be proportional to the intensity of light. Also, classical theory predicted that the photoelectric current is not dependent on the frequency of the light. However, experimental data did not uphold these relationships, especially at higher frequencies (ultraviolet). Planck created a formula that worked well with the experimental results, but it only worked if it was assumed that the energy of the excited particle was quantized. E=hf E = Energy h = Planck’s constant = 6.63 E -34 J-s f = radiation frequency Planck was able to create a formula that worked with the experimental results, but the photoelectric effect itself was not actually explained. In 1905, Albert Einstein made the radical proposal that the incident light consisted of particles called photons, which carry energy and have linear momentum. In Einstein’s photoelectric experiment it was shown that: 1) When light strikes a metal surface, current flows instantaneously, even for low intensity light. 2) At a fixed frequency, the magnitude of the current is directly proportional to the intensity of the incident light. 3) The stopping potential (Vo), and therefore the maximum energy of the liberated electrons, depends only on the frequency of the light and the type of metal used. 4) Each metal has a characteristic threshold frequency and work function (). The work function is the minimum amount of energy required for an electron to escape from a metal. 5) The energy of each photon is proportional to its frequency. 6) Each emitted electron is the result of the absorption of one photon. The maximum kinetic energy, KE, that any photon can have is given by: KEmax = hf - 7) The constant h is found to be the same for all metals and is equal to Planck’s constant. This constant was shown in two very different experiments: Blackbody Radiation and the Photoelectric Effect. 8) The entropy of waves in a box was exactly the same as the entropy of particles in the box if E = nhf. Materials and Supplies 1. computers for each lab group 2. Photoelectric Effect apparatus Plan This lab activity should take close to 3 lab periods to complete. The first day will be introduction, data collection, and time permitting, group collaboration. The second day will be for analysis and demonstrating the photoelectric effect apparatus. The third third will be spent collecting data from the apparatus. Analysis of that data will be a homework assignment. Lab: Photoelectric Effect Purpose: 1. The student will understand the importance of Einstein’s interpretation of this famous experiment. 2. The student will understand how this experiment provided evidence for the “particlelike” nature of light. 3. The student will utilize the scientific method appropriately in the lab design. 4. The student will correctly analyze and interpret graphs that are generated. Background: Einstein postulated that light contained a certain amount of energy based on its frequency. He believed that the energy of the light was transferred completely to an electron on the metal’s surface. The energy of the electron was divided up into two accounts: the energy needed to escape the metal’s surface, and the kinetic energy due to its movement after it escaped. Mathematically, this can be expressed as: Ephoton = Ekinetic + Eescape The kinetic energy can be measured indirectly by using what is known as the stopping voltage. As the electrons escape, they find themselves moving through an electric field that wants to stop them before they complete their journey to the other electrode. If the field is too great, they turn around and go back to the metal’s surface. If the field is too low, then all the electrons go to the other electrode, creating a large current. At just the right amount of voltage, only the electrons that had the greatest kinetic energy will reach the other electrode. (It the same idea that a ball thrown upward with the greatest KE will go the farthest against the gravity field.) Since the work done on the electron is equal to qV, the charge of the electron times the stopping voltage gives you the kinetic energy of the escaping electron. Rearranging the equation above gives this formula: KE = Ephoton – Eescape Max Planck had determined that the energy of the photon was equal to its frequency times a constant. Planck had no idea what the constant was, only that he needed it to make his calculations work. Therefore Ephoton = hf Where f is the frequency in hertz. This means the important formula for the photoelectric effect is: KE = hf – Eescape This is a linear formula, with the KE on y-axis, frequency on the x-axis, and the escape energy (known as the work function) the y-intercept. The slope of the line is Planck’s constant! Materials: 1. Computer simulation: http://phet-web.colorado.edu/web-pages/simulations-base.html Choose Photoelectric effect Lab Design: This simulation allows you to “see” the photons bombarding the metal plate as well as the electrons that come off it. There are several factors to be studied today: 1. The wavelength of the photons; 2. The intensity of the photons; and 3. The type of metal plate being used. This is too much for one group to handle in the period, so we will split up into smaller groups. Group Independent Variable Dependent Controls Variable A Wavelength Stopping Voltage Intensity; type of metal B Intensity Stopping Voltage Wavelength; type of metal C Same as Group A except that they will use a different metal Hints about the simulation and lab 1. You can either use the sliders to change the voltage, intensity, and wavelength, or you may manually enter the values. Manually will give you better control. 2. Under Options, select “show photons”. 3. Group A: select 5 different wavelengths. Use sodium as the metal. Be sure to include one UV wavelength. You will need to make the voltage as small as possible (negative) to create the least current. Make your intensity 100%. Be aware that some wavelengths will not cause any electron ejection. If that happens, you have to pick a shorter wavelength. 4. Group B: pick a wavelength in the violet/blue region to start. Use Sodium as the metal. Start with 100% intensity and find the lowest negative voltage necessary to get a current. Repeat at 3 other intensities with the same wavelength. (Make significant changes in the intensity. 100 90 is NOT significant.) 5. Group C: you will do the same experiment as Group A, except that you should select a different metal. Try to find 5 different wavelengths that give you results. Results: Group A: You need to record wavelengths and stopping voltages. Calculate the frequencies of each wavelength, and calculate the kinetic energies due to the stopping voltages. Graph KE vs. frequency and record the slope and y-intercept. Be sure to print out the graph. Group B: You need to record the stopping voltage at each intensity. If there appears to be a trend, you should graph this data. Group C: You should do the same thing as Group A. Analysis/Conclusions: Groups A and C: Use the Internet to find the work function for your metal. Calculate a percent error. (Note: you will probably find the results in eVolts. If so, to convert to Joules simply multiply by 1.6E-19.) Was your slope consistent with the actual value of h? Group B: What (if any) is the relationship between the intensity of the light and the stopping voltage? Questions for further thought: Everybody should do this. 1. In typical mechanic waves such as sound and water, what is the energy of the wave proportional to? For example, how do you recognize a high energy wave at the beach? 2. How do the results of this experiment seem to demonstrate that light wave energy is carried a different way? 3. Imagine 2 electrons on a plate of sodium metal. One electron is found right on the surface of the metal. The other electron is buried several layers below. A. Which electron needs the least energy to escape? Why? B. Which electron will have the greater KE when it absorbs the energy from a photon and escapes? Why? C. Which electron is more likely to overcome the electric field to reach the other metal? Why? 4. For sodium, even at 100% intensity, a green photon with a wavelength of 557 nm will never eject any electrons., but at 1% intensity, a UV photon at 235 nm always knocks out an electron. Einstein’s interpretation of this event (or one just like it) earned him a Nobel prize. It’s your turn. Why does this result clearly indicate particle-like properties of light (which Einstein referred to photons)?