Exp. #2-9 : Measurement of Planck Constant through the Photoelectric Effect

Transcription

1 PAGE 1/13 Exp. #2-9 : Measurement of Planck Constant through the Photoelectric Effect Student ID Major Name Team No. Experiment Lecturer Student's Mentioned Items Experiment Class Date Submission Time Submission Place Introductory Physics Office Report Box # Students should write down Student s Mentioned Items at the cover page of Experiment Reports, and then complete Experiment Reports by adding contents to the attached papers (if needed) in terms of the following sections. Contents of the reports should be written by hand, not by a word processor. Instead, it is allowed that figures and tables are copied and attached to papers. Completed Experiment Reports should be submitted to the place due to the time specified by Experiment Lecturers. The Experiment Report points per each Experiment Class are evaluated by max. 50 points (basically 15 points). Solutions of Problems in Experiment Reports are not announced to the public according to the General Physics Laboratory - Administration Rule. If a student permits other students to pirate one s Experiment Reports or a student pirates Experiment Reports of other students regardless of permission of original creators, the corresponding Experiment Report points and Active Participation points will be zero in case of exposure of such situation. Unless Experiment Reports are submitted to the place due to the time specified by Experiment Lecturers, the corresponding Experiment Report points will be zero. If the submission rate of Experiment Reports is less than or equal to two thirds, the grade of General Physics Laboratory will be F level. In order to decide grades of General Physics Laboratory at the end of current semester, the detailed scores of General Physics Laboratory will be announced at Introductory Physics Office homepage. Based on the announcement, students can raise opposition of score error. Since the public evidence is needed for the confirmation of opposition, students should keep one s Experiment Reports completed evaluation by Experiment Lecturers until the grade decision of General Physics Laboratory. If a student is absent from the Experiment Class because of proper causes, the corresponding student should submit documents related to absence causes to Introductory Physics Office regardless of cause occurrence time until the grade decision of General Physics Laboratory. If a student moves the Experiment Class arbitrarily without permission of Introductory Physics Office, it is noted that the total Experiment Scores will be zero. Lecturer's Mentioned Items Submission Time/Place Check Experiment Report Points Evaluation Completion Sign 50

2 PAGE 2/13 1. Objective Student ID Name The characteristics of the photoelectric effect by using the relation among the light frequency, the light intensity, and the maximum kinetic energy of photoelectrons can be understood, and Planck constant is measured in this experiment. 2. Theory (1) Photon as a light quantum If the light with sufficiently high frequency is incident on the surface of a metal, electrons are emitted from the surface of the metal. This phenomena is called the photoelectric effect. In the photoelectric effect experiment, it can be observed that the light with low frequency cannot emit electrons and the light with high frequency emits electrons without time delay regardless of the light intensity. These characteristics of the photoelectric effect cannot be explained when the light is considered as the wave. According to the Planck's quantum theory, the light can be treated as a flow of particles with energy, where is Planck constant and is the light frequency. Applying the Planck's quantum theory, Einstein succeeded in demonstrating that the characteristics of the photoelectric effect can be explained in terms of the light as the flow of particles with the following energy and momentum., (Eq. 1) (Eq. 2) Here, is the light speed in vacuum and is the light wavelength. This property is called the Einstein's light quantum theory, and a light quantum is called a photon. According to the theory of relativity, the energy of a particle with the rest mass and momentum is given by. (Eq. 3) For the case of a particle at rest, the relation can be made. For the case of a particle without rest mass ( ), the relation can be made. This relation is in accordance with (Eq. 1). (2) Characteristics of the photoelectric effect (i) The energy needed to separate electrons from the surface of a metal is called the work function. When the light with the frequency is incident on the surface of a metal, photons and electrons inside the metal collide with each other. If the photon energy is less than the work function, electrons cannot be emitted regardless of the light intensity. However, if the photon energy is greater than or equal to the work function, electrons emit regardless of the light intensity. The emitted electrons caused by the light are called photoelectrons. From the above consideration, the maximum kinetic energy of photoelectrons is given by max. (Eq. 4) (ii) The minimum light frequency needed to emit photoelectrons is called the cutoff frequency. If the light frequency is equal to the cutoff frequency, the energy of a photon is entirely used as the work function so that the maximum kinetic energy of photoelectrons becomes max. Fig. 1. Experimental instrument and the characteristic curves of the photoelectric effect. Therefore, the cutoff frequency and the work function will have the following relation., (Eq. 5) (iii) The emitted photoelectrons make an electric current called the photocurrent. If the electric potential with backward direction increases as shown in Fig. 1(a), the photoelectrons will move slower so that the photocurrent decreases. The electric potential that makes the photocurrent vanish is called the stopping potential. Since the work done to a photoelectron by the stopping potential stop and the maximum kinetic energy max of a photoelectron are equal to each other, the following relation can be made. max stop (Eq. 6) Here, means the electron charge.

3 PAGE 3/13 By using (Eq. 5) and (Eq. 6), (Eq. 4) can be rewritten as follows: stop, stop (Eq. 7) One can draw the graph of stop vs. as shown in Fig. 1(b), where the slope corresponds to and the distance between the origin and the intercepts in the horizontal and vertical axes correspond to and, respectively. In summary, the light frequency is proportional to the photon energy, and the light intensity is proportional to the number of photons reaching the surface of a metal. Therefore, the light with frequency less than the cutoff frequency cannot emit photoelectrons regardless of the light intensity. For the case of the light with the frequency greater than or equal to the cutoff frequency, the photocurrent increases with the light intensity increasing as shown in Fig. 1(c). Answer the following questions. 1. In the photoelectric effect experiment, the light source with the wavelength and the power causes the photocurrent. First, find the number of photons per unit time. Next, find the number of photoelectrons per unit time. Finally, determine the probability for the electron to emit from the surface of the metal due to the photon, that is, the ratio of the number of photoelectrons to the number of photons. (Use the electron charge, the light speed in vacuum, and Planck constant.)

4 PAGE 4/13 3. Experimental Instruments Items Quantity Usage Clean up method Photoelectric effect experimental instrument 1 set It is used to measure the characteristics of the photoelectric effect and Planck constant. It should be placed at the center of the experiment table. Photoelectric effect experimental instrument-to-wall power connection cable 1 ea. It is used to connect the photoelectric effect experimental instrument to the wall power. It should be placed inside the basket of the experiment table.

5 PAGE 5/13 4. Experimental Procedures (1) Measurement of the photocurrent vs. the electric potential 1) After confirming that the photoelectric effect experimental instrument is off, use a photoelectric effect experimental instrument-to-wall power connection cable to connect the photoelectric effect experimental instrument to the wall power and keep the photoelectric effect experimental instrument off. Answer the following questions. 2. Describe the physical principle about the polarizer which controls the light intensity by changing the angle of the polarizer axis. 2) After confirming that the GAIN and COLLECTOR knobs are set to the minimum and adjusting the ZERO-ADJ knob to the middle position, turn on the photoelectric effect experimental instrument. 3) While keeping the LIGHT SOURCE button off, rotate the GAIN knob to the maximum position and set the photocurrent to by rotating the ZERO-ADJ knob. 4) Select the purple color among the LIGHT SOURCE buttons, and set the angle of the polarizer axis to. Rotate the COLLECTOR knob to decrease the photocurrent by times the maximum photocurrent and control the electric potential so that the photocurrent becomes. Write down values of the electric potential and the photocurrent displayed in the photoelectric effect experimental instrument. 5) After changing the angle of the polarizer axis into,, and, repeat the experimental procedure 4). Draw the graph of the electric potential vs. the photocurrent, and determine the stopping potential from the intercepts in the horizontal axis. 6) Select the blue, green, yellow, or red color among the LIGHT SOURCE buttons, and repeat the experimental procedures 4) and 5). If the photocurrent is too small to decrease by times the maximum photocurrent, decrease the photocurrent by a proper ratio. 7) If all the measurements are finished, turn off the LIGHT SOURCE, set the GAIN and COLLECTOR knobs to the minimum, and then turn off the photoelectric effect experimental instruments. Finally, clean up the experimental instruments according to the suggested method (2) Measurement of Planck constant Draw the graph of the light frequency vs. the stopping potential, and interpret the meaning of the slope and the intercepts in the horizontal and vertical axes. Finally, calculate Planck constant and compare it with the reference value.

6 PAGE 6/13 5. Experimental Values (1) Measurement of the photocurrent vs. the electric potential 1) Purple color Angle of the polarizer axis cos # of Measurement #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 Stopping potential stop V Slope

7 PAGE 7/13 2) Blue color Angle of the polarizer axis cos # of Measurement #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 Stopping potential stop V Slope

8 PAGE 8/13 3) Green color Angle of the polarizer axis cos # of Measurement #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 Stopping potential stop V Slope

9 PAGE 9/13 4) Yellow color Angle of the polarizer axis cos # of Measurement #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 Stopping potential stop V Slope

10 PAGE 10/13 5) Red color Angle of the polarizer axis cos # of Measurement #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 Stopping potential stop V Slope

11 PAGE 11/13 (2) Measurement of Planck constant Electron charge (C ) Color Red Light frequency (Hz) Stopping potential stop Yellow Green Blue Purple Slope V s Hz V Planck constant Reference value (J s) Experimental value (J s) Error (%)

12 PAGE 12/13 6. Results and Discussions (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) Write down contents in terms of the following key points. 1. In the case of the specific color and the angle of the polarizer axis, explain the relation between the photocurrent and the electric potential. 2. For the identical change in the electric potential, guess why the photocurrent change at the low potential is greater than that at the high potential. 3. In the case of the specific color, explain the relation between the photocurrent at zero electric potential and cos. (In advanced level, estimate the nonzero angle of the polarizer axis from the intercepts in the photocurrent at zero electric potential vs. cos graph.) 4. Explain the change in the stopping potential according to the angle of the polarizer axis in terms of the particle property of the light. 5. Find the actual material with the work function closest to the value obtained from the stopping potential vs. light frequency graph.

13 PAGE 13/13 7. Solution of Problems (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) 8. Reference