Modern Physics Laboratory MP4 Photoelectric Effect

Transcription

1 Purpose MP4 Photoelectric Effect In this experiment, you will investigate the photoelectric effect and determine Planck s constant and the work function. Equipment and components Photoelectric Effect Apparatus (PASCO SE-6609) includes: Mercury light source enclosure, 60cm long track, Photodiode enclosure, DC current amplifier, tunable DC power supply. Background The emission of electrons from a material when it interacts with an incident light is called the photoelectric effect, which is an important phenomenon for understanding the nature of light. Figure 1 shows a typical setup investigate the photoelectric effect. Monochromatic light of frequency ν is produced by an optical filter F falls onto the cathode K of the photocell, some electrons in the material absorb the energy from photons and are emitted from the surface. These electrons are called photoelectrons. For electrons to escape from the surface, they must overcome an energy barrier called the work function. The work function,φ, determines how strong the electrons are bound to the material. The value of φ is a property of the material and is fairly constant independent of temperature and other external influences. The escaped electrons can be detected as a current if they are attracted to the anode A, by means of a potential difference V applied between the cathode and anode. The voltage V can be changed by a variable power supply. A sensitive ammeter G is used to measure the photoelectric current. Figure 1 Schematic representation of the experimental setup of the photoelectric effect. Figure 2 Photoelectric current as a function of the applied voltage V. Figure 2 shows two typical curves of the measured photoelectric current as a function of the potential difference V. If V is made large enough, the photoelectric current reaches a saturation value, at which all of the electrons emitted from the cathode are collected by the anode. If V is made negative - a condition when the emitted electrons are repelled by the anode - the current does not drop immediately to zero. This is because the photoelectrons are emitted with some kinetic energy and one needs to apply a large enough negative voltage to stop them from reaching the anode. The voltage V 0, at which the photocurrent drops to zero, is called the stopping potential. The stopping potential multiplied by the electron charge is the kinetic energy, K m =ev 0, of the fastest photoelectrons. It is seen from Fig. 2 that the stopping Revised: 12 August /10

2 potential is independent of the incident light intensity, while the saturation current is proportional to the incident intensity. Another important observation of the photoelectric effect is that the stopping potential is a function of the frequency ν of the incident light. As shown in Figure 3, there is even a cut-off frequency ν 0, below which the photoelectric effect does not occur regardless of the intensity of the light. Figure 3 Measured stopping potential as a function of frequency of the incident light. 14 (Cathode: sodium; cut-off frequencyν 0 = Hz ) There are two major features of the photoelectric effect, which cannot be explained by the classical electromagnetic theory: 1) The wave theory requires that the amplitude of the oscillating electric field vector E of the light increases with the intensity of the light beam. Since the force applied to the electron is ee, the kinetic energy of the photoelectrons should also increase with the intensity of the light beam. However, one finds from Fig. 2 that the maximum kinetic energy of the photoelectrons, which is proportional to the stopping potential V 0, is independent of the light intensity. 2) According to the wave theory, the photoelectric effect should occur at any frequency of the incident light, provided that the light has enough intensity to provide the energy needed for the electrons to overcome the work function. However, one finds from Fig. 3 that there is a cut-off frequency ν 0, below which the photoelectric effect does not occur regardless of the intensity of the light. The solution to this discrepancy between the classical theory and the experimental observations was proposed by Albert Einstein. He suggested that light is made of discrete photons, each having energy of hν, where h = 6.63 x joule.sec is Planck's constant. Einstein also proposed that one electron will absorb all of the energy of a single photon in order to be photoemitted. With these assumptions, one can explain the two main features of the photoelectric effect. 1) Increasing the intensity of the incident light only increases the number of photons but not the energy of each photon. As a result, increasing light intensity will only increase the photocurrent and the energy of the photoelectrons will remain unchanged. Thus, the kinetic energy, K m =ev 0, of the fastest photoelectrons will be independent of the light intensity, as observed in the experiment. 2) If the photon energy is less than the work function, then there will be no electron emitted. When the photon energy is greater than the work function, each electron should have gained an energy hν from the photon and lost φ to the work function with a resulting kinetic energy outside of the material Revised: 12 August /10

3 Km = hν φ (1) Thus, the observed stopping potential V 0 should be linearly proportional to the frequency ν. This behaviour is observed in Fig. 3. The cut-off frequency is also understood at the condition when the energy of incident photons matches the work function, hν0 = φ. In this case, the photoelectrons are emitted with zero kinetic energy. Procedure Experimental apparatus: Photodiode enclosure: The photocell mounted inside the photodiode enclosure has a spectral response range between 300 to 700 nm. This is an ideal range for visible and near ultra-violet lights. The photocell has Zinc oxide cathode and Nickel ring anode. The optical filters and the different size apertures are built into the entrance of the photodiode enclosure. To change the aperture size in order to investigate the effect of different light intensities, simply pull outward on the aperture dial and rotate it to different aperture. The filter wheel can be rotated independently of the aperture dial to select the five different spectral lines of the mercury light source. DC current amplifier: Instead of using a simple ammeter, a more sensitive DC current amplifier will be used to measure the photocurrent which is very small on the order of A. Tunable DC power supply: The tunable DC power supply provides potential difference to the photocell, which is shown on the voltage display. The power supply has two outputs: (i) A DC voltage output with two ranges, -4.5V to 0V and -4.5V to 30V which is used in this experiment and (ii) a filament voltage output (0 6.3V) that is not used. PRECAUTIONS: A) Do not look directly at the mercury lamp, which may damage your eyes. Always minimize the exposure to the mercury light. As a precaution, block the mercury light with the cap when it is not being used. B) The whole Mercury light source enclosure is very hot when it is turn on and please do NOT touch its surface during the experiment. C) Direct exposure of the photocell to excessive light will damage the cathode. Figure 4 Experiment setup for the photoelectric effect. Revised: 12 August /10

4 Initial setup: 1. Cover the exit of the mercury light source enclosure with a cap. Cover the window of the photodiode enclosure with a cap. 2. Mount the photodiode enclosure and the mercury light source enclosure on the 60 cm track. Loosen the thumbscrew that is near the bottom of the side panel of each enclosure. Set the enclosures on the track with the photodiode enclosure facing the mercury light source enclosure. Position the enclosures so that they are about 35 cm apart (as indicated by the metric scale on the side of the track). Tighten the thumbscrew at the bottom of each enclosure to hold it in place on the track. 3. Turn on the mercury lamp and wait at least ten minutes for lamp warm-up. *** Do NOT turn it off until all the measurement is finished. *** 4. Connect the -4.5V 0V output ports of the tunable DC power supply to the red and black 4mm jacks on the photodiode enclosure with cables. 5. Connect the BNC coaxial cable between the photodiode enclosure and the BNC input socket on the DC current amplifier. 6. Keep hands and other objects away from the BNC coaxial cable. 7. Turn on the tunable DC power supply and the DC current amplifier for warm-up. Part I Measurements of Planck s constant and the work function 1. On the tunable DC power supply, set the Voltage Range switch to -4.5V 0 V. 2. On the DC current amplifier, turn the CURRENT RANGES switch to A. 3. On the DC current amplifier, push in the SIGNAL button to the in position for CALIBRATION. Rotate the CURRENT ADJUST knob until the ammeter reading shows that the current is zero. 4. Press the SIGNAL button to the out position to return the DC current amplifier to MEASURE mode. 5. Gently pull the aperture dial away from the case of the photodiode enclosure and rotate the dial so that the 4 mm diameter aperture is aligned with the white index line. Then rotate the filter wheel until the 577 nm filter is aligned with the white index line. Finally, remove the cover cap. NOTE: Avoid touching the filters when the cover cap is removed. 6. Uncover the exit of the mercury light source. Spectral lines of 577 nm wavelength will shine on the cathode in the photocell. 7. Start with zero applied voltage by turning the voltage potentiometer knob of the DC power supply all the way clockwise. 8. Gradually decrease the applied voltage (increase in negative value) by turning the knob counter clockwise until the photocurrent goes to zero. 9. Record the magnitude of the stopping potential for the corresponding wavelength in Table Rotate the filter wheel until the 546 nm filter is aligned with the white index line. Spectral lines of 546 nm wavelength will shine on the cathode in the photocell. 11. Gradually increase the applied voltage by turning the knob counter clockwise until the photocurrent goes to zero. Record the stopping potential in Table Repeat the measurement procedure for the other three filters. Record the stopping potential for each wavelength in the Table Cover the exit of the mercury light source. 14. Repeat steps 5 13 for the other two aperture diameters, 2 mm and 8 mm. Revised: 12 August /10

5 Part II Photocurrent-Voltage characteristic measurement Constant frequency, different intensity 1. On the tunable DC power supply, set the Voltage Range switch to -4.5V 30 V. 2. On the DC current amplifier, turn the CURRENT RANGES switch to A. (If the A range is not large enough, please turn the CURRENT RANGES switch to A.) 3. On the DC current amplifier, push in the SIGNAL button to the in position for CALIBRATION. Rotate the CURRENT ADJUST knob until the ammeter reading shows that the current is zero. 4. Press the SIGNAL button to the out position to return the DC current amplifier to MEASURE mode. 5. Gently pull the aperture dial away from the case of the photodiode enclosure and rotate the dial so that the 2 mm diameter aperture is aligned with the white index line. Then rotate the filter wheel until the 436 nm filter is aligned with the white index line. 6. Uncover the exit of the mercury light source. Spectral lines of 436 nm wavelength will shine on the cathode in the photocell. 7. Gradually decrease the applied voltage by turning the knob counter clockwise until the photocurrent goes to zero. Record the voltage and current in Table Increase the applied voltage to about 0 V. Record the voltage and current in Table Increase the applied voltage by about 2 V. Record the voltage and current in Table Continue to increase the voltage by 2 V increment. Record the voltage and current each time in Table 2. Stop until the applied voltage to about 30 V. 11. Repeat steps 5 10 for the aperture diameters = 4 mm and the spectral line wavelength = 436 nm. 12. Cover the exit of the mercury light source. Revised: 12 August /10

6 Name Date Lab session (Day & time) Lab partner MP4 Photoelectric Effect Lab Report A. Answer the following question BEFORE the first lab session (6 pts each) 1. Discuss briefly the main properties of photons. 2. Discuss briefly the physical meaning of the work functionφ. Find the value of φ for a typical conductor. 3. It is seen from Fig. 2 that the stopping potential is independent of the incident light intensity, while the saturation current is proportional to the incident intensity. Please explain these two main features briefly. Revised: 12 August /10

7 Name LA ( ) B. Experimental results (32 pts) Table 1 Stopping potential versus wavelength (15 pts) Aperture diameter: Wavelength (nm) Stopping Potential (V) 4mm 2mm 8mm Table 2 Photocurrent-Voltage characteristic - Constant frequency, different intensity (17 pts) Aperture diameter = 2mm, Wavelength = 436 nm Aperture diameter = 4mm, Wavelength = 436 nm Applied Voltage (V) Photocurrent (x10-11 A) Applied Voltage (V) Photocurrent (x10-11 A) Revised: 12 August /10

8 C. Data analysis and questions (50 pts) 4. (12 pts) Use the data in Table 1 and plot the stopping potential as a function of the frequency of the incident light for all three different intensities (different aperture size) on the same graph. Fit the each set of data to a linear function and record the fitting results. Attach your plot to the lab report. 5. (14 pts) From the graph and your fittings for each set of data, determine Planck s constant h, the cut-off frequency ν 0 and the work function φ of the cathode. Tabulate your results below. Calculate the percentage differences of h compare with the published value? What is the potential source of errors in this experiment? Revised: 12 August /10

9 6. (6 pts) How does light intensity affect the stopping potential? 7. (10 pts) Use the data in Table 2 and plot photocurrent as a function of the applied voltage for the 436 nm spectral line for the two different intensities on the same graph. Attach your plot to the lab report. 8. (8 pts) How do the curves of photocurrent versus voltage for the one spectral line at different intensities compare? In other words, how are the curves similar to and differ from each other? Revised: 12 August /10