Name: Investigation #9 Partner(s): OBSERVATION OF THE PHOTOELECTRIC EFFECT As mentioned in the previous investigation, one well-known phenomenon that defied explanation based on the well-established theories of Newton and Maxwell was the ejection of electrons from a clean metal surface when illuminated with light of certain frequencies. That is, when electromagnetic radiation (i.e., light) is incident on a clean metal surface, electrons are emitted from the metal. However, this only occurs if the frequency of the light is greater than some minimum value that depends on the metal being illuminated. The kinetic energy of the ejected electrons is determined by measuring the potential difference across the illuminated metal (the cathode) and the collector plate (anode) necessary to stop these photoelectrons from reaching the collector plate. At the time, the classical theory of light behaving as waves made a few predictions as what should happen. The primary classical predictions were: As the intensity of the light is increased, the photoelectrons should acquire greater kinetic energy. The kinetic energy of the photoelectrons should be independent of the frequency of the incident light. Dim light should require a longer time for the electron to acquire enough energy to be ejected. These all turned out to contrary to the experimental result. However, in 1905, Albert Einstein suggested that the results of this photoelectric effect could easily be explained by treating the electromagnetic radiation as propagating in discrete packets of energy. To Einstein s contemporaries this notion was preposterous. Young s double-slit experiment and Maxwell s derivation showing that light as an electromagnetic wave had definitively established the wave theory for light. Still, Einstein was awarded the 1921 Nobel Prize for physics for his explanation of the photoelectric effect. Observations of other phenomena (such as Compton scattering) also demonstrated the particle-like behavior of light and later confirmed Einstein s hypothesis. Part I Qualitative Observation Your group will need the following material/equipment for this observation: 1 sensitive electroscope 1 piece of clean zinc metal (fine steel wool or sand paper to clean if necessary) 1 incandescent lamp with 200W (or greater) bulb 1 UV lamp with 15 W bulb 1 acetate strip (clear) or acrylic rod 1 PVC strip (white) or rubber rod paper
Procedure 1. Assure that the zinc metal is free of oxide contaminants by scrubbing the zinc metal with steel wool or sand paper until it is shiny. 2. Place the zinc metal on the electroscope 3. Rub the PVC (white) strip with paper to charge the PVC negatively. 4. Rub the negatively charged PVC strip on the zinc metal. 5. Observe the behavior of the electroscope for at least one minute. Question: Did the electroscope discharge itself during the one minute? 6. Touch the electroscope plate and note that the electroscope discharges. Question: Why did the electroscope discharge when you touched it with your finger? 7. Rub the acetate (clear) strip with paper to charge the acetate positively. 8. Rub the positively charged acetate strip on the zinc metal. 9. Observe the behavior of the electroscope for at least one minute. Question: Did the electroscope discharge itself during the one minute? 10. Again, touch the electroscope plate with your finger to discharge the electroscope. Question: Why did the electroscope discharge when you touched it with your finger? Perhaps the charged electroscope can be neutralized by bombarding the it with high intensity light in order to blow away the excess charge. 11. Charge the electroscope negatively with the PVC strip as you did in Steps 3 and 4. 12. With the 200-W incandescent bulb initially dark, carefully slide the electroscope under the 200-W bulb. Activate the switch to energize the bulb. 13. Observe the behavior of the electroscope for one minute.
Question: What effect does the high intensity white light have on the negatively charged electroscope? 14. If the electroscope discharged, then recharge the electroscope negatively with the PVC strip. 15. With the 15-W UV bulb initially dark, carefully slide the electroscope under the bulb. Activate the switch to energize the 15-W bulb. 16. Observe the behavior of the electroscope for one minute. Question: What effect does the low intensity UV light have on the negatively charged electroscope? Perhaps the UV light somehow makes the air conductive. Test this: 17. Charge the electroscope positively with the acetate strip and paper just as you did in Steps 7 and 8. 18. Shine the UV light on the zinc plate again. Question: What effect does the low intensity UV light have on the positively charged electroscope? Complete the Table 1 below by recording the behavior of the electroscope in each space. Table 1 High intensity white light caused the electroscope to... Low intensity UV light caused the electroscope to... Negatively charged electroscope Positively charge electroscope Question: If high intensity light were responsible for discharging the electroscope, which light source should have discharged the electroscope faster?
Question: Besides the intensity of the light sources, how is the UV light different from the white light? Although light has wave-like characteristics, it also behaves like a stream of particles called photons. Each photon carries a discrete amount of energy. When a photon is absorbed, its energy is given to whatever absorbs it. Question: According to your observations, which photons have more energy those of white light or those of UV light? The energy of the photon is proportional to the frequency of the light. That is, E = hf, where E is the photon energy, f is the frequency of the light and h is the proportionality constant known as Planck s constant. Photons of UV light have enough energy to kick out electrons held in the zinc metal. Question: When the zinc metal was positively charged, why did it not discharge when exposed to the UV light? Checkpoint: Consult with your instructor before proceeding. Instructor s OK: Part II Quantitative Observation Einstein s assumption was that electromagnetic radiation was delivered in discrete amounts or quanta of energy. The notion was that these quanta (now called photons) had an energy, E ph, that was proportional the frequency, f, of the light. That is, E ph = hf where the proportionality constant, h, is Planck s constant.
Einstein reasoned that an electron in the metal could absorb the energy of a photon. Some of this energy goes into removing the electron from the metal and the remainder would then appear as the kinetic energy of the photoejected electron. The minimum energy required to barely remove the electron from the metal is called the work function (denoted ) of the metal. In addition to overcoming the work function of the metal, a photoelectron can lose some additional energy as a result of collisions with other electrons during the ejection. As a result, the photoelectrons can take on a range of kinetic energy values from zero up to a maximum value, K max. Applying conservation of energy yields hf = K max + As stated earlier, the maximum kinetic energy can be measured by applying a voltage to repel the most energetic photoelectrons. This stopping voltage, V stop, is related to the maximum kinetic energy: K max = ev stop where e is the charge of the electron. Combining and manipulating these equations provides and expression the stopping potential as a function of frequency: V stop = h e f - F e. Since h, e and are constants, the stopping voltage is a linear function of the light frequency. By measuring and plotting the voltage required to stop the photoelectrons for various frequencies of light, an experimental determination of Planck s constant and the work function of the metal can be made. Your group will need the following materials/equipment for this part: 1 mercury lamp and power supply 1 photodiode 1 DC current amplifier and 1 DC voltage source Prediction: Qualitatively, how do you expect the maximum kinetic energy of the photoelectrons (as measured by the magnitude of the stopping potential) to behave as the wavelength of the light increases (frequency decreases)? Why do you think that?
Procedure 1. Confirm that the mercury (Hg) lamp is connected to the power supply and that the power supply is in the OFF position. Then plug in the power supply. 2. Turn on the mercury lamp and allow it to warm up for 10-15 min. CAUTION: The mercury lamp gets very hot! DO NOT TOUCH the lamp casing! 3. In the meantime, confirm that the voltage source is set on the 4.5 V - 0 V. 4. Turn on the current amplifier and set the current range to 10 11 A. 5. On the current amplifier, depress the calibration button so that it is in the CAL position and dial the current adjust knob until the current reads zero. 6. Switch the current range to 10 12 A and repeat Step 5. 7. Switch the current range to 10 13 A and repeat Step 5. Once the current is adjusted to zero on the scale, do not change this setting for the duration of the experiment. 8. Depress the calibration button again so that it pops out to the MEAS position. 9. Now connect the photodiode to the current amplifier (BNC cable) and to the voltage source ( banana plugs). Remove the cover from the photodiode. 10. Start with an aperture setting of 8 mm and wavelength of 365 nm. 11. Carefully remove the cover from the lamp being extremely careful not to touch the hot casing. If the cover is difficult to remove, use the hot glove to hold the casing. 12. Turn the VOLTAGE ADJUST knob on the voltage source until the ammeter on the current amplifier reads zero. This is the stopping potential required to turn away the most energetic electrons that have been ejected from the photodiode by the 365 nm light. Record this potential in Table 2-1 below. 13. Repeat Step 10 for each of the remaining four wavelengths by rotating the filter on the photodiode. (Be sure the aperture remains at 8 mm as you rotate the filter.) Wavelength (nm) 365 405 436 546 577 Table 2-1 Frequency f ( 10 14 Hz) Stopping Potential V stop (V)
Questions: What is the qualitative trend of the stopping potential as the wavelength increases (frequency decreases)? What does this imply about the kinetic energy of the ejected photoelectrons as wavelength increases? Question: How does the above result compare to your prediction regarding the stopping potential and the wavelength of the light? Now, you will investigate the effect that light intensity has on the kinetic energy of the photoelectrons for a particular wavelength. Prediction: What do you expect to happen to the stopping potential as the light intensity is decreased? Why do you think that? Procedure 1. Reset the wavelength back to 436 nm. 2. Enter the 436 nm stopping potential from Table 2 in the first line of Table 2-2. 3. Change the aperture to 4 mm by pulling the aperture ring out and turning until it clicks into place. Again, measure and record the stopping potential in Table 2-2. 4. Repeat Step 3 for the 2 mm aperture. Table 2-2: Aperture & Stopping Potential for = 436 nm. Aperture Width d (mm) 8 Stopping Potential V stop (V) 4 2
5. Reset the aperture to 8 mm and repeat Steps 2-4 for another wavelength of your choice and record the data in Table 2-3. Table 2-3: Aperture & Stopping Potential for = nm. Aperture Width d (mm) 8 Stopping Potential V stop (V) 4 2 Questions: For each of the two wavelengths, what is the qualitative trend of the stopping potential as the light intensity decreases? What does this imply about the kinetic energy of the ejected photoelectrons as a function of light intensity? Question: How does the above result compare to your prediction regarding the stopping potential and the intensity of the light? Checkpoint: Consult with your instructor before proceeding. Instructor s OK: Part III Computer Simulation In this final activity you will explore the photoelectric effect using a computer simulation. The simulator will allow you to shine light of variable frequency onto various metal targets. By adjusting the potential to stop the most energetic photoelectrons, the value of Planck s constant and the metal work functions can be measured. Procedure 1. Open the PhET Simulations alias on the computer desktop. Click on the Play with sims button, then click the Physics button, then click the Quantum Phenomena button. 2. Open and run the Photoelectric Effect Simulator.
3. Upon successful load, take a few moments to explore the simulator by adjusting the three sliders to get a feel for how the simulation works. Part III-A: Planck s constant The default target metal is sodium. In the far right column you can change the target metal by choosing from the drop down menu. In addition the target choice, there are three checkboxes that allow you to observe graphs while changing the sliders in the apparatus. These graphs are: Collector Current versus Battery Voltage Collector Current versus Light Intensity Maximum (Kinetic) Energy of the Photoelectrons versus Light Frequency 4. After exploring the simulation for a few minutes, choose the sodium target and set the battery voltage to zero. 5. Choose a light intensity of 25%. 6. Choose a random wavelength that ejects electrons from the sodium metal. Adjust the battery voltage until the collector current just drops to zero. Record the wavelength and the stopping potential in the first row of Table 3-1. (Watch your units!) 7. Calculate the frequency of the incident light and record in Table 3-1 below. Then reset the battery voltage back to zero. 8. Repeat Steps 6 and 7 for at least four more randomly chosen frequencies and complete Table 3-1. Wavelength (nm) Table 3-1: Low Intensity Light on Sodium Frequency f ( 10 14 Hz) Stopping Potential V stop (V) Prediction: If you were to repeat these measurements using light of a higher intensity, what do you expect to happen to the stopping potential?
9. Continuing with the sodium target, set the light intensity to 75% and repeat Steps 6-8 using the SAME wavelengths that you choose for Table 3-1. 10. Complete Table 3-2 below. Wavelength (nm) Table 3-2: High Intensity Light on Sodium Frequency f ( 10 14 Hz) Stopping Potential V stop (V) Question: How do the results compare with your prediction? Explain any differences. Checkpoint: Consult with your instructor before proceeding. Instructor s OK: Part III-B: Metal Work Functions As stated earlier, the work function of a metal is the minimum amount of energy required to knock an electron out of the material. Such an electron would have no kinetic energy once removed. In this final section, you will use the simulator to determine the work functions for all the metals available in the simulation including a mystery metal. Procedure 1. Starting again with the sodium target, set the light battery voltage to zero. 2. Adjust the wavelength slider to determine the cut-off wavelength. Calculate the cutoff frequency and determine the work function for sodium. Record you results in Table 3-3 below. 3. Repeat these measurements for the remaining metals including the mystery metal. Complete Table 3-3 on the next page.
Target Metal Sodium Zinc Copper Platinum Calcium?????? Table 3-3: Metal Work Functions Cut-off Wavelength Cut-off Frequency cut-off (nm) f cut-off ( 10 14 Hz) Work Function (ev) Questions: Rank these materials according to their work functions. Of these materials, which material has the loosest electrons? Which has the tightest electrons? In the homework section, you will be asked to plot the stopping potential as a function of frequency for Table 3-1 and then perform a linear fit the graph in order to obtain Planck s constant and the work function of the sodium metal. Question: Refer back to the equation for the stopping potential. What feature of the graph will provide Planck s constant? What feature will allow you to determine the work function of the target metal? Checkout: Consult with your instructor before exiting the lab. Instructor s OK: