THE PHOTOELECTRIC EFFECT Name ____________________________ Date __________________ Period _____ The photoelectric effect is one of the key experiments that supported early quantum theory. Light, prior to the early 20th century, was considered to be a wave phenomenon. In most ways, this idea reflects reality well—for instance, light is bendable when passed through a lens. The energy of a wave is given by amplitude of the wave squared, so a light wave of a certain frequency should be able to have any value for energy as long as there is a bright enough light source. However, when red light was shone on a metal surface, no electrons were ejected even when the brightest red light sources were used. On the other hand, when blue light was shone on the same metal surface electrons were ejected even when the source of light was weak (and brighter blue lights ejected more electrons) How could this be? The energy didn’t seem to depend on the amount of light hitting the metal but instead the frequency of light that hit the metal. Planck put us on the path leading out of this thicket of confusion when he theorized that light and other forms of energy comes in “packets” or discreet “bundles”. Light, in this theory, is considered to be a particle, which we now call a photon. The photoelectric effect was explained by Einstein when he conjectured that Planck’s bundles of energy (i.e. photons) were “knocking loose” the electrons—but only if the photons had enough energy to do the job (a two year old isn’t able to knock a football player off his feet, but a bull undoubtedly could). Einstein’s ideas gave further support to the theory that light energy really is not continuous with infinitely small increments of change (a wave), but is in fact “chunky”. Today’s lab involves a simulation of the photoelectric effect. You will be checking various metals for the point at which they begin to shed electrons, based on a specific threshold frequency—the exact point when the photons have enough energy to knock the electrons loose. This energy is called the work function (W) for the metal. Different metals hold on to their electrons more strongly or weakly due to atomic structure, so the work function for various metals varies. The formula for calculating W is as follows: h = Ek + W Where h is Planck’s constant is the frequency of the light Ek is the kinetic energy of the ejected electron W is the work function The kinetic energy of the electron refers to its actual movement once ejected. E k can effectively be ignored if we just reach the amount of energy to loosen the electron but not get it moving (Ek in these circumstances will essentially have a value of zero). You will be trying to achieve the lowest possible speed for the electrons you eject from the virtual metal surface. W can be obtained by calculating frequency and using Planck’s constant. The work function will be in joules, so in order to compare to published lists of work function values—which are in electron volts—your final value will require conversion into this unit. The “equipment” you will be working with looks like this: 1. Bring up the internet and go to the following site: http://phet.colorado.edu/index.php 2. Look for “Run our Simulations”, click “On Line”, then “Light and Radiation” (in the left hand column), then “Photoelectric Effect”, then “Run Now”. 3. Keep battery voltage at 0. Turn light intensity up to 100%. You will be testing sodium first (metals are changeable in the upper right hand box). 4. Adjust wavelength to a value which just allows electrons to leave the surface at a lowest possible speed. 5. Calculate W in electron volts using the following values and formulas: c = , where c = 2.998E17 nm/sec, is in nm and is in s-1 h = 6.626E-34 Js 1 electron volt = 1.60217646 × 10-19 joules h = Ek + W ***remember—Ek is set at zero 6. Calculate work function (in eV) for all other metals, including the mystery metal. 7. Identify the mystery metal and check the values obtained for the other metals. The following table of work functions for metals may be helpful Aluminum 4.08 eV Cesium 2.1 eV Lead 4.14 eV Potassium 2.3 eV Uranium 3.6 eV Beryllium 5.0 eV Cobalt 5.0 eV Magnesium 3.68 eV Platinum 6.35 eV Zinc 4.3 eV Cadmium 4.07 eV Copper 4.7 eV Mercury 4.5 eV Selenium 5.11 eV Calcium 2.9 eV Gold 5.1 eV Nickel 5.01 eV Silver 4.73 eV Carbon 4.81 eV Iron 4.5 eV Niobium 4.3 eV Sodium 2.28 eV Questions: 1. Choose a metal and choose a wavelength that ejects electrons at a reasonable speed. Turn the light intensity up and down. Make note of the number of electrons ejected. Now, move the slider that changes wavelength back and forth slowly. Make not of any changes you see. Explain both issues (results from change in intensity/change in wavelength), with reference to quantum theory. 2. Choose a metal and choose a wavelength that ejects electrons at a reasonable speed. Set intensity to 100%. Change the flow of electricity from the battery (at the bottom of the screen), making note of the change in charge at both ends of the electron chamber. Speculate as to why the flow of electrons is changed. 3. Reset the battery to zero, and turn on the electron energy vs. light frequency graph at the right of the screen. Play with light wavelength to generate data for the graph. Convert electron volts into joules, then calculate the slope of the line (be sure to use the exact values used in the graph). Explain why you obtained the value you did. 4. Kinetic energy for a particle is found by using the formula E = 1/2mv2, where m = mass in kg and v = velocity in m/s (the E is the same as the Ek in the formula above). Set the equipment to sodium, 100 % intensity, 100nm, and 0.00 battery voltage. Using the above information, calculate the velocity of the ejected electrons. The mass of one electron is 9.109 × 10-31 kilograms. The value for W will have to be converted back into joules before proceeding. Finding the work function for sodium 1. Place the intensity cursor at 10% and the battery cursor on 0V. 2. Move the wavelength cursor staring from IR to the left. As you move the cursor, do you increase or decrease the energy of emitted photons? _______________________________________________________ 3. Stop moving the cursor when you observe that the electrons are emitted from the plate. 4. Calculate the work function for sodium: _______________________________ Compare your calculations with the expected value for the work function. Finding KE of emitted electrons at 210 nm 1. As the electrons are being ejected, move the wave cursor to 210 nm. 2. Is the kinetic energy of the emitted electrons increasing or decreasing during the process of reaching the wavelength of 210 nm? ___________________________________________________ 3. Write the formula to find the KE of emitted electrons and then follow with the calculations. PART 3. Does the intensity of external light source affect the kinetic energy of the ejected electrons? Hypothesis: _____________________________________________________ 1. Move the cursor to intensity of 100% to check your predictions. 2. Was your hypothesis correct? _________________________________ PART 4. Analysis of Graph Energy of Ejected Electrons versus Frequency of the Source 1. Move back the intensity cursor to 10 % and the frequency cursor to the threshold frequency. 2. Highlight Energy versus Frequency Graph from the Right Side of the Manu. . 3. Predict the type of graph you would expect as you increase the wavelength of the external source of light? 4. Check your predictions. 5. What does the slope of the graph represent? 6. Calculate the slope and show your calculations. 7. Change the metal plates for copper. Do you expect the graphs Energy versus Wavelength to be identical (in terms of the x-intercepts and the slopes) for both metals? ____________________________________________ 8. Check your predictions_______________________ PART 4. Analysis of Intensity of External Source versus Intensity of Current Graph. 1. Highlight Current versus Light Intensity Box form the right menu. 2. As you move the wavelength cursor, do you expect the intensity of the current to change? Support your answer. 3. Check your predictions. 1. (1 pt) Suppose you set up the experiment so that the plate is ejecting electrons. Predict which of the following changes to the experiment could increase the maximum initial kinetic energy of the ejected electrons. (Select all that apply) Then test your prediction. A. Increasing the intensity of the light beam B. Decreasing the intensity of the light beam C. Increasing the wavelength of light D. Decreasing the wavelength of light E. Increasing the frequency of light F. Decreasing the frequency of light G. Increasing the voltage of the battery H. Decreasing the voltage of the battery I. Replacing the target with a material that has a larger work function J. Replacing the target with a material that has a smaller work function 2. (1 pt) Suppose now you set up the experiment so that the light intensity is non-zero but the plate is NOT ejecting electrons. Predict which of the following changes to the experiment could make the plate start ejecting electrons? (Select all that apply) Then test your prediction. A. Increasing the intensity of the light beam B. Decreasing the intensity of the light beam C. Increasing the wavelength of light D. Decreasing the wavelength of light E. Increasing the frequency of light F. Decreasing the frequency of light G. Increasing the voltage of the battery H. Decreasing the voltage of the battery I. Replacing the target with a material that has a larger work function J. Replacing the target with a material that has a smaller work function 3. (0.5 pts) What causes the electrons to be ejected from the left plate in this simulation? A. The force exerted on the electrons by the battery B. The beam of light shining on the plate C. Both A and B. D. Neither A nor B.
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