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L29. Determining Planck's Constant from the Photoelectric Effect

This lab uses a video clip.

About your report: You'll do all your work for this lab in a Logger Pro file.

 Goal

To determine Planck's constant by measuring stopping voltage as a function of incident light wavelength for a metallic photocathode.

 Prelab

  1. Review section 30.2 of your text and the problems related to the photoelectric effect on WebAssign E.30.01.

  2. Do the WebAssign prelab, L29PL.

 Equipment

This equipment is used in the video clip.

EP-05 Photoelectric Effect Apparatus (Daedalon Corp.)
Mercury Arc Lamp
Set of red, yellow, blue and violet filters
Adjustable stands (or stack of papers or thin containers) for adjusting heights of lamp and EP-05
Multimeter
Flashlight
Red and green diode lasers
He-Ne laser

 Method

This method is adapted from Daedalon Corp. Instruction Manual for EP-05.

Watch the video to see the method of data collection:  Streamed or MP4.  Use the instructions below for reference. You will not actually carry out the steps. Move on to the data after viewing the video.

  1. Set up the EP-05 Photoelectric Effect Apparatus on a table so that the aperture in front of the photodiode faces the mercury arc lamp. The aperture is 7 cm above the bench top, so the box or source may have to be raised to line them up. The phototube is very sensitive to small amounts of stray radiation, particularly shorter wavelengths than those being measured. Sunlight is very rich in these wavelengths, so it is often useful to construct a cardboard light shield around the box and the light source. The line power outlet should have a good ground connection to reduce any hum pickup.
  2. Connect a digital voltmeter to the red and black banana jacks on the top panel of the case. They are connected across the photodiode and measure the stopping potential across the tube. A digital voltmeter is best for this measurement, since the accuracy of the reading affects the accuracy of the result.
  3. Turn on the Photoelectric Effect Apparatus. With the "VOLTAGE ADJUST' knob turned completely counterclockwise and with no light entering the apparatus, adjust the "ZERO ADJUST" knob so that the photocurrent meter reads zero. The digital voltmeter should also read zero or nearly so.
  4. Turn on the mercury arc lamp. Take care: mercury lamps with quartz envelopes (such as the one you are using), emit ultraviolet radiation that is harmful to your eyes. Place the blue filter over the photodiode aperture. This filter will pass the blue wavelength at λ = 436 nm.
  5. If the zero drifts between readings, the radiation intensity on the photo surface is too high and a phenomenon known as fatigue is occurring on the photo surface. Reduce the intensity by moving the source away from the aperture. The amplifier is quite stable but, since the measurement is made at the scale zero, any drift causes an error. The zero adjustment should be frequently checked during the measurements.
  6. Turn the "VOLTAGE ADJUST" knob to its counter-clockwise limit. The voltmeter should read zero or very close to it. Move the apparatus until the radiation is striking the center of the photodiode. The reading on the output meter is helpful in making the adjustment. The radiation intensity should be adjusted so that the meter is approximately 10 on the scale. If the meter goes off scale, the photo surface won't be harmed. The meter won't be harmed either; the amplifier limits the current delivered to it.
  7. Measure (but don't record) the output current as a function of applied voltage. As the voltage increases, fewer and fewer electrons have enough energy to leave the cathode, and the current drops. The critical point on the curve is the stopping voltage at which the current just falls to zero. The current remains at zero for stopping voltages higher than the critical value. The value you need is when the current just reaches zero. Try to vary the applied voltage in sufficiently small increments (particularly as you approach zero current) so that you can determine the stopping voltage to at least 10% precision. Record the value you obtain for the stopping voltage.
  8. Repeat the procedure in steps 5 and 6 four more times, each time measuring and recording the stopping voltage for zero current, and resetting the zero after each setting.
  9. Change the filter, replacing the blue filter with the green one. This isolates the green line in the mercury spectrum at λ = 546 nm and this will be the effective wavelength of the radiation passed through it. Repeat steps 5 through 7. You will find the stopping potential is much smaller than for the previous wavelength.
  10. Repeat step 8, for the following light sources: mercury lamp with yellow filter (wavelength = 580 nm); mercury lamp with violet filter (wavelength = 405 nm); He-Ne laser (wavelength = 638 nm) with red filter; red diode laser (wavelength = 670 nm) with red filter; green diode laser (wavelength = 532 nm) with green filter. Using the filters will greatly reduce stray radiation that might strike the photo surface of the diode.

 Data

The following data were collected. Use this data for the analysis.

Filter or
light source
Wavelength
(nm)
Stopping Voltage (V)
Trial 1 Trial 2 Trial 3 Mean Mean Deviation % Mean Deviation
Violet filter 405 1.409 1.397 1.419 1.408 0.008 0.5
Blue filter 436 1.292 1.287 1.286 1.288 0.002 0.2
Green diode
laser
532 0.883 0.920 0.870 0.891 0.019 2.2
Green filter 546 0.846 0.827 0.810 0.828 0.012 1.5
Yellow filter 580 0.740 0.737 0.769 0.749 0.014 1.8
He-Ne laser 638 0.789 0.810 0.834 0.811 0.015 1.9
Red diode
laser
670 0.394 0.390 0.396 0.393 0.002 0.6

 Analysis

  1. Enter the data for wavelength and the mean stopping voltage in Logger Pro. Add a calculated column for the frequency of the light in units of Hz. Also add a column for the % mean deviation. Plot stopping voltage vs. frequency and perform a linear fit. Add error bars using the % mean deviation column.

  2. Provide the usual matching table and equation of fit in a textbox.

 Interperetation

Do the remainder of the report on a second page of your file.

  1. Determine the following using coefficients of the fit and the value of the elementary charge, e. Show your work.

    1. Planck's constant

    2. work function of the emitter

    3. cutoff frequency

  2. Calculate the experimental error in your determination of Planck's constant.

  3. Would the stopping voltages you measured be different if you had used more intense light sources but kept the same wavelengths? If so, how? Explain.

 Conclusion

The experiment that was shown in the video clip is a typical method of determining Planck's constant. Sometimes, the AP exam includes free-response problems in which you have to describe how to carry out an experiment to reach a particular goal. For example, one AP exam asked for descriptions of the methods of determining the index of refraction of a block of glass and of the wavelength of light passed through the glass. You may recognize these as being the methods of L17 and L19A. Suppose you were asked on an AP test to describe a method of determining Planck's constant. What equipment would you use, what would you measure, and how would you analyze the data in order to reach the goal? Your answer to this question will be your conclusion to this lab. In writing your answer, think in terms of what an AP grader would be looking for. They wouldn't be looking for all the detail given in the list of 10 instructions above. They don't care about how to set the dials on particular pieces of equipment. So don't paraphrase the instruction list. Provide an original overview that would make it clear to the grader that you knew how to carry out the experiment and that you understood the physics necessary to determine Planck's constant from the data.