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2. Photoelectric Effect, Stopping Voltage Method

2.1 Theory & Apparatus

The textbook example of the photoelectric effect uses a stopping voltage method. In this part of the lab a Mercury light source provides a broad spectrum of photons. Specific wavelengths from the source are selected using a series of interference filters and/or a prism. The light is focused onto a conducting screen inside a vacuum tube (see Fig. 1). Inside the vacuum tube a thin wire is biased by a retarding voltage, Vr (see Fig. 2). The field from the detector wire allows photoelectrons with energies greater than approximately Vr to leave the screen. Those with energy less than ~Vr are turned around by the detector field and are eventually readsorb in the screen.


Figure 1: Schematic of the stopping potential method apparatus arranged on optical bench. The details of the photocell are shown in Fig. 2.

The electrons that are emitted from the screen cause a positive current from the screen. This screen current is amplified and converted to a voltage proportional to the photoelectron current, Vi. In this way the wire makes the screen act like a diode, allowing electrons to flow when the electrons have energy greater than Vr. A DC offset voltage can be added to the amplifier output to compensate for stray light and internal bias currents in the electronics.


Figure 2: Photocell internal schematic drawing and preamplifier electrical connections.

To understand the photoelectron current refer to the energy diagram in Fig. 3. For a potential, VR, applied between the screen and detector Fermi energies, electrons emitted from the Fermi level have the largest Kinetic energies (see Fig. 3a). All electrons with KE < 0 have sufficient energy to be collected at the detector wire. As the retarding potential is increased fewer electrons are collected until the threshold voltage, VR,min, is reached (Fig. 3b). At this voltage the current to the detector goes to zero.


Figure 3: Energy diagram of the photoelectric effect. (a) Two transitions above and below the threshold retarding voltage, VR,min. (b) Threshold transition.

At threshold the following relationship holds:

  Eq. (1)

By measuring the threshold potential for light with different incident frequencies, a plot of V versus ν should be a straight line with slope h/e and intercept φd.

Unfortunately the threshold voltage is not so easily identified. The reason for this is that the number of energy state, N(E), in the metal near EF may be very small. In general the number of electron states increase below EF. So even though the retarding voltage is below the threshold for emission, very few electrons are in fact emitted. This means that the current rises very slowly with retarding voltage even below threshold.

2.2 Equipment

  1. Mercury light source, housing, stand, shield
  2. Black screen for lamp
  3. Optical bench with 5 riders (tan tape marks enlarged hole)
  4. Lens, F=5 cm, with holder, "condensing" lens
  5. Lens, F=12.5 cm, with holder, focusing lens
  6. Adjustable slit (lever adjusts sides, top and bottom also adjustable)
  7. Filter holder, with heat adsorbing filter (towards light source)
  8. Direct vision prism, used only to qualitatively observe effect of filters
  9. Stand with pointer, to help line up optics
  10. Large black & white card
  11. Small black & white card
  12. Bond paper, to detect UV light
  13. Light with stand Photocell & current detector unit, with stand
  14. Voltmeter, 0 - 3 volts, to measure retarding voltage
  15. Millivoltmeter (18 mV, 360 ohms), to monitor photocell current
  16. Aperture Card (cardboard) to place in front of photocell to reduce light
  17. Computer and A/D interface
  18. LabView program
  19. Folder with notes on interference filters (O’Shea)
  20. Filters: All filters are interference filters:
    UV465 nm
    Violet405 nm
    Blue436 nm
    Green546 nm
    Yellow578 nm

2.3 Precautions

Personal
The mercury light emits ultra violet radiation which is harmful to the eyes. Do not light the bulb unless all shielding is in place. Do not look directly into the light. Also note that the mercury light and adjacent shield get very hot so you should not touch them. Do not leave the equipment running while unattended since there is a possible fire hazard!

Apparatus
Unless you are making measurements in the dark, you should normally maintain the maximum retarding voltage(knob fully clockwise (CW)). This prevents excessive currents to the preamp.

Do not turn the mercury light off and then immediately back on. To extend the lamp lifetime it is best to run it continually.

Current Detector Unit.
The photocell current is monitored with a voltmeter! The photocell current runs through a large resistor, and the voltage developed across this resistor is monitored by an op-amp circuit. All of this is internal in the photocell unit. The output of the op-amp can be monitored either by an internal meter (which is disconnected for out experiments) or by an external meter, which happens to be a millivoltmeter.

2.4 Procedure

Part A: Optical Arrangement and Filters. (refer to Fig. 1)

A.1. Make sure the 5cm focal length lens is placed 5cm after the Hg Lamp window. Arranged this way, the lens will roughly collimate the light so that it strike the interference filter at normal incidence. The filter transmission coefficient depends on the incident angle the light makes with its surface. They are designed for normal incidence. The collimation by this lens is not very good because the light source is extended, but this should not be a serious problem.

A.2. During the photocell measurements, the slit adjustment may be used to control the amount of light reaching the photocell. The slit is controlled by slides through a lever on top of the slit. Additional control of the light intensity to the photocell is possible by moving the F=12.5 cm lens, i.e., by defocusing the light beam at the photocell.

A.3. To demonstrate the use of the filters, place the direct vision prism between the slits and the 12.5 cm focal length lens. Place a piece of bond paper after the lens as a viewing screen for the spectrum (the GT letter head paper is a high "rag" quality paper). You want to adjust the slit so that it is very narrow. This allows all the colors in the Hg spectrum to be clearly resolved. You will need to adjust the prism angle and the 12.5 cm lens position to get a good sharp spectrum on the paper. Insert each filter into the beam and verify that they filter out a single line. To view the UV line you must remove the prism because it absorbs UV radiation. Also the bond paper contains phosphor that will glow when the UV light hits it. By rotating the filter you can observe how sensitive the filter is to the angle of incidence the light makes with the filter normal.

In your report, include a descriptive account of how the interference filters work. A diagram(s) will help in your description.

Part B: Measuring Planck's Constant.

B.1. Remove the prism for all of the subsequent experiments.

B.2 Intall the LabView program. This program allows you to adjust the zero light level in the detection electronics and acquire multiple retarding voltages versus emission current data sets. When the program is first started it continuously displays the emission current. This output is used to zero the detector electronics. Make sure that the output from the detector electronics are plugged into the correct analog input channel on the interface box. The program displays the correct channel names.

The program reads both the retarding voltage and the collector current (i.e., a voltage proportional to the actual electron current). You manually adjust the retarding voltage (starting from the highest voltage) and the program reads the current in equal voltage increments determined by the voltage increment you set. Typically the increment should be 0.025V. You must change the voltage slowly. If you go too fast the program will not have time to record the current. If you change the voltage too fast, the program will stop and wait for you to go back above the last data point displayed on the computer. At that point you can continue to lower the voltage to zero and finish the scan. A scan is completed when the voltage has been lowered below 0.1V.

When the scan is finished the program will either wait for you to start another scan, determined by the scan number you set when you start the program, or ask for a file name to save your data. To take another scan you must increase the retarding voltage above 3V and then begin lowering it back to zero. When all scan are finished the data will be saved as voltage vs multiple currents, one for each scan.

B.3. For each of the five wavelengths for which filters are provided, obtain data for plots of photocell current (i.e., a voltage proportional to the current) versus retarding voltage. This is called an "IV" curve. For best results, you should use a minimum of 10 scans for each filter. After the data is taken you can use a spread sheet to average the scans into a single current vs. voltage plot.

    Data Range and Zero: The data near zero current is the most important as explained earlier. It is therefor important to make sure your zero line does not drift too much between measurements. After every filter, set the retarding voltage to its highest value, mask off the detector aperture and use the zero adjust to set the computer read current to a fixed value. A value of 0.005V is a good choice.


Figure 4. Schematic "IV" data set showing the zero and the best range of data.

    The most important current range is for voltages on the current meter between 1 to 10mV. This may change depending on the light intensity you are using. To determine this range take a quick set of data for one filter and plot I (in mV) versus VR. The curve will have a knee in it above which the current increases rapidly (see Fig. 4). The most important current range is below the knee. I suggest you take 10 IV data sets per filter below the knee.

    Light Intensity too High: You should check that your light intensity is not too high because it may saturate the current to voltage amplifier and distort your current measurements. To check this set the retarding voltage as high as possible. Even with light on the photocell you should read your zero voltage. If masking the light to the photocell influences this zero, your light level is probably too high. If this is the case you should either reduce the slits or defocus the beam with the 12.5cm lens.

    Adjusting Light Intensity: The experiment does not seem to work well with very low light levels. It also helps to make the light level into the photocell the same for all filters. There are a couple of ways of doing this. First you can use the slits or the 12.5 cm lens to get a light level, at zero retarding voltage, that is a little below the saturation value of the amplifier. I would suggest you measure what the saturation value is and shoot for a light intensity ~80% of that value for each filter.

    A second option is to have a light level, at zero retarding voltage, that saturates the amplifier for the fixed slit width that you use for measure the "IV" curve (you must measure the slit separation so you can go back to it). You then reduce the slit size to a known second value so the amplifier is not saturated and adjust the light intensity to get a fixed current. After measuring the light level for VR=0 you open the slit to the larger value for the "IV" measurement. This allows you to set the incident light level but still have a high enough light level for the measurement. You could also use a diffuser plate or a blackened mask in front of the photocell to make the incident light level measurement. That way you do not have to adjust the slit each time you take an "IV" measurement.

B.4. Does VR,min depend on the incident light level? This is an important aspect of the quantum behavior of the photoelectric effect. To test this choose two filters (the yellow filter is a bad choice because of the low light level at this wavelength). Obtain data of the photocell current versus retarding voltage ("IV" curve) for two different light levels than the one used in part B.2. What ever method you used in part B.2 to set the light level, use it here to set a level that is loweror higher by a factor ~2.

B.5. Data Analysis: Interpretation of the data obtained in parts B.2 and B.3 is not straightforward because there is no sharp cutoff of the current when VR is increased above threshold. Therefore, judgement is needed in assigning a stopping voltage value for each filter.

    B.5.1. Choosing VR,min: The best method is to pick VR,min as the voltage when the derivative of the current vs. VR begins to increase.

    The advantage of this is that I(VR) is an integral of the number of electrons emitted with an energy between VR and VR,min:

  Eq. (2)

    N(E) goes to zero faster than its integral making the onset of emitted current more apparent. In order to take a derivative of your "IV" curve directly, the signal to noise ratio in the data must be low. This is why you need to average at least 10 IV curves. It is best to do the data analysis in the lab to see whether or not your averages are large enough to make the derivative smooth and not noisy.

    B.5.2. Determine h/e: From the five stopping voltages determined in B.4.1, plot stopping voltage versus frequency. Determine h/e from the slope of a straight line fit to the points. Also determine the work function from the intercept. Work function determinations generally have unclear interpretations because surfaces imputity greatly affects the work function. Comment on the linearity of the fit; the error bars you estimate for h/e and compare your value to the published value.

    B.5.3. VR,min vs Light Intensity: From the data gather in part B.3, comment on whether or not VR,min depends on the incident intensity. You should plot the three "IV" curves in the same figure in your report. How does this fit into the quantum theory of the photoelectric effect?


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