The Photoelectric Effect

In this experiment, the photoemission of electrons from potassium is studied, and the value of Planck's constant is determined.

A. References

Melissinos describes the photoelectric experiment (pg. 18) and the mercury spectrum (pg. 50; figure 2.13 is actually mercury, not hydrogen, as the caption says). The photoelectric effect is discussed in the text (T–Z, § 5.3, pp. 109–112) as well as elsewhere –Tipler (pp. 1148-1152) is quite good, and Lea and Burke is excellent (§35.1.1, page 1112-1116. I really recommend the L&B reference, especially for the lovely plot from Millikan's original paper, Fig 35.3. Now that's a challenge!)

N.B. - The mercury lines are listed in the Chem. Rubber Handbook under "Persistent Lines of the Elements."

B. Theory

Light from a low-pressure mercury discharge tube is diffracted by the grating of a monochrometer and one of several bright mercury lines can be selected at the exit slit. The light falls on a photocathode, a thin layer of potassium coating the inside of an evacuated glass tube, and some of the electrons ejected from the potassium are collected by a platinum ring. The resulting current is measured with a Keithley electrometer. By applying a potential to the platinum ring, one can either attract the electrons to it (positive potential) or repel them (negative potential). The potential required to prevent any electrons from reaching the ring, the "stopping potential," gives a measure of the maximum kinetic energy of the photoelectrons. Measurements for several different frequencies of incident light permit a calculation of Planck's constant.

 

Contact Potential.

Exact measurement of the accelerating voltage seen by the photoelectrons is complicated by the fact that they are accelerated between two dissimilar metals, as shown in figure 1. The voltage read by a meter connected to the two metals has to be corrected for the work functions of the two metals, as indicated below, before it represents the actual potential difference between the two metal surfaces.

A diagram showing electron energies inside the two metals and at their surfaces is given in figure 2. The crosshatched regions represent electron states in the conduction bands inside the metals. The effect of applying a voltage difference V with a battery is to make the tops of the conduction bands different by an amount V. The energy of an electron at the surface of either metal is greater than the energy of the top of the conduction band by an amount equal to ef, where f is the work function of the metal. One can see from figure 2, that for an electron ejected by a photon from the top of the conduction band in potassium to just reach the surface of the platinum ring, we must have:

The voltage that satisfies this condition is called the stopping voltage. In this experiment the stopping voltage is determined for several frequencies. If the stopping voltage is extrapolated to zero frequency, equation (1) says that the extrapolated value should be equal to minus the work function of platinum.

The Mercury Spectrum. The emission lines of a mercury discharge tube can be found in the CRC handbook under Spectra, persistent lines of the elements, and are seen in the accompanying figure. The values for some of these important lines are presented on the next page. Be sure to use these values as the exact values for your fit, don't use the approximate values you might observe from the monochrometer scale ( the scale has not been accurately calibrated, either by you or by anyone else).

Lines of Hg

2536.519

UV

(absorbed by glass)

»3000

UV

 

3650.1ü

 

 

3654.8ý

UV

 

3663.3þ

 

 

4046.6

violet

 

4358.4

blue

 

5460.7

green

 

5769.6

yellow

 

5789.7

yellow

 

6907.5

red

too weak - don't use

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C. Procedure

1. CAUTION: Don't look directly into the exit slit of the monochrometer without wearing glasses, as it transmits harmful ultraviolet radiation.

2. Inspect the optical system. Look through a piece of ground glass, to absorb the UV lines. (Does this make you wonder what the material is the exit slit is made of?) See how the monochrometer works by passing white light through it. In particular, notice the effect of setting the height and width of the slits. In general, the entrance and exit slits should be set the same.

 

3. Set the slits fairly narrow, and measure the wavelength of the most prominent mercury lines. (CAUTION: DO NOT FORCE the slit adjusting screw!) Compare with the values given above. Note that the values given by the micrometer readings on the monochrometer are only approximate, so that you need to calibrate the readings by the known values of the Hg spectrum. Find the ultraviolet lines (use the fluorescent chalk. You really need these lines in order to get the spread you need in order to linearize the results.)

4. Set up the phototube with a positive bias of about 3 V, and see if it detects the lines. It should see lines in the ultraviolet, too! When you are tuned on an UV line, try and detect it with fluorescent chalk - make a mark on a black lab book and hold it in front of the monochrometer. For fun, you can also see if the UV passes through a piece of glass. Glass "cuts off" typically at around 3000A.

5 Now set the slits as wide as you can have them and still separate the lines. Note, however, that there will be error due to scattering of other wavelengths if the slit is too wide. (Will this be more important at longer or shorter wavelengths? Why?) Try about 4 mm wide and 10 mm high, for both entrance and exit slits.. Run one complete curve of voltage vs. current, from about 3 V retarding potential to 10 V accelerating potential, plotting the data as you go (First go to the ends of the range to see what range you need on your graph.); make smaller steps of voltage should be used near the stopping point. Use the "fast feedback" setting on the Keithley. Try to use the same setting on the large round scale-select knob throughout, changing the sensitivity with the "multiplier" knob only, during one set of data.

6. Plot your data. Does the curve flatten off at both ends? Why? At this point you will begin to appreciate the difficulties in this experiment. There is likely to be an easily measurable "back-current" due to the flow of evaporated potassium ions from the platinum cathode to the anode. For some, it may be relatively easy to determine where the current starts to rise in the "forward direction" Others may have to resort to rather arbitrary techniques.

7. Determine values for the stopping voltage and its error for your first set of data.

8. Now take the rest of your data. This is not as easy as it sounds. It can take so long (more than one day) that one suspects that the different sets of data don't "fit together," possibly due to changes in the apparatus from week to week. In fact, they probably don’t fit together! The following is suggested:

Set up the graph carefully in you lab book, and plot the data directly on the graph (write the numbers down too). The graph should go from -3 V to +1 V on the horizontal scale. The vertical scale should go from about from -10 to +20 in arbitrary "meter units." Choose a scale on the Keithley such that at -3 V the current reads about -7 (out of -10 full scale). Then move the voltage, choosing steps as you go so that the break point of the curve is well determined. When the current goes off of your graph, go on to another wavelength.

Try to take data from all wavelengths during one lab session. Include at least one ultraviolet line, to increase the range of frequencies spanned by your data. Don't use the red line - it is too weak, and is probably contaminated with light of other wavelengths (Why? –you should comment - this is an important point to think about in terms of uncertainty.)

Estimate the stopping voltage and its error for each of your wavelengths. There are several different methods for estimating this voltage. This estimation is probably the most challenging – and the most important factor to good results in this exercise.

9. Fit your data for stopping voltage (y axis) vs. frequency (x axis) to a straight line, either by hand and with a hand calculator, or using a computer and a spreadsheet program, or a "plot" program.. You should get values for the slope and intercept, with errors.

10. Compare with the expected result:

 

 

 

(note that hf can be more conveniently expressed as hc/l, and that brings in the useful combination, hc, and also the wavelength which you are getting from the table.)

Assuming e to be known, calculate values, and errors, for h and fPt.

Compare with accepted values. Discuss!

D. Equipment

Photoelectric tube in light-shield

10V Power supply

Voltmeter

Monochrometer

Mercury Lamps

Tensor Lamps

Keithley electrometer and cables

ground glass, UV-sensitive chalk