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 e, where  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).
2536.519
UV
3000
UV
(absorbed by glass)
3650.1
3654.8
UV
3663.3
6907.5
red
4046.6
violet
4358.4
blue
5460.7
green
5769.6
yellow
5789.7
yellow
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/and that brings to the useful combination, hc, and the
wavelength which you are measuring.)
Assuming e to be known, calculate values, and errors, for h and Pt.
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