= 10-8 cm):Purpose
To verify the quantum nature of light and measure the value of Planck's constant h by observing the relation between the light frequency used to induce photoemission and the energy of the electrons emitted.
Equipment
Preparation and lab work
In this experiment, you will essentially duplicate Lenard's 1902 researches. Rather than having to construct the electrode system and place it in a cumbersome vacuum system, however, you will use a two element phototube such as is often used in door controls. Surprisingly, using this simple tube and a few electrical components (plus your oscilloscope), together with a light source and some color filters, you will be able to arrive at a reasonably close determination of Planck's constant h.
The light source is a mercury discharge lamp whose light is concentrated
at a few discrete wave- lengths. It is customary to designate these narrow
wavelength intervals as "lines", since on the photographic record from a
spectrograph these emissions indeed appear as bright lines whose positions
correspond to wavelengths. The wavelengths of the prominent lines of mercury
which shall be useful to us are, in units of angstroms (1
= 10-8 cm):
5770
5451 (green)
4358 (blue)
4047 (violet)
3650
3132 (ultraviolet)
2537
We place these lines on a wavelength scale as in Fig. 3.
Figure 3
The arrows indicate the wavelengths that are passed by special filters you can
place in a holder on the mercury light housing. These "interference" filters
pass only wavelengths within about 50 
of the wavelength marked on the edge of the filter. They thus permit the
selection of 4 specific mercury emission lines. The marked wavelengths,
m, correspond to light incident at 
= 90deg.. At
other angles, the wavelengths passed by the filter becomes m
/cos. This means that a 10o misalignment is likely to cause
difficulties.
You will recall that Lenard's method was to apply a retarding potential V between the electrodes until the current just stopped, so that
.
But these fastest electrons are produced by the highest frequency, or
shortest wavelength illumination, and it will make no difference if
longer wavelengths are also present. Therefore, if we employ no filters over
the lamp, only the 2537 
line will determine the "cutoff" voltage.
At this point in your preparation you should make certain that you can obtain a numerical value of Planck's constant from a graph of cutoff voltage vs. maximum light frequency. Be especially careful about your units.
Your oscilloscope will be used here as an indicator of photo-cell
current (Channel 1). Since its input resistance is 1 MegaOhm
(106 ohms), the voltage you read will be one volt for each
microampere (10-6 ampere) of current. The electrical circuit is
shown in Fig. 4a. The variable resistance voltage divider allows the
application of retarding potentials between zero and 4. 5 volts to the cathode.
You can easily show from Fig. 4b that VOut =
so by varying the ratio Rl/R2 you can vary
Vout from zero to Vbatt. Since we now use oscilloscopes
with two input channels, the second channel is used to measure Vout.
You may display both the anode signal and the Vout level (straight
line) at once or switch back and forth.
Figure 4
The mercury lamp is operated from the 60 cycle power lines, and its intensity fluctuates 120 times per second. The number of photoelectrons ejected per second is proportional to the intensity of the light, so the photocurrent in your circuit will also rise and fall at a frequency of 120 cycles per second, As you increase the retarding voltage by turning the voltage divider knob on top of the phototube enclosure, you will notice that the amplitude (negative voltage) of the 120 cps signal decreases, reaches zero, and goes somewhat positive at still larger values of the retarding voltage. This unexpected observation is caused by photoelectrons emitted from the anode instead of the cathode. The number of anode electrons is kept small by shielding the anode from the direct light of the mercury source, but we cannot control reflections within the tube itself.
The anode electrons are accelerated rather than decelerated by the voltage applied to the tube; and therefore, even when the cathode's photoelectrons are completely stopped by the retarding voltage, there will still be a nonvanishing anode electron current in the opposite direction. Since essentially all of the anode electrons are collected at the cathode for even very small "retarding voltages" across the tube, the residual current contributed by them should be independent of small changes in the voltage. Thus, the value of the retarding voltage when the total current (anode plus cathode electrons) just ceases to vary with voltage is the value which just prevents the most energetic of the cathode electrons from reaching the anode. This unfortunate experimental complication makes the exact location of the cutoff voltage difficult to find unless you are very careful.
A good procedure is to plot the current, I, versus retarding voltage, V, to determine the cutoff voltage Vc:
Figure 5
Only the region around Vc needs to be plotted. Note that the voltage at which the amplitude is zero corresponds to the point where the number of electrons reaching the anode happen to exactly match the number of anode electrons which are leaving the anode and is therefore of no particular interest.
You will probably wish to open the metal box which contains the phototube and battery, and examine it more closely. The semi-cylindrical electrode is the cathode, and the tin rod is the anode. A piece of tape on the tube envelope shields the anode rod from the light. When you replace the tube, make sure you rotate it so the anode cannot be seen through the entrance aperture. The metal box and shielded cable to the oscilloscope are necessary to prevent interference from nearby power circuits in the building.
The light source is started by first setting the toggle switch to start and pressing the red start button; then the toggle switch must be set to operate, or else the life of the discharge tube will be greatly reduced. DO NOT LOOK DIRECTLY INTO THE DISCHARGE TUBE WHEN THE LAMP IS OPERATING since ultra violet radiation damages the unprotected eye. Place the light source and phototube housing an inch or so apart and cover both with the light shield hood. This shield hood is necessary to keep the room light out of the cell. (Fluorescent lights also contain the mercury spectrum') The battery switch is located on top of the phototube box. Be sure that this switch is turned off when you are through with the measurements.
Basic lab measurements
Measure the cathode electron cutoff voltage for each of the four filters shown in Fig. 3, and also for no filter. Make about 4 determinations of the cutoff voltage for each filter to get an idea of reproducibility. Find the highest frequency present in the light for each measurement and plot your measured cut off voltage as a function of the maximum light frequency on a piece of graph paper. Each data point on the graph should have error bars indicating the precision of your measurements. Draw an average straight line through your data and from this line determine Planck's constant. The uncertainty in your result can be obtained by noting the range of different lines you can draw through your data. How does your result for h compare with the commonly accepted value? Can you give a plausible explanation of any disagreement?