General Theory
The photoelectric effect occurs when light falls upon a metal and electrons are ejected from the surface of the metal. The electrons escape the surface as a result of the kinetic energy they obtain from the absorption of a single photon. Only if the energy of the photon is greater than the work function of the metal, can the electron escape. The maximum kinetic energy possible will be the energy of the absorbed photon minus the work function of the metal.
The photon's energy is proportional to the frequency of the light and is given by
where h is Planck's constant. A plot of the maximum KE of the photoelectrons vs the frequency of incident light is shown for an idealized PE effect experiment.
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The intercept on the frequency axis is called the threshold frequency, below which the photon's energy is less than the work function of the metal. Hence,  The equation becomes
where h is the slope of the line. |
Fig 1
Experimental Setup
The experiment is performed using the cathode-anode phototube arrangement, shown in Figure 2. Light from a source strikes the cathode and some of the ejected electrons reach the anode. This constitutes a current in the circuit and is measured with the current amplifier.
The maximum KE of the photoelectrons is measured with a stopping potential Vs, which is applied between the cathode and the anode. The stopping potential is increased, decreasing the photocurrent until it just reaches zero. Hence, the maximum KE of the photoelectrons is just the electron's charge times this potential. Measured in electron-volts (eV), this is the same value as the stopping voltage itself.
Fig. 2
Procedure
Connect the phototube and/or phototube module, current amplifier, power supply, and voltmeter as directed by the instructions with your setup. The current amplifier is very sensitive and easily damaged, so have the instructor inspect your connections before starting the experiment.
The light source is a Beckman Spectrophotometer (Figure 3), which consist of an incandescent source, a narrow slit, and a variable prism. The wavelength of light is controlled with the large knob at the rear of the device. The light intensity is controlled by a rheostat or power supply to the bulb.
Turn on the incandescent bulb in the Beckman and set the wavelength to about 500 nm. Disconnect the phototube module and check the zero adjustment on the current amplifier. Place the phototube close to and in front of the slit, checking visually that the light strikes the cathode. You may wish to mark the position of the phototube module. Turn off the room lights. With the stopping voltage at zero, a photocurrent should register. If not, check your alignment and connections. Adjust the intensity until a mid-scale reading is obtained on the sensitive scale (nA scale) of the current amplifier.
Find the approximate value of the threshold by decreasing the wavelength until the photocurrent stops. You will find the stopping voltage for ten different wavelengths between the threshold value and 400 to 350 nm. Space the wavelengths evenly. (If you use the filters, choose 10 filters within this range.)
Set the Beckman to each of the wavelengths, adjusting the intensity of the Beckman each time to give a mid-scale reading on the sensitive scale of the current amplifier. (If you are using the filters, adjust the wavelength until the intensity is maximized and use the wavelength given on the filter.) Slowly increase the stopping potential from zero recording both the potential and value of the photocurrent at ten points until the photocurrent is near zero. Check the zero adjustment on the current amplifier between each wavelength setting.
Because of electronic noise and dark current (coming from the anode), it may not be clear exactly at what point the current is zero. Make a plot of current vs stopping voltage for each wavelength. Fit a curve and extrapolate the data to find the voltage at which the photocurrent becomes zero.
Plot KEmax vs frequency using the stopping voltage values inferred from the plots of photocurrent vs voltage. Determine the value of Planck's constant from this graph.
