clc 2/21/04

Planck’s constant

You will measure Planck’s constant using the photoelectric effect. For his interpretation of this effect, Einstein was awarded the Nobel prize in 1905. The principle is simple: a photo tube is exposed to light of a known wavelength. Electrons ejected from the cathode of this tube emerge with some maximum kinetic energy, and these electrons cause a current to flow in the tube. You measure the current. If you now apply a retarding voltage V to the tube, between cathode and anode, electrons whose kinetic energy is below eV, where e is the charge of the electron, will no longer be able to reach the anode, and the current will drop. The current will cease altogether when eV becomes equal to the maximum kinetic energy with which the electrons leave the photocathode. You will measure the dependence of current on V for different wavelengths of light incident on the tube. As described in Tipler and Lewellyn (fourth edition) , section 3-3, a plot of current versus V will enable you to determine a “stopping voltage” V_o for each wavelength. Then a plot of V_o versus the frequency of the light will enable you to deduce a value of

h/e from the slope and the work function of the photocathode from the intercept.

Procedure:

The apparatus is a self-contained system made by Sargent-Welch. An external mercury vapor lamp serves as the light source. Turn on this lamp and let it warm up for at least five minutes. Avoid looking directly at it: it is very bright. The main spectral lines coming from the mercury are at 577 (yellow) , 546(green) and 435 (violet) nm. The apparatus incorporates three band-pass filters which isolate one of these lines at a time. Arrange the lamp so that it illuminates the entrance aperture to this filter holder, behind which the tube is located. The wiring diagram is shown on the apparatus. Use multimeters to measure the current drawn by the tube and the voltage across the tube. The 3 V is supplied by an external power supply. Connect this supply as shown on the apparatus, set it at 3 V and leave it there. You can then vary the voltage across the tube using the variable resistors built into the apparatus.

Make measurements of current (use the most sensitive meter scale) versus stopping voltage , taking points every 0.5 volts at least, more closely spaced near the cutoff. Make a graph of current versus voltage. Do this for each of the three wavelengths. Once you have started a set of measurements, do not move the source or the lamp until you have finished the entire experiment. However, you may then want to move the source closer or farther away and repeat the entire experiment to see if the results depend on the intensity of the light.

From each graph of current versus voltage, deduce a stopping voltage. This is not trivial: adopt a procedure for doing this, and use it consistently for all graphs.

Make a plot of stopping power versus frequency of the light, similar to that in 3-13, p 144 of TL. Deduce h/e and the work function from your graph. If you used more than one intensity, you may put all the points on the same curve.

Comment on your results, and make it clear you understand how the photoelectric effect works. Be sure all graphs and data tables are in your data book.