Photoelectric effect

A video of this demonstration is available at this link.

Charge the plastic rod by rubbing it with the felt cloth, then stroke the rod against the zinc plate atop the electroscope. (Since the rod is an insulator, to transfer the maximum charge, you must slide it against the plate.) This charges the innards of the electroscope negative, causing the needle to deflect. Shining the white light (shown at left) on the zinc plate has no effect, whereas using the ultraviolet lamp (to the right of the white lamp) causes electrons to leave the plate, discharging the electroscope and causing the needle to fall back to zero. The letters of the “Physics” sign at lower right are drawn with fluorescent chalk. You can use this sign to show that ultraviolet light is being emitted by the UV lamp. The heat lamps in front keep the air around the demonstration dry, to minimize leakage of charge from the electroscope.

What is happening?

When you charge the electroscope, the electrons in the zinc disc are bound within the disc by attractive forces (between them and the positively-charged zinc nuclei). Light incident on the surface of the disc interacts with the electrons, thus transferring energy to them. If the energy is sufficient to overcome the forces that bind the electrons to the surface of the disc, electrons are ejected from the surface. If not, no electrons are ejected. If the energy is greater than that required to eject electrons, the electrons emerge with kinetic energy equal to the excess.

The energy necessary just to overcome the forces holding an electron within the metal surface is called the work function of the metal, which for zinc is 4.33 eV (http://environmentalchemistry.com/yogi/periodic/Zn.html#Chemical; 4.25 eV according to H. Moormann, D. Kohl and G. Heiland, Surface Science, 80, 261-264 (1979), 4.3 eV according to http://hyperphysics.phy-astr.gsu.edu/hbase/tables/photoelec.html#c1). An eV (electron-volt) is the product of an electron charge, 1.602 × 10-19 coulombs (C), and a volt, which is a N·m/C, or a J/C, so 1 eV equals 1.602 × 10-19 J. So 4.33 eV × 1.602 × 10-19 J/eV equals 6.94 × 10-19 J.

The energy of a photon (quantum of light, vide infra), E, equals hν, where ν is the frequency of the light, or hc/λ, where λ is the wavelength of the light. Since E is inversely proportional to λ, this gives us the maximum wavelength of light that will have sufficient energy to eject an electron from the surface. We find this, of course, by rearranging: λ = hc/E = (6.626 × 10-34 J·s)(2.998 × 108 m/s)/6.94 × 10-19 J = 2.86 × 10-7 m, or 286 nm. The visible spectrum falls between roughly 400 and 800 nm, and the white light in this demonstration emits little or no light of wavelengths shorter than 400 nm. 400 nm corresponds to an energy of 3.1 eV, significantly lower than the work function for zinc. The UV lamp, on the other hand, emits light whose wavelength is 254 nm. This corresponds to an energy of 7.82 × 10-19 J, or 4.88 eV, which is enough energy to eject electrons from the surface and in addition impart to them a maximum kinetic energy of 0.55 eV.

Deposition of oxides or dirt on the surface of the zinc disc can raise the effective work function, so it may be necessary to clean the surface with the fine sandpaper (600 grit) shown in the photograph above.

You can also use a glass rod rubbed with silk to charge the electroscope positive, in which case nothing happens when you shine either the white light or the UV light on the zinc plate.

Some background:

In the late 1880s, Heinrich Hertz found that it is easier to produce an electric discharge between two electrodes when ultraviolet light shines on one of them. Phillip Lenard then showed that the reason for this was that the ultraviolet light caused electrons to be emitted from the surface of the cathode. One can study this effect by means of an apparatus that has a disc-shaped cathode and a cup-shaped anode facing each other and housed within an evacuated glass envelope with a quartz window at the anode end. Quartz passes UV light down to a wavelength of about 200 nm, or up to an energy of about 6 eV, whereas ordinary glass absorbs UV. A hole in the anode allows light through to the cathode. The cathode and anode are connected via a potentiometer to a battery or other DC power source. The potentiometer allows for variation of the applied voltage, and a polarity reversing switch allows the operator to make either the cathode or the anode positive with respect to the other. An ammeter placed in series with one of the electrodes reads the current. With such an apparatus, one can measure, at constant light intensity (and wavelength), the current as a function of applied voltage. In 1914, Millikan very carefully performed such measurements, for which, along with his work to determine the elementary charge (his famous oil drop experiment), he was awarded the Nobel prize in 1923. (You can read his Nobel lecture here.)

When one shines light of more than sufficient energy to eject electrons from the cathode, the electrons emerge with a maximum kinetic energy equal to the excess over the work function, or Kmax = hν - w0. If one begins the experiment with the cathode negative and the anode positive, then as one raises the voltage, the current increases until it reaches a limiting value, which depends on the intensity of the light striking the cathode. If one reverses the potential (i.e., cathode now positive, anode negative), then as one increases the voltage, the current decreases until at some point it goes to zero. The voltage at which this happens is called the stopping potential, which we can denote V0. At this potential, the photoelectrons having the maximum kinetic energy are stopped, or Kmax = eV0.

If one then plots stopping potential versus the frequency of incident light, one obtains a straight line whose slope is h/e, Planck's constant divided by the electron charge, 1.620 × 10-19 C. You can explore an applet that runs a computer simulation of this experiment here. This applet gives you a choice between a cesium cathode and a sodium cathode.

The confirmation of the idea of a light quantum:

Some time before Millikan and others were doing their research on the photoelectric effect, Max Planck had introduced the idea of the quantization of energy. In studying blackbody radiation, he discovered that the only way he could formulate a model that would correctly describe it was to introduce the idea that the amount of energy emitted or absorbed by something could not vary continuously, but instead must change by discrete quantities. Scientists, however, still thought of light as “ether waves,” which is how Millikan himself refers to them in the second half of his Nobel address (see link above). Interference and diffraction experiments had physicists largely convinced of the wave nature of light. Einstein, in 1905, influenced by Lenard’s and Planck’s work, proposed the quantum theory outlined above, in which light energy comes in localized, integral packets of hν. This theory explains three major features of the photoelectric effect that cannot be explained by the classical wave model:

1) The maximum kinetic energy of the photoelectrons, Kmax, equals eV0 (e multiplied by the stopping potential), and is independent of the intensity of the light striking the cathode. The wave model would predict that the electric vector, E, of the light increases in amplitude with the intensity of the light, so that the force applied to the electron, eE, and thus the kinetic energy, should also increase with the intensity of the light. (What does increase with light intensity is the photoelectric current, as noted above.)

2) As with Kmax, the wave theory would predict that light of any frequency should be able to eject electrons from the cathode, as long as the light is intense enough. Experiments with the photoelectric effect show that for each metal, there is a minimum frequency, ν0, below which light, no matter how intense, is incapable of ejecting electrons.

3) In the classical wave theory, the electron to be ejected from the metal surface would absorb energy from a wave as it impinges on the metal plate. Assuming that the electron absorbs this energy from an area that corresponds to an atomic radius, if one estimates the portion that this represents of the approaching wavefront, then calculates the energy per time deposited on the target area by a feeble light source of a particular intensity, one finds that it takes significant time for enough energy to be deposited to eject an electron. Based on this, the classical wave theory would predict that there is a time lag between when the light is switched on and when electrons begin to leave the cathode. No one has ever measured such a time lag. The quantum theory, in introducing the concept of the photon, has the energy deposited in a particular atom all at once, and so is consistent with this observation.

When Einstein proposed his quantum theory of light, he suggested that examining the photoelectric effect was one way to test it. When Millikan performed his experiments in 1914, it became clear that Einstein’s theory described this phenomenon quite accurately. For his prediction of the photoelectric effect, Einstein was awarded the Nobel prize for 1921. The Royal Swedish Academy of Sciences decided to reserve the Nobel prize in physics that year, and they awarded Einstein the 1921 prize in 1922. You can find information about that prize here. The announcement of the 1921 prize came on November 9, 1922. Einstein was too far away from Sweden to be able to attend the ceremony. On December 10, 1922, Svante Arrhenius, who was the chairman of the Nobel committee for physics of the Royal Swedish Academy of Sciences, made a presentation speech for Einstein’s award, which you can read here.

References:

1) Eisberg, Robert and Resnick, Robert. Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (New York: John Wiley and Sons, Inc., 1974), pp. 31-37.
2) David Halliday and Robert Resnick. Physics, Part Two, Third Edition (New York: John Wiley and Sons, Inc., 1978), pp. 1096-99, A37.
3) Robert A. Millikan. The electron and the light-quant from the experimental point of view, Nobel Lecture, May 23, 1924 (available through link above).