# Photoelectric Effect

A discussion at one of our recent group meetings, reminded me of the interesting history behind the observation of the Photoelectric Effect. Some of these classic papers are quite impressive, especially as experimental feats. While the photoelectric effect was first observed by Heinrich Hertz, Phillip von Lenard, and others, it was the experiment of Robert Andrews Millikan that finally showed Einstein’s theory to be correct.

To briefly review, the Photoelectric Effect describes the emission of negative particles (electrons) from a metallic surface when it is exposed to light. The key features of the effect are that 1) increasing the intensity of the incident light increases the number of electrons emitted from the surface, 2) the kinetic energy of the emitted electrons depends linearly on the frequency of the light, and 3) there is no minimum light intensity required to emit electrons. The first feature was not surprising, this follows our increased-energy-in means increased-energy-out intuition. The second feature indicates that the energy of light corresponds to its frequency, this was a very new idea at the time, especially since the concept of the photon had only barely been introduced. The third feature also contradicted the picture of light at the time, physicists expected that if the intensity were low enough, the metal surface would never accumulate enough energy to eject an electron, and even if it did, the electron energy would have to be lower for lower intensities.

This effect is all nicely explained by Einstein’s equation:

$E_{kmax}=hf-\phi$

Which equates the maximum kinetic energy of the emitted electron to the difference between the photon energy $hf$ and the work function of the metal, $\phi$. This has been widely considered as proof of the photon picture, however in the 1960’s, Lamb and Scully showed that the photoelectric effect can be explained by assuming that the detector atoms are quantized, but that the field is not (i.e., by assuming light to be a classical wave) [1]. In any case, it is compelling evidence for quantum theory and, as the title to Millikan’s paper indicates, it allows one to determine Plank’s constant. Millikan reports 6.57e-27 and 0.5 percent accuracy, while the established value is 6.626e-27 erg sec, which means the modern value was just above his error bar.

## The experimental apparatus

Millikan recognized, after von Lenard’s experiment, that the metal surface must be very clean, something that was difficult to do at the time even in moderate vacuum because alkali metals oxidize so quickly. What he conceived of was a “a machine shop in vacuo,” where he would make a fresh cut of the metal under vacuum and then perform the experiment. This may not sound crazy today, but between 1905 and 1915, in the early days of the Ford Model T and the telephone, Millikan was able to construct at least 9 versions of his impressive apparatus.

The apparatus consists of one large glass bulb kept under vacuum. Within the bulb is a wheel with three cylinders of metal: sodium, lithium, and potassium. The wheel can be rotated, such that one metal cylinder faces a knife (K) which can be actuated toward the metal sample via electromagnet (F). Various stops and collars (M,N,M’) regulate the depth of the cut. Shavings from each cut gather in the enlarged lower portion of the bulb. After a fresh cut is made, the sample wheel rotates to present the sample to light entering the window at (O). Electrodes (B,C) are used to determine the photocurrent for various potential differences between the sample and the Faraday cylinder (indicated by dashed lines).

The details of the detector are described in various places, and aren’t particularly unique to this experiment. The cool part is how Millikan recognized that to make an accurate measurement he needed a freshly-cut sample. But beyond recognizing, he made it work, in the face of plenty of things that could have—and probably did—go wrong. In particular, I am curious about a statement on page 362 of his article: “The measurements, herewith reported related only to the sodium and the lithium, an accident having prevented the inclusion of data on potassium at the present time.” Given how dramatically all of these elements react to water vapor, I hope that accident wasn’t too serioius.

This experiment is still impressive 90 years later, and even though we have much better equipment now, it would be quite a project to put a machine shop inside a vacuum chamber.

[1] W. E. Lamb, Jr. and M. O. Scully, “The photoelectric effect without photons,” in Polarization, Matière et Rayonnement (Presses University de France, Paris, 1969).

## 3 thoughts on “Photoelectric Effect”

1. primson says:

Who do you think manufacture the best photoelectric sensors for industrial applications in the US?