More Precisely 4-1

MORE PRECISELY 4-1 The Photoelectric Effort

Einstein developed his insight into the nature of radiation partly as a means of explaining a puzzling experimental result known as the photoelectric effect. This effect can be demonstrated by shining a beam of light on a metal surface (as shown in the accompanying figure). When high-frequency ultraviolet light is used, bursts of electrons are dislodged from the surface by the beam, much like when one billiard ball hits another, knocking it off the table. Curiously, the speed with which the particles are ejected from the metal is found to depend only on the color of the light, not on its intensity. For lower-frequency light—blue, say—an electron detector still records bursts of electrons, but now their speeds, and hence their energies, are less. For even lower frequencies—red or infrared light—no electrons are kicked out of the metal surface at all.

These results were very difficult to reconcile with a wave model of light. Einstein realized that the only way to explain the presence of an abrupt cutoff at the detector—that is, that the detector registered nothing when the frequency of the incoming radiation dropped below a certain level—and the increase in electron speed with light frequency was to envision radiation as traveling as "bullets," or particles, or photons. To account for the experimental findings, the energy of any photon had to be proportional to the frequency of the radiation:

If we suppose that some minimum amount of energy is needed just to "unglue" the electrons from the metal, then we can see why no electrons are emitted below some critical frequency—red photons just don't carry enough energy. Above the critical frequency, photons have enough energy to dislodge the electrons; moreover, any energy they possess above the necessary minimum is imparted to the electrons as kinetic energy, the energy of motion.

Thus, as the frequency of the radiation increases, so too does the photon energy, and hence the speed of the electrons that they liberate from the metal.

The constant of proportionality in the foregoing relation is now known as Planck's constant, in honor of the German physicist Max Planck, who first determined its numerical value. It is always denoted by the symbol h. The equation relating photon energy Eto radiation frequency f is thus

As noted in Chapter 3, the SI unit of energy is is the joule (J) (More Precisely 3-2). The value of Planck's constant is a very small number—6.63 10^-34 joule seconds (J·s). Consequently, the energy of a single photon is tiny—even a very-high-frequency gamma ray (the most energetic type of electromagnetic radiation) with a frequency of 10²² Hz has an energy of only 7 10^-12 joule—about the same energy as is carried by a flying gnat. Nevertheless, this energy is more than enough to damage a living cell. The basic reason that gamma rays are so much more dangerous to life than, say, visible light, is that each gamma-ray photon carries billions of times more energy than a photon of visible radiation.

The realization and acceptance of the fact that light can behave both as a wave and as a particle is another example of the scientific method at work. Despite the enormous success of the wave theory of radiation in the nineteenth century, the experimental evidence led scientists to the inevitable conclusion that the theory was incomplete—it had to be modified to allow for the fact that light sometimes exhibits particle characteristics. In addition to bringing about the birth of a whole new branch of physics—the field of quantum mechanics—this new theory radically changed the way physicists view light and all other forms of radiation.