peefect.htm(Ó R. Egerton)

In the 1890's, it was discovered that metal surfaces in vacuum which are exposed to ultraviolet light emit electrons. This was convincing evidence that atoms contain electrons. In 1902, the German physicist Philipp Lenard started to investigate this photoemission phenomenon in detail, using an apparatus involving two electrodes in a vacuum tube, as shown schematically in Fig. 2.14. By adjusting the potentiometer setting so as to vary the voltage V applied to the "collector" electrode, the photocurrent A could be plotted against applied voltage, as in Fig. 2.15a.

For a given intensity I of the ultraviolet light, the photocurrent increased with increasing positive voltage. This is easily explainable in terms of the positive collector electrode attracting a larger fraction of emitted negatively-charged electrons. When the light intensity was increased, the photocurrent also increased, indicating that more photoelectrons were being produced. When the battery leads were reversed so that the applied bias V was negative, the photocurrent decreased and became zero if the magnitude of the negative bias exceeded a certain value Vs . This behaviour can be explained in terms of the negative collector repelling the photoelectrons, reducing the photocurrent or suppressing the photocurrent entirely (by stopping the electrons reaching the collector) when V reaches the stopping voltage Vs . At that point, even the most energetic photoelectrons (those released with a kinetic energy Kmax, assuming there is some spread in kinetic energy K) will exchange all of their kinetic energy for potential energy eVs by the time they reach the collector, in other words Kmax = Vs.

What cannot be explained on the basis of classical physics is the fact that the value of Vs is independent of the light intensity I . According to classical theory, larger I implies a stronger electric (and magnetic) field E in the incident electromagnetic wave. It is this electric field which is presumed responsible for attracting electrons out of the metal into the vacuum and larger E should result in electrons with higher kinetic energies, requiring a larger negative Vs to stop them reaching the collector.

Also at odds with classical theory is the fact that Vs (or Kmax) varies with frequency f of the incident light; in fact the experimental data lie on a straight line with intercept f0; see Fig. 2.15b. For a given light intensity, we would expect the electric field E to be independent of frequency or wavelength, on the basis of classical physics.

In one of his papers published in 1905, Einstein came up with an explanation for these discrepancies. In fact, his explanation of the photoelectric effect (not the more controversial theory of relativity) was cited as his greatest contribution to physics when he was awarded the Nobel Prize in 1922. Einstein had recognized an inconsistency between Planck's idea of quantization of oscillators (in the walls of a cavity) and the usual assumption that cavity radiation consists of continuous electromagnetic waves. Using ideas derived from thermodynamics, he showed that cavity radiation could be treated as a system of particles, which we now refer to as photons, each carrying a quantum of energy of magnitude hf .

Extending this idea to all cases of electromagnetic waves, the energy of the radiation is present in "bundles" ; see Fig.2.16b. In the photoelectric effect, each photon donates all of its energy hf to an electron in the metal. If this process occurs at the metal surface, the electron is released into the vacuum with a kinetic energy given by:

Kmax = hf - phi

where phi is the work function of the metal; it represents the minimum energy which must be supplied to release an electron from the metal. For convenience, this work function is normally measured in units of electronvolts (eV): 1 eV = 1.6 ´ 10^-19 J . Values range from 2.2 eV (for the alkali metal lithium) to 6.35 eV (for the noble metal platinum).

Einstein's concept explains the two puzzling features of the photoelectric effect. Increasing the light intensity increases the number of photons per second arriving at the metal electrode but does not change the energy of each photon, so the photoelectron energy Kmax and the stopping voltage Vs remain the same (Fig. 2.15a). However, increasing the light frequency will increase the photon energy, resulting in more energetic photoelectrons (Fig. 2.15b). Conversely, if the light frequency is decreased below the threshold value f0 , the photons will not have enough energy to overcome the work function; at the threshold frequency f0 photons would be released but with zero kinetic energy, so that

hf0 = phi

This last equation provides a means of measuring work functions of different materials.

The fact that some electrons are emitted with lower kinetic energies K is partly due to the fact that the conduction electrons in a metal have a spread of energies (they occur in an energy band rather than all having the same energy). The other reason is that, if the energy exchange takes place below the surface, the ejected electrons interact with surrounding atoms and lose some of their energy in escaping,.

The photoelectric effect has been utilized in devices called photocells, consisting of two electrodes in a sealed vacuum tube. By coating one electrode (the photocathode) with a alkali metal of low work function, a photocurrent could be generated even from visible light (photon energy roughly 2 eV to 4 eV) so the photocell was used for measuring light intensity or for converting the "optical" sound track of early movie film into an electrical current which could be fed to loudspeakers. Nowadays, solid-state devices (photodiodes) are used in such applications but a related vacuum-tube device, the photomultiplier tube (PMT), is still used in scientific applications (Fig. 14.20) because it provides high internal amplification without adding much electronic noise.

Generally speaking, the quantum picture of electromagnetic radiation (Fig. 2.16b) is needed to explain momentary interactions of light and matter, processes which usually occur on an atomic scale. On the other hand, the wave picture (Fig. 2.16a) remains successful in describing the propagation of light over long time intervals. Further evidence for the quantum nature of electromagnetic radiation comes from considering the generation and scattering of x-rays.