The mere existence of the photoelectric effect is not, as is sometimes assumed, a difficulty for classical physics. You learned in Chapter 22 that electrons are the charge carriers in a metal. The electrons move freely but are bound inside the metal and do not spontaneously spill out of an electrode at room temperature. But a piece of metal heated to a sufficiently high temperature does emit electrons in a process called thermal emission. The electron gun in an older television or computer display terminal starts with the thermal emission of electrons from a hot tungsten filament.

A useful analogy, shown in FIGURE 38.4, is the water in a swimming pool. Water molecules do not spontaneously leap out of the pool if the water is calm. To remove a water molecule, you must do work on it to lift it upward, against the force of gravity. A minimum energy is needed to extract a water molecule, namely the energy needed to lift a molecule that is right at the surface. Removing a water molecule that is deeper requires more than the minimum energy. People playing in the pool add energy to the water, causing waves. If sufficient energy is added, a few water molecules will gain enough energy to splash over the edge and leave the pool.

FIGURE 38.4 A swimming pool analogy of electrons in a metal.

Similarly, a minimum energy is needed to free an electron from a metal. To extract an electron, you would need to exert a force on it and pull it (i.e., do work on it) until its speed is large enough to escape. The minimum energy $E_0$ needed to free an electron is called the work function of the metal. Some electrons, like the deeper water molecules, may require more energy than $E_0$ to escape, but all will require at least $E_0$. Different metals have different work functions; TABLE 38.1 provides a short list. Notice that work functions are given in electron volts.

Heating a metal, like splashing in the pool, increases the thermal energy of the electrons. At a sufficiently high temperature, the kinetic energy of a small percentage of the electrons may exceed the work function. These electrons can “make it out of the pool” and leave the metal. In practice, there are only a few elements, such as tungsten, for which thermal emission can become significant before the metal melts!

Suppose we could raise the temperature of only the electrons, not the crystal lattice. One possible way to do this is to shine a light wave on the surface. Because electromagnetic waves are absorbed by the conduction electrons, not by the positive ions, the light wave heats only the electrons. Eventually the electrons’ energy is transferred to the crystal lattice, via collisions, but if the light is sufficiently intense, the electron temperature may be significantly higher than the temperature of the metal. In 1900, it was plausible to think that an intense light source might be able to cause the thermal emission of electrons without melting the metal.