Absolutely Small - Michael D. Fayer [38]
FIGURE 7.2. Incoming photon wave packets are diffracted from a grating. The different colors reflect off of the grooves. For a particular color, there is a direction in which the waves corresponding to that color constructively interfere. They add to make a large amplitude wave, so the color looks very bright in that particular direction.
Electrons Act Like Bullets in a Cathode Ray Tube
Diffraction of light from a grating brings out the wave property of the photon wave packets, while the photoelectric effect demonstrates the more localized particle like properties of a photon wave packet. In the discussion of the de Broglie wavelength, which relates the momentum to a wavelength through the relation p = h/λ, it was mentioned that the descriptions of electrons and other types of “particles” are the same as the description of photons. Both photons and electrons are described in terms of probability amplitude waves. Both are more or less localized wave packets (see Figure 6.7). For an electron that is a free particle (no forces are acting on it) the wave packet is a superposition of the free particle momentum eigenstates. The uncertainty in the electron’s position, Δx, is determined by the uncertainty (spread) in the momentum, Δp, through the Heisenberg’s uncertainty relationship, ΔxΔp ≥ h/4π. The equality sign holds for Gaussian wave packets, which are the shapes shown in Figure 6.7.
To illustrate both the particle nature and wave nature of electrons, two examples are discussed: how a cathode ray tube (CRT) works and low energy electron diffraction from a crystal surface. Cathode ray tubes used to be ubiquitous. They are the devices that produce the pictures in the original televisions and computer monitors. CRTs are the large, boxy TVs and monitors that are rapidly being replaced by other devices, such as liquid crystal displays (LCDs). (There are actually several technologies used to make large-screen thin TVs, but thin computer monitors are all LCDs.)
Figure 7.3 is a schematic diagram of a CRT. Inside the CRT is a vacuum in which electrons can move without colliding with air molecules. The process that produces the picture begins with the filament, a piece of wire (left side of figure). An electrical current is passed through the filament, which causes it to get very hot like the filament in a conventional light bulb, the element in an electric stove, or the element in an electric space heater. The heat from the filament heats the cathode until it is also very hot. The cathode is a piece of metal that is connected to a negative voltage, like the negative end of a battery, but at a much higher voltage. The cathode becomes so hot that electrons boil off. Heat is a form of energy. The electrons are held in the metal by a binding energy that depends on the type of metal. When the metal is hot enough, the thermal energy can overcome the electron binding energy and some electrons will leave the metal. In the photoelectric effect, a photon provided the energy to overcome the electron binding to the metal. In a CRT, heat provides the energy to eject the electrons from the metal. The electrons that leave are replaced by the connection to the negative power supply that puts