Absolutely Small - Michael D. Fayer [41]
FIGURE 7.5. The lattice from Figure 7.4, with examples of different rows of atoms shown by the lines. For each line passing through the centers of atoms in a row, it is possible to draw more lines that are parallel to the initial line and that also pass through the centers of atoms. The spacings between these distinct parallel rows are different. Each set of rows causes diffraction in a different direction.
Because there are many different atom-to-atom spacings with the “grooves” running in different directions, the electrons’ waves will be diffracted in many different directions. Figure 7.6 is an example of low-energy electron diffraction from a crystal surface. The black circle in the center is a piece of metal called a beam stop. It is supported by another piece of metal that appears as the vertical bar below the beam stop in the picture. The beam stop prevents the portion of the electron beam that is reflected from the crystal from hitting the detector. The brighter and dimmer white spots are produced by the diffracted electrons hitting the detector. From the location of the spots, the spacing and arrangement of the atoms can be determined. Electron diffraction from crystal surfaces is an important tool in the science of understanding the nature of surfaces. The electron diffraction pattern demonstrates conclusively that electrons can behave as waves, just like photons.
FIGURE 7.6. Experimental data showing diffraction of electrons from the surface of a crystal. The various light spots are the electron diffraction spots. There are many spots because the diffraction occurs from the many different parallel rows of atoms (see Figure 7.5).
ELECTRONS AND PHOTONS ARE PARTICLES AND WAVES, BUT BASEBALLS ONLY PARTICLES
Electrons act as particles in a CRT just as photons act as particles in the photoelectric effect. Electrons act as waves in low-energy electron diffraction just as photons act as waves when they diffract from a diffraction grating. In reality, photons, electrons, and all particles are actually wave packets that are more or less localized. Wave packets can display their wavelike properties or their particlelike properties depending on the circumstances.
If photons and electrons can show both wavelike and particlelike properties, why don’t baseballs? To see the reason that baseballs act like particles in the classical mechanics sense, we need to look at the wavelengths associated with particles versus their size.
First consider an electron in an atom such as hydrogen. We are going to talk about the quantum description of the hydrogen atom and other atoms in Chapters 10 and 11, but for now, we will only use a very simple qualitative discussion of the wavelike characteristics of the hydrogen atom. The de Broglie relation tells us that the wavelength λ = h/p. The momentum is p = mV, the mass times the velocity. The mass of an electron is me = 9.1×10-31 kg. In an atom, the typical velocity of an electron is V = 5.0×106 m/s. Then the de Broglie wavelength is
Note that 1.5 Å is approximately the size of an atom. Therefore, the wavelength of an electron in an atom is about the size of the atom. The wave properties of electrons will be very important when electrons are in systems that are very small like atoms.
What about a baseball? According to the rules of Major League Baseball, a baseball must weigh between 142