Absolutely Small - Michael D. Fayer [140]
Electrons are negatively charged. When a battery or other electrical source is connected to a piece of metal, for example a piece of copper wire, the electrons will be drawn to the positive battery electrode and move away from the negative battery electrode. The electrons are accelerated toward the positive side of the battery, which increases their kinetic energy. However, the electrons are not the only types of wave packets moving about in a metallic crystal. The mechanical vibrations of atoms in a crystal lattice have quantized energy levels. As with the electron bands in a macroscopic piece of metal, because there are so many atoms, there are a vast number of quantized vibrational levels that form bands of mechanical energy levels. The quantized delocalized mechanical motions of the coupled atoms in a lattice are called phonons. These delocalized phonon waves combine to form phonon wave packets. These phonon wave packets propagate through the lattice.
Electron wave packets and phonon wave packets collide. The collision is called an electron-phonon scattering event, illustrated in Figure 19.7. Some of the extra kinetic energy that the electron picked up because of its acceleration by the electric field is transferred to the phonon. The electron has less energy and the phonon has more energy after the scattering event. Many such electron-phonon scattering events cause the bath of phonons to have increased energy. Mechanical energy is heat. Temperature is a measure of the amount of kinetic energy in a substance. So the electron-phonon scattering events slow the electrons, which is what we call electrical resistance. The increase in phonon energy increases the temperature of the metal; it gets hot. The heating of a piece of wire as electricity (electrons) flows through it is caused by the collisions of electron and phonon wave packets. The scattering of these two types of wave packets is an intrinsically quantum mechanical phenomenon. The more electricity (current) that flows through the metal, the more collisions occur, and the hotter the metal gets. This is what happens when you turn up an electric stove. You are increasing the current (number of electrons flowing), and therefore, you are increasing the number of electron-phonon scattering events. Increasing the number of electron-phonon scattering events increases the energy transformed into heat, which causes the temperature to rise. When the metal stove element gets hot enough, it glows read because the black body emission has moved into the visible part of the spectrum. The net result is that turning on an electric stove or electric space heater, and seeing the heating element emit red light, involves a number of quantum phenomena. So every time you see a red hot stove element, rather than it being a complete mystery like the moon to a toddler, think quantized electron states, electron wave packets, phonon wave packets, electron-phonon scattering generating heat, and finally black body radiation. Every day observations are filled with quantum phenomena.
ABSOLUTELY SMALL
All of the quantum physical phenomena that surround us come ultimately from the fact that size is absolute, and absolutely small particles just don’t behave the way classical objects, that is, absolutely big objects, behave. Baseballs are classical particles. Sound waves are classical waves. Baseballs and sound waves are big. In classical mechanics, the theory of big things, we have waves and particles. We discussed that light comes in discreet packets called photons. The description of photons and electrons as wave packets is profoundly different from anything in classical mechanics. Absolutely small particles, such as photons and electrons, are neither waves nor particles, as we saw in Chapters 4 through 7.