Absolutely Small - Michael D. Fayer [42]
This is an unbelievably small number. The size of one atom is about 1 Å. The size of the nucleus of an atom is about 10-5 Å. Then the wavelength of a baseball is 0.0000000000000000001 of the size of one atomic nucleus. This wavelength is small beyond small. It is so small that it will never be manifested in any measurement. There can never be a diffraction grating with line spacing small enough to show diffraction for a wavelength that is a ten millionth of a trillionth of the size of an atomic nucleus. Because this wavelength is so small we never have to worry that a baseball will diffract from a baseball bat. It will always act like a classical particle. Objects that are large in the absolute sense have the property that the wavelengths associated with them are completely negligible compared to their size. Therefore, large particles only manifest their particle nature; they never manifest their wave nature. In contrast, particles that are small in the absolute sense have de Broglie wavelengths that are similar to their size. Such absolutely small particles will act like waves or act like particles depending on the situation. They are wave packets. In the manner that we have discussed, they are both waves and particles.
8
Quantum Racquetball and the Color of Fruit
IN THE PREVIOUS CHAPTERS, the fundamental concepts of quantum theory were introduced and explained. The examples given, however, looked only at the behavior of free particles. It was shown that electrons could behave as particles in the discussion of how a CRT works, but they behaved as waves in the description of electron diffraction from crystal surfaces. A free particle can have any energy. Its energy, which is kinetic, is determined by its mass and its velocity. As the velocity increases, the energy increases. A tiny increase in velocity produces a tiny increase in energy. A large increase in velocity produces a large increase in energy. The steps in energy can be any size; they are continuous. Bound electrons were discussed briefly in connection with the photoelectric effect. It was pointed out that if the energy of the incoming photon is insufficient to overcome the binding of electrons in the metal, no electrons will be ejected from the metal. Electrons bound to nuclei of atoms are responsible for the properties of atoms and molecules. It was also mentioned that Planck explained black body radiation, which will be discussed in detail later, by postulating that bound electron energies can only change in discreet steps. To understand the properties of the atomic and molecular matter that surrounds us in everyday life, it is necessary to treat bound electrons with quantum theory.
The essential feature of electrons bound to an atom or molecule is that their energy states are discreet. We say that the energies an electron can have are quantized, that is, an electron bound to an atom or molecule can only have certain energies. The energy goes in steps, and the steps are certain discreet sizes. The energy states are like a staircase. You can stand on one stair, or you can stand on the next higher stair. You cannot stand halfway between two stairs. These discreet or quantized energies are frequently called energy levels. Unlike a staircase, the energy levels are not generally equally spaced.
An important area of modern quantum theory research is the calculation of the electronic quantum states of molecules. This field is called quantum chemistry. Such calculations yield the quantized energies of electrons in molecules (energy levels), and they also calculate the structures of molecules. Molecular structure calculations give the distances between atoms and the positions of all atoms in a molecule within limits set by the uncertainty principle. Thus, quantum mechanical calculations are able to determine the size and shapes of