Absolutely Small: How Quantum Theory Explains Our Everyday World

By Michael D. Fayer | Go to book overview

9
The Hydrogen Atom:
The History

IN CHAPTER 8, we discussed the particle in a box problem. We imagined an electron confined to a very small one-dimensional box, as shown in Figure 8.1. The particle in a box is a useful problem because the math is simple enough to find the quantized energy levels without great difficulty. A formula was obtained that showed that the energy states of the particle in a box come in discreet steps that depend on a quantum number n, where n is an integer that starts at 1 and can take on any integer value. However, it was pointed out that this is a very artificial example of quantum confinement. In nature, there are no truly one-dimensional systems. Furthermore, the walls of the box are infinitely high and completely impenetrable. This is also physically unrealistic. As discussed in connection with the photoelectric effect in Chapter 4, if a photon has sufficient energy to overcome the binding energy of electrons to the atoms in a piece of metal, the interaction of the photon with an initially bound electron can eject the electron from the metal (see Figure 4.3).

However, for a number of reasons it is very useful to examine the particle in a box. First, we found that the energy levels are quan-

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