Bohr’s hypothesis was a bold new idea, yet there was still one enormous stumbling block: What are the stationary states of an atom? Everything in Bohr’s model hinges on the existence of these stationary states, of there being only certain electron orbits that are allowed. But nothing in classical physics provides any basis for such orbits. And Bohr’s model describes only the consequences of having stationary states, not how to find them. If such states really exist, we will have to go beyond classical physics to find them.
To address this problem, Bohr did an explicit analysis of the hydrogen atom. The hydrogen atom, with only a single electron, was known to be the simplest atom. Furthermore, as we discussed in Chapter 37, Balmer had discovered a fairly simple formula that characterized the wavelengths in the hydrogen emission spectrum. Anyone with a successful model of an atom was going to have to predict, from theory, Balmer’s formula for the hydrogen atom.
Bohr’s paper followed a rather circuitous line of reasoning. That is not surprising because he had little to go on at the time. But our goal is a clear explanation of the ideas, not a historical study of Bohr’s methods, so we are going to follow a different analysis using de Broglie’s matter waves. De Broglie did not propose matter waves until 1924, 11 years after Bohr’s paper, but with the clarity of hindsight we can see that treating the electron as a wave provides a more straightforward analysis of the hydrogen atom. Although our route will be different from Bohr’s, we will arrive at the same point, and, in addition, we will be in a much better position to understand the work that came after Bohr.
NOTE Bohr’s analysis of the hydrogen atom is sometimes called the Bohr atom. It’s important not to confuse this analysis, which applies only to hydrogen, with the more general postulates of the Bohr model of the atom. Those postulates, which we looked at in Section 38.5, apply to any atom. To make the distinction clear, we’ll call Bohr’s analysis of hydrogen the Bohr hydrogen atom.