Warped Passages - Lisa Randall [64]
You can think of Bohr’s atom with its fixed electron orbits as a multistory building in which you’re restricted to the even-numbered floors, the second, fourth, sixth, and so on. Since you could never set foot on the in-between floors, such as the third and the fifth, you would be eternally stuck on the even-numbered floor you were on. There would be no way to reach the ground floor and exit.
Bohr’s waves were an inspired assumption. He did not claim to know their meaning; he made his assumption simply to account for the stable electron orbits. Nevertheless, the quantitative nature of his proposal allowed it to be tested. In particular, Bohr’s hypothesis correctly predicted atomic spectral lines. Spectral lines give the frequency of light that an un-ionized atom—a neutral atom with all its electrons that carries zero net charge—emits or absorbs.† Physicists had noticed that spectra show a barcode-like pattern of stripes rather than a continuous distribution (i.e., with all frequencies of light contributing). But no one understood why. Nor did they know the reason for the precise values of the frequencies they saw.
With his quantization hypothesis, Bohr could explain why photons were emitted or absorbed only at the measured frequencies. Although the electrons’ orbits were stable for an isolated atom, they could change when a photon with the right frequency—and hence, according to Planck, the right energy—delivered or removed energy.
Using classical reasoning, Bohr calculated the energy of the electrons that obeyed his quantization assumption. From these energies he predicted the energies, and hence the frequencies, of the photons that the hydrogen atom, which contains a single electron, emitted or absorbed. Bohr’s predictions were correct, and these correct predictions made his quantization assumption highly plausible. And this was what convinced Einstein, among others, that Bohr must be right.
The quantized packets of light, which could be emitted or absorbed and could thereby change electron orbits, can be compared to lengths of rope placed by the windows of the multistory building in our earlier analogy. If each piece of rope is precisely the length required to go from your floor to any of the other even-numbered floors, and only the windows to even-numbered floors are open, the rope would provide the means to change floors—but only between the even-numbered ones. In the same way, spectral lines could take only certain values, the values of the differences in energy between electrons that occupied permissible orbits.
Even though Bohr offered no explanation for his quantization condition, he certainly appeared to be correct. Many spectral lines had been measured, and his assumption could be used to reproduce them. If such agreement was a coincidence it would have been miraculous. Ultimately, quantum mechanics justified his assumption.
Particles’ Commitment Phobia
Important as the quantization proposals were, the quantum mechanical connection between particles and waves began to gel only with the advances made by the French physicist Prince Louis de Broglie, the Austrian Erwin Schrödinger, and the German-born Max Born.
The first key step off the random walk of the old quantum theory onto the road of a real theory of quantum mechanics was de Broglie’s brilliant suggestion of turning Planck’s quantization hypothesis on its head. Whereas Planck had associated quanta with the waves of radiation, de Broglie—like Bohr—postulated that particles could also act like waves. De Broglie’s hypothesis meant that particles should exhibit wavelike properties and that those waves are determined by a particle’s momentum. (For low speeds, momentum is mass multiplied by speed. For all speeds, momentum tells how something responds to an applied force. Although at relativistic speeds, momentum is a more complicated function of mass and speed,