Warped Passages - Lisa Randall [63]
In the summer of 2002 I attended the annual string theory conference, which happened to be held that year at the Cavendish Laboratory in Cambridge. Many important pioneers of quantum mechanics, including two of its heads, Rutherford and Thomson, did much of their important research there. The hallways are decorated with reminiscences of the exciting early years, and I learned some amusing facts while wandering the hallways.
For example, James Chadwick, the discoverer of the neutron, had studied physics only because he was too shy to point out that he had mistakenly waited in the wrong line when matriculating. And J.J. Thomson was so young when he became head of the lab (he was twenty-eight) that a congratulation read, “Forgive me if I have done wrong in not writing to wish you happiness and success as a professor. The news of your election was too great a surprise to permit me to do so.” (Physicists aren’t always the most gracious.)
Yet despite the coherent picture of the atom that had developed by the early twentieth century at the Cavendish and elsewhere, the behavior of its components was about to wreak havoc with physicists’ most fundamental beliefs. Rutherford’s experiments had suggested an atom consisting of electrons that traveled in orbits around a central atomic nucleus. This picture, simple as it was, had an unfortunate drawback: it had to be wrong. Classical electromagnetic theory predicted that when electrons orbited in a circle, they would radiate energy through photon emission (or, classically speaking, electromagnetic wave emission). The photons would thereby remove energy and leave behind a less energetic electron, which would orbit in ever smaller circles, spiraling in towards the center. In fact, classical electromagnetic theory predicted that atoms could not be stable, and would collapse in less than a nanosecond. The atom’s stable electron orbits were a complete mystery. Why didn’t electrons lose energy and spiral down into the atomic nucleus?
A radical departure from classical reasoning was required to explain the atom’s electron orbits. Pursuing this logic to its inevitable conclusion exposed chinks in classical physics that could be filled only by the development of quantum mechanics. Niels Bohr made just such a revolutionary proposal when he extended Planck’s notion of quantization to electrons. This, too, was an essential component of the old quantum theory.
Electron Quantization
Bohr decided that electrons couldn’t move in just any old orbit: an electron’s orbit had to have a radius that fit a formula he proposed. He found these orbits by making a lucky and ingenious guess. He decided that electrons must act as if they were waves, which meant that they oscillated up and down as they circulated about the nucleus.
In general, a wave with a particular wavelength oscillates up and down once over a fixed distance; that distance is the wavelength. A wave that goes around a circle also has an associated wavelength. In this case the wavelength sets the extent of the arc over which the wave will go up and down once as it winds around the nucleus.
An electron that orbits in a fixed radius cannot have any wavelength. It can only have a wavelength that would permit the wave to go up and down a fixed number of times. That implied a rule for determining the allowed wavelengths: the wave has to oscillate an integer* number of times when going around the circle that defined the electron’s orbit (see Figure 42).
Figure 42. Possible wave patterns for an electron according to the Bohr quantization.
Although Bohr’s proposal was radical and its meaning obscure, his guess did the trick: if true, it would guarantee stable electron orbits. Only particular electron orbits would be allowed. Intermediate