The Quantum Mystery (Kindle Single) by John Gribbin

Author:John Gribbin [Gribbin, John]
Language: eng
Format: epub
Published: 2016-01-21T00:00:00+00:00

FIVE

Waving With Electrons

Louis de Broglie made one of those inspired leaps that are both truly profound and yet so simple that it leaves other people wondering, “why didn’t I think of that?” Einstein’s explanation of the photoelectric effect in terms of light quanta saw those quanta as real particles, which carried energy, related to their wavelength, or frequency, by the equation E = hν. But real particles also have a property called momentum, which physicists denote by the letter p, since m is reserved for mass. In the course of developing his special theory of relativity, Einstein also came up with an equation for the momentum of a photon, which is simply p = E/c, where c is the speed of light. It was de Broglie who put the two equations together and said that in that case the momentum of a photon is related to its frequency by the equation p = hν/c. Or, since wavelength, denoted by the Greek letter lambda, l, is simply the speed of light divided by the frequency, for light quanta p = h/l. This curious equation relates a fundamentally particle property, momentum, to a fundamentally wave property, wavelength. Weird enough for photons. But de Broglie didn’t stop there. His inspired leap was to say that this equation must apply to any particle that has momentum, which means any particle. and to any wave which has wavelength, which means any wave. In particular, it must apply to electrons. Electrons should have a wavelength which could be measured by the same diffraction techniques used to study X-rays.

De Broglie presented his big idea in his Ph.D. thesis in 1924. His baffled Ph.D. supervisor, Paul Langevin, sent a copy to Einstein to ask what he thought of it. Einstein endorsed the idea with the comment, “I believe that it involves more than a mere analogy.” So de Broglie got his Ph.D., and the experimenters set out to test the idea.

Some experiments, in fact, had already been hinting at the wave-particle relationship, without anyone realizing it. Clinton Davisson was an American researcher who, in the early 1920s, had been looking at the way electrons bounce off a nickel surface. In 1926, he was on a visit to Britain, where he attended a lecture given by the German physicist Max Born. Born described de Broglie’s idea and its implications, then, to Davisson’s surprise, pointed out that the results of some of the scattering experiments carried out by Davisson and already published matched up with what would be expected if de Broglie was right. As soon as he was back in the USA, Davisson and his colleagues adapted their experiment to make a proper test of the electron wave theory.

The wavelength to be measured is predicted by turning de Broglie’s equation round to read l = h/p. Planck’s constant, h, is a very small number, so the predicted wavelength is unmeasurably tiny except for very small particles such as electrons, which have correspondingly small momenta. Davisson and his colleague Lester

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