We toyed with an intriguing possibility to explain why electrons exist in only certain orbits with certain energies within the atom. If matter particles, electrons in particular, were actually waves in some sense, then perhaps the special orbits in atoms were the ones for which a whole number of wavelengths fit exactly around the circumference of the orbit. Though we coyly wrote it off as an impossibility, in 1923 a young French nobleman actually took it seriously. His name was Louis de Broglie.
De Broglie didn’t have much of a reputation in the scientific community when he came up with his radical idea. In fact, he was still a graduate student, and he chose to write his doctoral thesis on the concept of something he termed “matter waves.” Besides the possibility that standing waves could explain stationary states of electrons in atoms, he was inspired by the dual wave-particle behavior of photons. Since light waves sometimes behaved like localized particles, wouldn’t it be nice if particles returned the favor, and sometimes behaved like waves?
LOUIS DE BROGLIE
Being an egalitarian lot, scientists don’t generally emphasize Louis de Broglie’s full honorific title: Louis-Victor-Pierre-Raymond, Seventh Duc de Broglie. In fact, he was both a French duke and a German prince. Louis de Broglie was born in 1892 to a noble family in Dieppe, France. He lived to the ripe old age of 94, so he was able to see many of the fruits of the quantum physics he helped start as a young man.
De Broglie originally intended to make the humanities his field of study, but shortly after finishing a history degree in 1910, his attraction to science and mathematics took over. His older brother was already an experimental physicist, and, fortunately for the development of quantum physics, de Broglie turned to physics right after the First World War.
In 1924, he submitted a 16-page doctoral thesis containing his radical ideas about massive particles having wavelike properties. His examiners weren’t quite sure whether this kid had made a stunning theoretical breakthrough or was just trying to bluff his way to a PhD with a bunch of baloney. In an admirable act of humility, they sent the thesis to Albert Einstein asking for his opinion. To his mounting credit, Einstein quickly replied that de Broglie’s insight was possibly the real deal.
Among many honors, de Broglie was awarded the Nobel Prize in physics in 1929, after his hypothesis about matter waves was experimentally verified. Interestingly, he did not support the mainstream interpretation of quantum mechanics in his later years. He often took Einstein’s side in objecting to a purely probabilistic view of quantum physics as it continued to develop. We’ll be revisiting this topic.
The third guiding factor for de Broglie was Einstein’s work on the theory of relativity, which among other things revealed that mass was actually a form of energy. De Broglie looked for a way to assign a wavelength to particles of matter, something that would be consistent with Einstein’s mass-energy relation (E = mc2) and the fact that a photon’s energy was proportional to the frequency of the radiation it embodied (E = hf). By doing so, he derived a very simple and elegant relation for the wavelength associated with any massive particle. This property is now named the de Broglie wavelength after its creator. If we assign the Greek symbol λ to the wavelength, then de Broglie’s relation is given by , where m is the particle’s mass and v is its velocity. Note that the denominator in this expression is just the momentum of the particle.
DEFINITION
The de Broglie wavelength characterizes the wavelike properties of any particle with mass, and it is given simply as Planck’s constant divided by the momentum of that particle.
The idea that massive particles could have wavelike properties showed promise, but it didn’t answer everything. De Broglie’s hypothesis fit perfectly with Bohr’s quantization of angular momentum in electron orbits. But what was actually doing the waving?
Imagining the electron wiggling up and down as it traveled didn’t really work. For one thing, it just added more acceleration of a charged particle to radiate energy away, and for another, the speed of these new waves could actually be faster than the speed of light, something Einstein had already shown was impossible. For these reasons and the lack of any direct evidence in support, few people took de Broglie seriously at first.
QUANTUM QUOTE
He [de Broglie] has lifted a corner of the great veil.
—Albert Einstein in a letter to de Broglie’s mentor, Paul Langevin, 1924
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