Modern Physics

Electrons like waves

Louis Victor Pierre Raymond (1892-1987)

Einstein’s explanation for the photoelectric effect was accepted by the scientific community after his Nobel Prize in 1921: the Compton effect had undisputed experimental support. The set of mathematical works based on Planck’s quantum hypothesis produced considerable results, such as precise calculations of constants that before could only be determined experimentally (such as Avogadro’s number). The increasing improvement of the equipment confirmed the accuracy of the calculated values. Thus, the debate over the nature of light has never been more heated.

In the year 1924, a French prince surprised everyone. Louis De Broglie presented his thesis to the community. De Broglie suggested that the dualism that held for radiation should also hold for particles. Imagining that somehow wave-particle dualism was inherent in quantum phenomena, he proposed that there would be a symmetry between the behavior of electrons and photons.

Thus, in a manner analogous to the corpuscular behavior manifested by light, de Broglie suggested that electrons should exhibit wavelike behavior. From a mathematical point of view, the solution can be shown relatively simply. It had already been established, for the photon, that the linear momentum was:

Since, for particles with mass, the linear momentum is given by the product:


The combination of the two suggests that, according to de Broglie, an electron, of mass m and endowed with velocity v , must behave like a wave, whose wavelength would be:

Called the de Broglie wavelength .

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