01/07/2020

In Folha, Viana discusses the wave nature of matter.

Imagem: Sociedade Americana de Física

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

Early 20th-century physics discoveries suggested that each atom consists of a positively charged nucleus around which electrons orbit, like planets around a star. But this model is incompatible with the laws of electromagnetism: the electrons would have to emit energy and would quickly fall back into the nucleus.

In 1913, Niels Bohr postulated that electrons could only occupy certain orbits around the nucleus, instantly jumping from one to another when the atom absorbs or emits energy. The first explanation for this strange behavior would only be given ten years later by the young Frenchman Louis de Broglie , based on two fundamental discoveries by Albert Einstein.

The most famous equation in physics, E= ^mc² , published by Einstein in 1905, states that the mass m of a body is proportional to the amount E of energy it contains. The letter c represents the speed of light, approximately 300,000 km/s, which is an enormous number: even bodies with small mass contain colossal amounts of energy. This principle underlies nuclear energy and its peaceful and other applications.

In another work published in the "wonderful year" of 1905, in which he explained the electrical effect, Einstein introduced another fundamental equation: E=hv, where E represents the energy of a quantum of light (photon), v is the respective frequency, and h is called Planck's constant. The combination of the two formulas suggests that a quantum of light with frequency v has mass m such that mc²=hv.

De Broglie had the remarkable idea of reversing the reasoning. "After long solitary reflection, I suddenly had the idea in 1923 that the discovery made by Einstein in 1905 should be generalized to all material particles." Just as light waves have corpuscular properties, such as mass, he proposed that electrons have wave properties, such as frequency.

De Broglie was a lover of chamber music and knew well that a musical string (of a guitar, for example) can only produce certain notes, such that the length of the string is an integer multiple of the wavelength.

De Broglie proposed that, analogously, the wave-like behavior of the electron explains why only certain electron orbits around the nucleus are possible: the orbits postulated by Bohr would be precisely those in which the wave associated with the electron performs an integer number of vibrations.

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