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How did Louis de Broglie extend wave-particle duality to electrons?

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A horizontal gradient bar displays the visible light spectrum from violet to red, labeled with corresponding frequency in terahertz, wavelength in nanometers, and photon energy in electron volts. — light When white light is spread apart by a prism or a diffraction grating, the colours of the visible spectrum appear. The colours vary according to their wavelengths. Violet has the highest frequencies and shortest wavelengths, and red has the lowest frequencies and the longest wavelengths.

In 1924, French physicist Louis-Victor de Broglie proposed a unifying hypothesis that extended the concept of wave-particle duality from light to matter. While light had been shown to exhibit both wave and particle characteristics, de Broglie suggested that material particles, such as electrons, also possess wave properties.123

He hypothesized that the wavelength ( $λ$ ) of a particle is inversely proportional to its momentum ( $p$ ), expressed by the equation:
$λ = \frac{h}{p}$
where $h$ is the Planck constant.14

This wave nature of electrons was experimentally confirmed in 1927 by Clinton Davisson and Lester Germer, who observed the diffraction of electrons by a nickel crystal. These de Broglie waves are fundamental to quantum mechanics, explaining phenomena such as electron configurations in atoms and the ability of particles to penetrate barriers.123