De Broglie wavelength

The wavelength associated with a particle’s momentum, given by Planck’s constant divided by momentum. It relates particle motion to wave behavior in quantum mechanics.

De Broglie relation: The relation λ = h/p, connecting a particle’s wavelength λ to momentum p through Planck’s constant h. It gives the defining equation for the wavelength.
Electron diffraction: The scattering of electrons by a structure in a pattern governed by their wave behavior. Electron wavelengths make crystal diffraction measurable.
Louis de Broglie: French physicist who proposed in 1924 that particles have wave properties related to their momentum. He introduced the wavelength now bearing his name.
Classical mechanics: The theory describing motion through quantities such as position, velocity, force, and momentum. It omits matter-wave behavior when wavelengths are negligible at the scale studied.
Planck constant: The fundamental constant setting the scale of quantum effects, denoted h. Its value converts momentum into the associated wavelength.
Davisson–Germer experiment: A 1927 experiment in which electrons scattered from nickel produced a diffraction pattern. Its observed pattern confirmed the wavelength predicted for electrons.
Wave-particle duality: The principle that quantum objects exhibit both wave-like and particle-like properties. De Broglie extended this duality from light to matter.
Compton wavelength: A particle’s characteristic wavelength h/(mc), defined using its rest mass and the speed of light. Unlike the de Broglie wavelength, it depends on rest mass rather than the particle’s current momentum.
Momentum: A measure of motion equal to mass times velocity in classical mechanics and generalized in quantum mechanics. It is the quantity whose inverse determines the de Broglie wavelength.
Electron microscope: A microscope that uses electrons rather than visible light to form images. Short electron wavelengths permit finer resolution than visible-light microscopy.

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