De Broglie's matter wave theory, also known as wave-particle duality, is a fundamental concept in quantum mechanics that suggests particles, such as electrons, exhibit both particle-like and wave-like properties. The theory proposes that every particle with momentum has a corresponding wavelength associated with it, known as the de Broglie wavelength.
The de Broglie wavelength (λ) of a particle is given by the equation λ = h / p, where h is the Planck constant and p is the momentum of the particle. This equation implies that even macroscopic objects, in theory, have associated wavelengths. However, the de Broglie wavelength becomes extremely small for macroscopic objects due to their large momentum, making the wave-like behavior effectively negligible at the macroscopic scale.
In practice, the wave-like behavior associated with de Broglie's theory becomes prominent and observable in experiments involving particles with very small mass, such as electrons, protons, and other subatomic particles. These particles exhibit interference and diffraction patterns similar to classical waves when passing through narrow slits or encountering obstacles. This behavior has been experimentally verified in various experiments, including the famous double-slit experiment.
For macroscopic objects, the wave-like behavior predicted by de Broglie's theory becomes effectively undetectable due to the extremely small de Broglie wavelengths involved. Therefore, in everyday life, classical physics is sufficient to describe the behavior of macroscopic objects, and quantum mechanical effects are typically not observable.
In summary, while de Broglie's matter wave theory can be applied to particles with very small mass, its wave-like properties become practically negligible for macroscopic objects due to their large momentum and associated extremely small de Broglie wavelengths.