No, the double-slit experiment does not reject the hypothesis of de Broglie. In fact, the double-slit experiment is one of the key experiments that supports the wave-particle duality concept proposed by de Broglie.
De Broglie's hypothesis states that particles, such as electrons or other elementary particles, exhibit wave-like properties. According to de Broglie, just like light can behave both as a wave and a particle (photon), particles also possess wave-like characteristics. The wavelength associated with a particle is inversely proportional to its momentum, according to the de Broglie equation: λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.
The double-slit experiment demonstrates the wave-like behavior of particles. When a beam of particles, such as electrons, is directed towards two slits, an interference pattern is observed on the screen behind the slits. This interference pattern is characteristic of waves interfering with each other. It indicates that the particles, despite being individual entities, are exhibiting wave-like behavior.
This experiment supports de Broglie's hypothesis by showing that particles can undergo interference, which is a distinctly wave-like phenomenon. The interference pattern arises due to the superposition of the particle's wavefunction passing through the two slits and interfering with itself. This behavior is consistent with the wave nature of particles as described by de Broglie.
Therefore, the double-slit experiment actually provides evidence in favor of de Broglie's hypothesis and the wave-particle duality of particles. It demonstrates that particles can exhibit wave-like behavior, as predicted by de Broglie's concept.