In the double-slit experiment, the wave behavior gradually diminishes and the particle behavior becomes more pronounced as the size of the particles increases. The transition from wave-like behavior to particle-like behavior is not determined by a specific size cutoff but rather by the relative scale of the particle's de Broglie wavelength to the size of the slits.
The de Broglie wavelength is given by λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. For larger particles, such as macroscopic objects or even molecules, their momentum is relatively large, resulting in a small de Broglie wavelength. As a result, the wave-like behavior is significantly diminished, and the particle behaves more classically, following a definite trajectory through one of the slits.
On the other hand, for particles with very small masses, such as electrons or even photons, their momentum is relatively small, resulting in a larger de Broglie wavelength. In this case, the wave-like behavior dominates, and interference patterns can be observed on the detection screen behind the double slits.
Therefore, there is no specific particle size at which the wave behavior disappears. The transition depends on the ratio of the particle's de Broglie wavelength to the size of the slits and the experimental setup.