The largest particle that can pass through a double-slit experiment and still exhibit wave-like behavior is not a fixed size, but rather depends on the specific experimental setup and the characteristics of the particles involved.
In a typical double-slit experiment, a beam of particles, such as electrons or photons, is directed toward two slits. Beyond the slits, a screen or detector is placed to capture the pattern produced by the particles after passing through the slits.
The key condition for observing wave-like behavior, such as interference patterns, is that the de Broglie wavelength of the particle should be comparable to the slit separation. The de Broglie wavelength is calculated using the particle's momentum and mass, according to the de Broglie equation: λ = h / p, where λ is the wavelength, h is the Planck constant, and p is the momentum of the particle.
For macroscopic objects, such as everyday objects like baseballs or people, their large mass and momentum result in extremely small de Broglie wavelengths, making any wave-like behavior negligible and essentially impossible to observe in a double-slit experiment.
However, for microscopic particles like electrons or even larger particles, such as small molecules, the de Broglie wavelengths can be significant and comparable to the size of the slit separation. This allows for wave-like interference patterns to emerge.
The specific size or mass limit for observing wave-like behavior in a double-slit experiment is not precisely defined since it depends on various factors, including the experimental setup, the properties of the particles involved, and the desired level of interference pattern visibility. Generally, the larger the mass of the particle, the smaller its associated de Broglie wavelength, and the less pronounced the wave-like behavior.
In summary, the largest particles that can exhibit wave-like behavior in a double-slit experiment are typically microscopic particles, such as electrons or small molecules, with de Broglie wavelengths comparable to the slit separation. Macroscopic objects, due to their large mass and negligible de Broglie wavelengths, do not exhibit noticeable wave-like behavior in such experiments.