No, all particles do not have the same wavelength in the double-slit experiment. The wavelength of a particle is determined by its momentum and is given by the de Broglie wavelength, λ = h/p, where h is the Planck constant and p is the momentum of the particle.
In the double-slit experiment, a beam of particles, such as electrons or photons, is directed towards a barrier with two narrow slits. The particles can pass through the slits and then interact with a screen placed behind the barrier. As the particles pass through the slits, they diffract and interfere with each other, creating an interference pattern on the screen.
The interference pattern arises because the particles exhibit wave-like behavior. The wave nature of particles is described by their de Broglie wavelength. However, the de Broglie wavelength is determined by the momentum of the particles, and since different particles can have different momenta, their wavelengths can vary.
For example, in the case of electrons, which are commonly used in the double-slit experiment, their wavelengths are typically in the nanometer to sub-nanometer range. Photons, which are particles of light, have wavelengths that can span a wide range from radio waves to gamma rays, depending on their energy.
Therefore, in the double-slit experiment, different particles with different momenta and energies will have different wavelengths associated with them. This can lead to variations in the observed interference pattern on the screen, depending on the distribution of particle energies and momenta in the beam.