Yes, the double-slit experiment can be performed with electrons over long distances. In fact, the double-slit experiment has been successfully conducted with various particles, including electrons.
The key requirement for the double-slit experiment is maintaining the coherence of the particle waves over the distance between the slits and the screen. In the case of electrons, their de Broglie wavelength is determined by their momentum, given by the equation λ = h / p, where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the electron.
Electrons can have relatively small de Broglie wavelengths, especially if they are accelerated to high energies. This allows for the observation of interference effects even over macroscopic distances. However, there are practical challenges associated with performing the experiment with electrons over long distances, such as maintaining the coherence of the electron waves and minimizing interactions with the environment.
To overcome these challenges, experimental setups often use specialized techniques. For example, to reduce interactions with the environment, the experiment can be conducted in vacuum conditions to minimize scattering and decoherence. Additionally, the double-slit apparatus can be designed to ensure the stability and control of the electron beams.
Various experiments have successfully demonstrated the wave-particle duality of electrons and observed interference patterns similar to those seen with light in the double-slit experiment. These experiments have played a crucial role in confirming the quantum nature of particles and the fundamental principles of quantum mechanics.