What underlying principle explains why electrons exhibit diffraction patterns when passed through a double-slit apparatus?

Electrons act like waves because they have a wavelength given by de Broglie's relation λ = h/p, where h is Planck’s constant and p is the electron’s momentum. When a beam of electrons hits a barrier with two narrow openings, each opening acts as a new source of a wavefront. These two wavefronts spread out and overlap, and where they overlap constructively or destructively, bright or dark bands appear – this is interference. The resulting pattern of alternating bright and dark fringes is the diffraction pattern, showing that the electron’s wavefunction interferes just as a water wave does. A simple example is a silver atom beam striking a double‑slit screen and producing a series of bright lines on a detector screen, exactly like light diffracting through two slits.