Final answer:
When electron wave vector k is far from the Brillouin zone boundary, electron energy approaches that of a free electron with energy primarily determined by its momentum since the crystal potential's influence is minimized.
Step-by-step explanation:
When k is far from the boundary of the Brillouin zone, the energy of an electron tends towards that of a free electron, described by the equation E ≅ h²k²/2me, where h is Planck's constant, k is the wave vector, and me is the electron mass. This occurs because the Brillouin zone describes the periodic potential that electrons experience in a crystal lattice. Near the zone boundaries, this potential significantly affects electron motion, leading to band gaps and dispersions different from free electrons. However, far from these zones, the crystal potential's influence is diminished, and electrons behave more like they would in free space, with their energy largely determined by their momentum in accordance with classical kinetic energy equations.