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Energy gap:
In solid-state physics, an energy gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes. Especially in condensed-matter physics, an energy gap is often known More abstractly as a spectral gap, a term which need not be specific to electrons or solids.
Band gap
A band gap is the distance between the valence band of electrons and the conduction band. Essentially, the band gap represents the minimum energy that is required to excite an electron up to a state in the conduction band where it can participate in conduction.[1] The lower energy level is the valence band, and thus if a gap exists between this level and the higher energy conduction band, energy must be input for electrons to become free. The size and existence of this band gap allows one to visualize the difference between conductors, semiconductors, and insulators
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