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In terms of band theory , what is the difference between a conductor and an insulator ?

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`to` In case of metals (conductors) the atomic orbitals which are close in energy to each other as to form a band called valency band . If this band is partially filled (or ) it overlaps with a higher energy unoccupied band called conduction band . Then electrons can flow easily under an applied electric field and the metal shows conductivity .
`to` In case of insulators the gap between filled valence band and the next higher un occupied band is large , electrons cannot jump to it and such a substance has very small conductivity .
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