There are energy bands in a solid. Do we have really continuous energy variation in a band or do we have very closely spaced but still discrete energy levels?

A single atom has discrete energy levels. Let us now take N atoms and assume that it is possible to vary the inter-atomic distance. When the inter-atomic distance (distance between the two atoms) is large, the energy levels of total N atoms coincide with those of a single atom. Let us now reduce the inter-atomic distance. This causes an atom to exert an electric force on its neighbors. The closely packed atoms have energy levels overlapped and hence closely spaced energy levels are formed so that the system now obeys Pauli Exclusion Principle. These closely spaced energy levels are discrete and called as energy bands. We don’t have continuous energy variation in a band.


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