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When the spacing  between adjacent atoms is large, each atom has sharply defined energy levels which are denoted by  etc. As the atoms are far apart their orbitals do not overlap. In particular if each atom is in its ground state, the electrons in each atom occupy identical quantum states. As the distance starts decreasing, the orbitals overlap. The electrons of different atoms cannot remain in the same state because of Pauli Exclusion Principle. Pauli principle states that a particular state can at most accommodate two electrons of opposite spins. Thus when  atoms are brought together, the levels must split to accommodate electrons in different states. Though they appear continuous, a band is actually a very large number of closely spaced discrete levels. |
