The answer explains quantum theory of free electrons in metals, the effect of periodic potential on electron energy levels, and the band theory of solids.
Quantum Theory of Free Electrons in a Metal: In quantum theory, electrons in metals are described by wave functions. When confined to a line of length L, the wave function and energy values for electrons can be obtained by solving the Schrödinger equation for the given potential barriers.
Effect of Periodic Potential on Energy of Electrons: The periodic potential in crystals affects the energy levels of electrons, leading to the formation of energy bands separated by band gaps. The Kronig-Penny model helps explain the origin of band gaps in crystals, distinguishing between conductors, semiconductors, and insulators based on their electron energy states.
Band Theory of Solids: The energy levels of electrons in crystals are determined by solving Schrödinger's equation for a periodic potential. In metals, the valence electrons exhibit molecular orbitals that span the entire crystal lattice, contributing to the unique electronic properties of metals.
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