Answer to Question #49856 in Atomic and Nuclear Physics for Tahir Ahmad khan

Question

reasons that why the electrons cannot reside in energy gap or forbidden band gap?

Answer 1

From quantum mechanics we know that electrons in isolated atom cannot reside anywhere between allowed discrete
energy levels. This is the origin of energy gap.
Quantum theory shows that when two atomsare brought close enough together to interact, each of the allowed electron
energy levels within the atoms splits into two distinct but closely spaced
energy levels as the atoms combine to form the two-atom system. In a six-atom system, each allowed electronenergy level is split into a set of six separate but closely spaced energy
levels. Clearly then, as we pack moreand more atoms closely together each set of split energy levels contains more
and more levels spread over the same energy range allowed at that particular
radius from the nuclei. So, in a crystallinesolid, such as a metal or a diamond, where billions upon billions of atoms are
packed closely together, the energy levels within each set become so closely
spaced in energy that they form a practically continuous energy band.
The forbidden band gap corresponds to thegaps between electron energy levels within the isolated atoms.