According to Kroning Penny model the energy spectrum of an electron is developed by alternate regions of allowed and forbidden energy of equal width.
a) True
b) False
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the answer to this question is false
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Answer:
The correct answer is option b
Explanation:
- The Kronig-Penney model is a solvable problem in quantum mechanics that can either be viewed as an approximation of an electron in a 1D crystal potential or a generalization of a potential-barrier problem to a 1D chain of potential barriers. The problem consists of a particle inside an array of equally spaced potential wells or potential barriers, all which have the same width and depth/height. This can be viewed as a simple model for a 1D monatomic crystal, which is characterized by electrons existing around positively charged nuclei, each equally spaced from its neighbor.
- Most significantly, solutions to the Kronig-Penney model manifest ‘band gaps’—a band of energies that electrons cannot assume, which are physically seen in real materials, most notably semiconductors.
- A conduction electron in a metal experiences constant (or zero) potential and is free to move inside the crystal but will not leave the metal because an infinite potential exists at the surface, according to the quantum free electron theory of metals. Electrical conductivity, specific heat, thermionic emission, and paramagnetism are all satisfactorily explained by this theory. Numerous other physical characteristics, such as the distinction between conductors, insulators, and semiconductors, the positive Hall coefficient of metals, and the lower conductivity of divalent metals compared to monovalent metals, are not adequately explained by this theory.
- The periodic potentials caused by the positive ions in a metal have been taken into consideration to solve the aforementioned issues. depicted in Fig. (a),
- An electron encounters various potentials as it passes through these ions. An electron's potential is zero and at its highest when sandwiched between two positive ions. The potential an electron encounters as it travels in a straight line through positive ions is depicted in Fig (b).
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