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UNIT 10 BAND THEORY OF SOLIDS Structure 10.1 Introduction Objectives 10.2 An Electron in a Periodic Potential Kronig-Penney Model Energy Bands and Motion of Electrons Classification of Solids in Metal, Insulator and Semiconductor 10.3 10.4 10.5 10.6 10.7 Energy Bands and Brillouin Zones Hall Effect Summary Terminal Questions Solutions and Answers 10.1 INTRODUCTION In Unit 9, you have studied the free electron theory of metals. One of the basic assumptions of this theory is that positively charged ions in a metal crystal do not influence the motion of free electrons. Obviously such an assumption over-simplifies the actual situation in crystalline solids including metals. Still, the theory gives good insight into wide range of metallic properties such as electrical conduction, heat capacity and thermal conductivity. Some important questions, however, remained unanswered. For example, free electron theory predicts that electrical conductivity is directly proportional to the number density of free electrons implying thereby that bivalent and trivalent metals should have larger electrical conductivities than those of monovalent metals. But this inference is not supported by experimental observations. Further, it also does not explain why some solids are conductors and some others are not. Most of such limitations of free electron theory were overcome by considering a more realistic model of solid. It was proposed that in a solid, electrons move under the influence of a periodi ...
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