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Note for ENGINEERING PHYSICS - EP By nishant yadav

  • ENGINEERING PHYSICS - EP
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  • Visvesvaraya Technological University Regional Center - VTU
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$ ' LECTURE NOTES ON ENGINEERING PHYSICS Revised Edition 2014 As per latest VTU syllubus Dr. J. Balasubramanyam Formerly, Professor and Head, Department of Physics, KSIT, Bangalore-61 Presently, BASE Educational Services Private Ltd, Bangalore Prof. K. S. Mahesh Lohith Marata Mandal College of Engineering, Belgaum Sujith Thomas Formerly, Assistant Professor, Department of Physics, BNMIT, Bangalore Presently,Silicon Labs, Bangalore & %

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Contents I Module 1: Modern Physics and Quantum Mechanics 3 1 Modern Physics 5 1.1 Introduction to Blackbody radiation spectrum . . . . . . . . . . . . . . . . 5 1.2 Spectrum of blackbody radiation . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Wein’s distribution law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Rayleigh-Jeans law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Planck’s Radiation Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Reduction of Planck’s law to Wein’s law and Rayleigh-Jeans law . . . . . . 8 1.7 Photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.8 Einstein’s explanation of photoelectric effect . . . . . . . . . . . . . . . . . 9 1.9 Compton Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.10 De-Broglie’s hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.11 Expression for De-Broglie wavelength (from analogy) . . . . . . . . . . . 11 1.12 Experimental verification of De-Broglie’s hypothesis (Davisson and Germer experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.13 Phase velocity and Group velocity . . . . . . . . . . . . . . . . . . . . . . 15 1.14 Expression for group velocity . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.15 Relation between Group velocity and phase velocity . . . . . . . . . . . . . 17 1.16 Relation between group velocity and particle velocity . . . . . . . . . . . . 18 1.17 Expression for de-Broglie wavelength(From Group velocity) . . . . . . . . 19 1.18 Properties of Matter waves . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Multiple Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Descriptive Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Quantum Mechanics 27 2 iii

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2.1 Heisenberg’s uncertainty Principle and its Physical significance . . . . . . . 27 2.2 Application of Uncertainty Principle . . . . . . . . . . . . . . . . . . . . . 28 2.3 Time independent Schrodinger wave equation . . . . . . . . . . . . . . . . 28 2.4 Interpretation of wave function and its properties . . . . . . . . . . . . . . 30 2.5 Motion of an electron in an one dimensional potential well of infinite height (Particle in a box) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Energy eigenvalues of a Free particle . . . . . . . . . . . . . . . . . . . . . 35 Multiple Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Descriptive Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6 II 3 Module 2:Electrical properties of materials 41 Electrical Conductivity in Metals and Semiconductors 43 3.1 Classical free electron theory of metals . . . . . . . . . . . . . . . . . . . . 43 3.2 The Drift Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 Relaxation Time, Mean collision time and Mean free path . . . . . . . . . . 44 3.4 Ohms Law : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.5 Expression for electrical conductivity . . . . . . . . . . . . . . . . . . . . 45 3.6 Effect of temperature and impurity on electrical resistivity of metals. . . . . 48 3.7 Failure of classical free electron theory . . . . . . . . . . . . . . . . . . . . 50 3.8 Quantum free electron theory of metal . . . . . . . . . . . . . . . . . . . . 51 3.9 Fermi-Dirac Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.10 The dependence of Fermi factor on Energy and Temperature . . . . . . . . 53 3.11 Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.12 The Fermi-Dirac Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.13 Expression for electrical conductivity based on quantum theory . . . . . . . 58 3.14 Merits of Quantum free electron theory . . . . . . . . . . . . . . . . . . . 58 3.15 Conductivity of Semi conducting materials . . . . . . . . . . . . . . . . . . 60 3.16 Concentration of electrons and holes inintrinsic semiconductors . . . . . . 61 3.17 Fermi level in an intrinsic Semiconductor . . . . . . . . . . . . . . . . . . 62 3.18 Hall effect, Hall coefficient, Measurement of hall voltage and Hall angle . . 63 Multiple Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Descriptive Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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