A.k.jha

A Textbook of Applied Physics

A Textbook of Applied Physics Volume II Second Edition

Dr. A.K. Jha

M.Sc. (DU), Ph.D. (IITD) Department of Applied Physics Delhi Technological University Delhi-110042 Presently Professor & Head Applied Sciences Department Ambedkar Institute of Advanced Communication Technologies & Research, (GGSIPU) Geeta Colony, Delhi-110031

I.K. International Publishing House Pvt. Ltd. NEW DELHI

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BANGALORE

2ubliIhA@ by I.K. International Publishing House Pvt. Ltd. S-25, Green Park Extension Uphaar Cinema Market New Delhi–110 016 (India) E-mail: [email protected] Website: www.ikbooks.com ISBN 978-93-81141-76-2 10

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© 2012 I.K. International Publishing House Pvt. Ltd. All rights reserved. No part of this book may be reproduced or used in any form, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written permission from the publisher. Published by Krishan Makhijani for I.K. International Publishing House Pvt. Ltd., S-25, Green Park Extension, Uphaar Cinema Market, New Delhi–110 016. Printed by Rekha Printers Pvt. Ltd., Okhla Industrial Area, Phase II, New Delhi–110 020.

Preface

This gives me immense pleasure in bringing out the second edition of volume II of Textbook of Applied Physics. I hope that the book will be helpful to the students of B.E. / B.Tech/ B.Sc. and Diploma in Engineering. Due to the short duration of semester, the students need to have subject materials in a simple and easy to understand way. This is where the book is intended to serve the students. To further cover the syllabi of various other universities four new chapters, namely, Physics of Semiconductors; Dielectric, Ferroelectric and Piezoelectric Properties of Materials; Superconductivity; and Nanomaterials have been added in the present edition. This addition will make this book useful for Materials Science paper also. Despite our best efforts, some mistakes might have crept in. We shall be thankful to the students and teacher colleagues who kindly point out such mistakes to us. We wish reader students grand success and a bright future.

Dr. A. K. Jha E-mail: [email protected]

Contents

Preface

v

1. Quantum Physics 1.1 Introduction–Limitations of Classical Mechanics 1.2 Planck’s Radiation Law—Quantum Theory 1.3 Photons 1.4 Interaction of Photons with Atoms 1.5 Photoelectric Effect 1.6 Einstein’s Photoelectric Equation 1.7 Photoelectric Cells 1.8 Compton Effect 1.9 Pair Production and Annihilation 1.10 Dual Nature of Radiation: De-Broglie Waves-Matter Waves 1.11 De-Broglie Wavelength of Electron 1.12 Davisson and Germer Experiment–Verification of Matter Waves 1.13 Wave Packet: Group Velocity and Phase (or Wave) Velocity 1.14 Uncertainty Principle 1.15 Wave Function 1.16 Bra-Ket Notation in Quantum Mechanics 1.17 Expectation Values 1.18 Operators in Quantum Mechanics 1.19 Schrödinger Equation: Time Dependent Form 1.20 Schrödinger’s Equation: Steady State Form (Time Independent) 1.21 Eigenvalues and Eigenfunctions 1.22 Degenerate and Non-degenerate Eigenfunctions 1.23 Particle in a Box 1.24 Simple Harmonic Oscillator 1.25 Rectangular Potential Barrier: Tunnel Effect

3 3 3 7 8 9 12 14 21 27 28 29 30 32 35 41 43 44 45 47 48 49 49 50 52 55

2. Statistical Mechanics 2.1 Introduction 2.2 Microscopic and Macroscopic Systems

67 67 67

viii

Contents 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13

Phase Space Equal Probability Hypothesis Statistical Equilibrium Maxwell-Boltzmann Distribution Law Maxwell’s Speed Distribution Law Law of Equipartition of Energy Quantum Statistics Bose–Einstein Statistics Fermi-Dirac Statistics Fermi Distribution Function–Fermi Energy Energy of a Fermi-Dirac System

68 69 69 70 71 74 76 76 79 81 82

3. Nuclear Physics 3.1 Introduction 3.2 Structure of Nucleus 3.3 General Properties of Nucleus 3.4 Nuclear Force 3.5 Nuclear Binding Energy–Stability of Nuclei 3.6 Decay of Unstable Nuclei 3.7 The Radioactive Decay Law 3.8 Artificial (or Induced) Radioactivity 3.9 Applications of Radioactivity 3.10 Alpha Decay 3.11 Beta Decay 3.12 Gamma Decay 3.13 Nuclear Reactions 3.14 Nuclear Models 3.15 Nuclear Fission 3.16 Nuclear Reactor 3.17 Nuclear Fusion 3.18 Nuclear Holocaust 3.19 Accelerators 3.20 Linear Accelerator (LINAC) 3.21 Cyclotron 3.22 Betatron 3.23 Nuclear Radiation Detectors 3.24 Geiger-Muller (GM) Counter 3.25 Solid State Detectors 3.26 Scintillation Detectors 3.27 Cloud Chamber 3.28 Bubble Chamber

89 89 89 90 93 96 100 101 108 119 110 115 119 120 123 128 131 133 135 138 140 141 144 147 149 150 150 151 151

4. Electromagnetic Theory 4.1 Introduction 4.2 Motion of Charged Particles in Electric and Magnetic Force 4.3 Magnetic Focussing 4.4 Gauss's Law

157 157 157 160 161

Contents

ix 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15

Applications of Gauss's Law Maxwell's Displacement Current Continuity of Current Maxwell's Equations Wave Equation for Plane Electromagnetic Wave in Vacuum Sinusoidal Electromagnetic Waves Energy and Momentum in Electromagnetic Waves Poynting's Theorem: Energy in Electromagnetic Waves Electromagnetic Waves in a Dielectric Medium Electromagnetic Waves in a Conducting Medium The Electromagnetic Spectrum

163 176 178 182 183 186 188 192 196 198 201

5. X-rays Production and Properties & Ultrasonics 5.1 X-rays: Production and Properties 5.2 Ultrasonics and Acoustics of Buildings

207 207 217

6. Physics of Semiconductors 6.1 Formation of Energy Bands in Solids 6.2 Distinction between Metals, Insulators and Semiconductors 6.3 Current Carriers (Electrons and Holes) in Semiconductors 6.4 Intrinsic Semiconductors 6.5 Doping of Semiconductors: Extrinsic Semiconductors 6.6 Types of Extrinsic Semiconductors: N- and P-type Semiconductors 6.7 Comparison between Intrinsic and Extrinsic Semiconductor 6.8 Comparison between N- and P-type Semiconductors 6.9 Characteristics of a Semiconductor 6.10 Electrical Conductivity of Extrinsic Semiconductors 6.11 Carrier Concentration in Intrinsic Semiconductors 6.12 Electrical Conductivity: Variation with Temperature 6.13 Drift and Diffusion Currents: Einstein’s Equation 6.14 Generation and Recombination of Minority Carriers 6.15 Hall Effect 6.16 Formation of p-n Junction Diode 6.17 Depletion Layer and Barrier Potential in a p-n Junction Diode 6.18 Biasing of p-n Junction Diode 6.19 Characteristics of a p-n Junction Diode 6.20 Zener Diode 6.21 Tunnel Diode

239 239 240 243 245 245 245 248 248 249 249 254 258 260 263 264 270 271 272 273 277 280

7. Dielectric, Ferroelectric and Piezoelectric Properties of Materials 7.1 Dielectric Materials: Introduction 7.2 Review of Basics 7.3 Dipole Moment and Polarization 7.4 Dielectric Constant 7.5 Dielectrics and Coulomb’s law 7.6 Gauss’s Law in Dielectrics 7.7 Electrical Susceptibility and Polarizability

286 286 287 288 288 291 291 293

x

Contents 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19

Local Electric Field: Claussius-Mossotti Equation Types of Polarization Electronic Polarization Dielectric Dispersion: Dielectric Loss Dielectric Smart Materials Piezoelectricity Pyroelectricity Ferroelectricity Electrets Ceramics Electrostriction Dielectric Strength/Breakdown

297 302 304 307 308 308 311 311 318 319 319 320

8. Superconductivity 8.1 Discovery of Superconductivity 8.2 Zero Resistance - Persistent Current 8.3 A.C. Resistivity in Superconductors 8.4 Effect of Magnetic Field: Critical Magnetic Field 8.5 Meissner Effect – Flux Exclusion 8.6 Type I and II Superconductors 8.7 Penetration Depth 8.8 Thermal Properties 8.9 Absorption of Electromagnetic Radiation 8.10 Isotope Effect 8.11 London Equation 8.12 BCS Theory 8.13 Magnetic Flux Quantization 8.14 Tunnelling of Single Particle 8.15 Josephson Effect-Cooper-Pair Tunnelling 8.16 Macroscopic Quantum Interference - SQUID 8.17 High-Temperature Superconductors 8.18 Superconducting Fullerides 8.19 Applications of Superconductors

325 325 328 328 329 333 335 337 338 342 343 344 348 353 354 355 359 361 364 365

9. Nanomaterials 9.1 Introduction 9.2 Nano Science & Technology: Past and Future 9.3 Nanoparticles: Deviation from Bulk Behaviour 9.4 Metal Nanoclusters 9.5 Quantum Structures: Dimension Effects 9.6 Carbon Nanostructures 9.7 Other Applications of Nanomaterials Index

370 370 371 372 373 375 379 387

395

Unit VI Unit III

1 Quantum Physics

1.1 INTRODUCTION–LIMITATIONS OF CLASSICAL MECHANICS We start studying mechanics based on Newton’s laws of motion from early classes. The mechanics based on the Newton’s laws, particularly second law of motion, is often referred to as classical mechanics or Newtonian mechanics. The classical mechanics successfully explains the motion of macroscopic bodies including terrestrial bodies. However, it fails to explain the motion of atomic particles. For example, if classical mechanics is applied to an atom, the electrons moving around the nucleus experience centripetal acceleration and hence must radiate energy in the form of electromagnetic waves. Therefore, the energy of the electrons should decrease continuously and ultimately they should collapse in the nucleus, contrary to the reality. The classical mechanics also failed to explain photoelectric effect, Compton effect, Raman effect, black body radiations, discrete nature of atomic spectra, etc. These problems could be overcome with the development of quantum mechanics or wave mechanics. The development of quantum mechanics revolutioned the different branches of physical sciences. Planck played an important role in establishing the quantum nature of radiation. Later Schrodinger, Heisenberg and other developed what we call quantum or wave mechanics. Not only physics but entire physical sciences such as chemistry, materials science, etc. are interpreted using quantum mechanics. 1.2 PLANCK’S RADIATION LAW—QUANTUM THEORY It was observed from the black body radiation curves (energy E vs wavelength l) that the energy is not uniformly distributed in radiation spectrum. At a given temperature, the intensity of radiation increases with increase of wavelength and becomes maximum at a particular wavelength (Fig. 1.1). Beyond this wavelength intensity of heat radiation decreases. An increase in temperature causes a decrease in lm such that lmT = const. = 0.2896 cm K (Wien’s displacement law). Also, an increase in temperature causes an increase in energy emission for all wavelengths. It was difficult to understand the black body radiations using the existing classical theory. In order to explain the experimentally observed distribution of energy in the spectrum of black body,

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A Textbook of Applied Physics

Planck in 1901 introduced the extremely important idea of quantum theory of heat radiation. According to Planck, energy is emitted in the form of packets or quanta called photons. Each photon has an energy hn, where h is the Planck’s constant and n is the frequency of radiation.

13

00

K

150

El

0K

1650 K

00

K

11

900 K 1

Fig. 1.1

2

3 4 l in microns

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Energy spectrum of black body radiations.

Plank derived this law by making the following assumptions. (i) A chamber containing black body radiations contains simple harmonic oscillators or resonators of molecular dimensions (known as Planck’s oscillators or resonators) which can vibrate with all possible frequencies. (ii) The frequency of radiation emitted by an oscillator is the same as the frequency of its vibration. (iii) An oscillator can emit (or absorb) energy in the multiples of a small unit called quantum (photon) and cannot emit (or absorb) energy in a continuous manner. An oscillator vibrating with frequency n can emit (or absorb) energy in units or quanta of magnitude hn, i.e. an oscillator can emit (or absorb) only discrete energy values of hn, 2hn, 3hn,….. or nhn where n = 1, 2, 3,….. In other words, exchange of energy between radiation and matter cannot take place continuously but only in discrete values, integral multiple of hn. If N is the total number of Planck’s oscillators and E their total energy, then average energy per Planck’s oscillator is given by

E ...(1.1) N According to Maxwell distribution law, if e is a certain amount of energy, the probabilities that a system will have oscillator with energies 0, e, 2e, 3e,….. are in the ratio

e=

1 : exp

FG -e IJ : exp FG - 2e IJ : exp FG - 3e IJ : ..... H kT K H kT K H kT K

Quantum Physics

5

where k is Boltzmann constant and T the absolute temperature. If No is the member of oscillators having zero energy, then the number of oscillators N1 having e energy will be N0 e–e/kT. Similarly, the number of oscillators N2 having energy 2e will be N0 e–2e/kt. In general, the number of oscillators Nr having re energy will be N0 e– re/k T. Therefore, the total number of oscillators is given by N = N0 + N1 + N2 + .... + Nr + .... = N0 + N0e–e/kT + N0e–2e/kT + .... + N0e–re/kT + .... = N0 [1 + e–e/kT + e–2e/kT + ... + e–re/kT + ....] Putting e–e/kT = y, we get N = N0[1 + y + y2 + .... + y r + .... ] =

N0 1- y

The total energy of Planck’s oscillators is given by E = 0 × N0 + e × N1 + 2e × N2 + .... + re × Nr + ..... = 0 + e N0e–e/kT + 2e N0e–2e/kT + .... re N0e– re/kT + .... = N0e [e–e/kT + 2e–2e/kT + .... + re–re/kT + .....] = N0e [y + 2y 2 + .... + ry r + .....] Let

S = y + 2y2 + ...... ry r + ..... Sy = y2 + 2y3 + .... + (r – 1)y r + ....

\ Subtracting, we get

S – Sy = y + y2 + ..... + y r + ...... S (1 – y) = or

S=

y 1- y y (1 - y ) 2

E = N0 e S = N0 e

y (1 - y) 2

Therefore, the average energy is given by

E e= = N

=

y (1 - y) 2 N0 1- y

N0 e

ey ee - e / kT = (1 - y) 1 - e - e / kT

...(1.2)

A Textbook of Applied Physics

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