Fisica Moderna

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  • Copyright 2009, 2002, New Age International (P) Ltd., PublishersPublished by New Age International (P) Ltd., Publishers

    All rights reserved.No part of this ebook may be reproduced in any form, by photostat, microfilm,xerography, or any other means, or incorporated into any information retrievalsystem, electronic or mechanical, without the written permission of the publisher.All inquiries should be emailed to rights@newagepublishers.com

    PUBLISHING FOR ONE WORLD

    NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS4835/24, Ansari Road, Daryaganj, New Delhi - 110002Visit us at www.newagepublishers.com

    ISBN (13) : 978-81-224-2922-0

  • PREFACE TO THE SECOND EDITION

    The standard undergraduate programme in physics of all Indian Universities includes courses onSpecial Theory of Relativity, Quantum Mechanics, Statistical Mechanics, Atomic and MolecularSpectroscopy, Solid State Physics, Semiconductor Physics and Nuclear Physics. To provide study materialon such diverse topics is obviously a difficult task partly because of the huge amount of material andpartly because of the different nature of concepts used in these branches of physics. This book comprisesof self-contained study materials on Special Theory of Relativity, Quantum Mechanics, StatisticalMechanics, Atomic and Molecular Spectroscopy. In this book the author has made a modest attempt toprovide standard material to undergraduate students at one place. The author realizes that the way hehas presented and explained the subject matter is not the only way; possibilities of better presentationand the way of better explanation of intrigue concepts are always there. The author has been verycareful in selecting the topics, laying their sequence and the style of presentation so that student maynot be afraid of learning new concepts. Realizing the mental state of undergraduate students, everyattempt has been made to present the material in most elementary and digestible form. The author feelsthat he cannot guess as to how far he has come up in his endeavour and to the expectations ofesteemed readers. They have to judge his work critically and pass their constructive criticism either tohim or to the publishers so that they can be incorporated in further editions. To err is human. Theauthor will be glad to receive comments on conceptual mistakes and misinterpretation if any that haveescaped his attention.

    A sufficiently large number of solved examples have been added at appropriate places to make thereaders feel confident in applying the basic principles.

    I wish to express my thanks to Mr. Saumya Gupta (Managing Director), New Age International(P) Limited, Publishers, as well as the editorial department for their untiring effort to complete thisproject within a very short period.

    In the end I await the response this book draws from students and learned teachers.

    R.B. Singh

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  • PREFACE TO THE FIRST EDITION

    This book is designed to meet the requirements of undergraduate students preparing for bachelor'sdegree in physical sciences of Indian universities. A decisive role in the development of the presentwork was played by constant active contact with students at lectures, exercises, consultations andexaminations. The author is of the view that it is impossible to write a book without being in contactwith whom it is intended for. The book presents in elementary form some of the most exciting conceptsof modern physics that has been developed during the twentieth century. To emphasize the enormoussignificance of these concepts, we have first pointed out the shortcomings and insufficiencies ofclassical concepts derived from our everyday experience with macroscopic system and then indicatedthe situations that led to make drastic changes in our conceptions of how a microscopic system is to bedescribed. The concepts of modern physics are quite foreign to general experience and hence for theirbetter understanding, they have been presented against the background of classical physics.

    The author does not claim originality of the subject matter of the text. Books of Indian andforeign authors have been freely consulted during the preparation of the manuscript. The author isthankful to all authors and publishers whose books have been used.

    Although I have made my best effort while planning the lay-out of the text and the subject matter,I cannot guess as to how far I have come up to the expectations of esteemed readers. I request themto judge my work critically and pass their constructive criticisms to me so that any conceptual mistakesand typographical errors, which might have escaped my attention, may be eliminated in the next edition.

    I am thankful to my colleagues, family members and the publishers for their cooperation duringthe preparation of the text.

    In the end, I await the response, which this book draws from the learned scholars and students.

    R.B. Singh

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  • CONTENTS

    UNIT I

    SPECIAL THEORY OF RELATIVITY

    CHAPTER 1 The Special Theory of Relativity .............................................................................. 3461.1 Introduction ............................................................................................................................... 31.2 Classical Principle of Relativity: Galilean Transformation Equations ..................................... 41.3 Michelson-Morley Experiment (1881) ..................................................................................... 71.4 Einsteins Special Theory of Relativity ..................................................................................... 91.5 Lorentz Transformations ........................................................................................................ 101.6 Velocity Transformation .......................................................................................................... 131.7 Simultaneity ............................................................................................................................. 151.8 Lorentz Contraction................................................................................................................. 151.9 Time Dilation ........................................................................................................................... 16

    1.10 Experimental Verification of Length Contraction and Time Dilation ..................................... 171.11 Interval ..................................................................................................................................... 181.12 Dopplers Effect ...................................................................................................................... 191.13 Relativistic Mechanics ............................................................................................................. 221.14 Relativistic Expression for Momentum: Variation of Mass with Velocity ............................. 221.15 The Fundamental Law of Relativistic Dynamics ................................................................... 241.16 Mass-energy Equivalence ........................................................................................................ 261.17 Relationship Between Energy and Momentum ....................................................................... 271.18 Momentum of Photon ............................................................................................................. 281.19 Transformation of Momentum and Energy ........................................................................... 281.20 Verification of Mass-energy Equivalence Formula ................................................................ 301.21 Nuclear Binding Energy .......................................................................................................... 31

    Solved Examples ..................................................................................................................... 31Questions.................................................................................................................................. 44Problems .................................................................................................................................. 45

  • x Contents

    UNIT II

    QUANTUM MECHANICSCHAPTER 1 Origin of Quantum Concepts ................................................................................. 4977

    1.1 Introduction .......................................................................................................................... 491.2 Black Body Radiation ............................................................................................................ 501.3 Spectral Distribution of Energy in Thermal Radiation ........................................................ 511.4 Classical Theories of Black Body Radiation ........................................................................ 521.5 Plancks Radiation Law ........................................................................................................ 541.6 Deduction of Stefans Law from Plancks Law ................................................................. 561.7 Deduction of Wiens Displacement Law ............................................................................. 57

    Solved Examples ................................................................................................................... 581.8 Photoelectric Effect .............................................................................................................. 60

    Solved Examples ..................................................................