com This page intentionally left blank www.com Copyright © 2009, 2002, New Age International (P) Ltd., Publishers Published 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 retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to rights@newagepublishers.com ISBN (13) : 978-81-224-2922-0 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.com PREFACE TO THE SECOND EDITION The standard undergraduate programme in physics of all Indian Universities includes courses on Special Theory of Relativity, Quantum Mechanics, Statistical Mechanics, Atomic and Molecular Spectroscopy, Solid State Physics, Semiconductor Physics and Nuclear Physics. To provide study material on such diverse topics is obviously a difficult task partly because of the huge amount of material and partly because of the different nature of concepts used in these branches of physics.
This book comprises of self-contained study materials on Special Theory of Relativity, Quantum Mechanics, Statistical Mechanics, Atomic and Molecular Spectroscopy. In this book the author has made a modest attempt to provide standard material to undergraduate students at one place. The author realizes that the way he has presented and explained the subject matter is not the only way; possibilities of better presentation and the way of better explanation of intrigue concepts are always there. The author has been very careful in selecting the topics, laying their sequence and the style of presentation so that student may not be afraid of learning new concepts.
Realizing the mental state of undergraduate students, every attempt has been made to present the material in most elementary and digestible form. The author feels that he cannot guess as to how far he has come up in his endeavour and to the expectations of esteemed readers. They have to judge his work critically and pass their constructive criticism either to him or to the publishers so that they can be incorporated in further editions. To err is human.
The author will be glad to receive comments on conceptual mistakes and misinterpretation if any that have escaped his attention. A sufficiently large number of solved examples have been added at appropriate places to make the readers 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 this project within a very short period.
In the end I await the response this book draws from students and learned teachers.com This page intentionally left blank www.com PREFACE TO THE FIRST EDITION This book is designed to meet the requirements of undergraduate students preparing for bachelor's degree in physical sciences of Indian universities. A decisive role in the development of the present work was played by constant active contact with students at lectures, exercises, consultations and examinations. The author is of the view that it is impossible to write a book without being in contact with whom it is intended for. The book presents in elementary form some of the most exciting concepts of modern physics that has been developed during the twentieth century.
To emphasize the enormous significance of these concepts, we have first pointed out the shortcomings and insufficiencies of classical concepts derived from our everyday experience with macroscopic system and then indicated the situations that led to make drastic changes in our conceptions of how a microscopic system is to be described. The concepts of modern physics are quite foreign to general experience and hence for their better 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 and foreign authors have been freely consulted during the preparation of the manuscript.
The author is thankful 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 them to judge my work critically and pass their constructive criticisms to me so that any conceptual mistakes and 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 during the preparation of the text.
In the end, I await the response, which this book draws from the learned scholars and students.com This page intentionally left blank www.com CONTENTS UNIT I SPECIAL THEORY OF RELATIVITY CHAPTER 1 The Special Theory of Relativity .2 Classical Principle of Relativity: Galilean Transformation Equations .3 Michelson-Morley Experiment (1881) .4 Einstein’s Special Theory of Relativity .10 Experimental Verification of Length Contraction and Time Dilation .14 Relativistic Expression for Momentum: Variation of Mass with Velocity .15 The Fundamental Law of Relativistic Dynamics .16 Mass-energy Equivalence .17 Relationship Between Energy and Momentum .18 Momentum of Photon .19 Transformation of Momentum and Energy .20 Verification of Mass-energy Equivalence Formula .21 Nuclear Binding Energy .com x Contents UNIT II QUANTUM MECHANICS CHAPTER 1 Origin of Quantum Concepts .2 Black Body Radiation .3 Spectral Distribution of Energy in Thermal Radiation .4 Classical Theories of Black Body Radiation .5 Planck’s Radiation Law .6 Deduction of Stefan’s Law from Planck’s Law .7 Deduction of Wien’s Displacement Law .12 The Dual Nature of Radiation. 75 Questions and Problems. 76 CHAPTER 2 Wave Nature of Material Particles .2 de Broglie Hypothesis .3 Experimental Verification of de Broglie Hypothesis .4 Wave Behavior of Macroscopic Particles .6 The Wave Packet .7 Particle Velocity and Group Velocity .8 Heisenberg’s Uncertainty Principle or the Principle of Indeterminacy. 89 Questions and Problems.
96 CHAPTER 3 Schrödinger Equation .2 Schrödinger Equation .3 Physical Significance of Wave Function y .4 Interpretation of Wave Function y in terms of Probability Current Density .5 Schrödinger Equation in Spherical Polar Coordinates .6 Operators in Quantum Mechanics .com Contents xi 3.7 Eigen Value Equation .8 Orthogonality of Eigen Functions .9 Compatible and Incompatible Observables .11 Commutation Relations for Ladder Operators .14 Superposition of States (Expansion Theorem) .15 Adjoint of an Operator .16 Self-adjoint or Hermitian Operator .17 Eigen Functions of Hermitian Operator Belonging to Different Eigen Values are Mutually Orthogonal .18 Eigen Value of a Self-adjoint (Hermitian Operator) is Real. 129 Questions and Problems. 144 CHAPTER 4 Potential Barrier Problems .1 Potential Step or Step Barrier .3 Particle in a One-dimensional Potential Well of Finite Depth .4 Theory of Alpha Decay. 167 CHAPTER 5 Eigen Values of Lˆ 2 and Lˆ z Axiomatic: Formulation of Quantum Mechanics .1 Eigen Values and Eigen Functions of L̂2 And L̂z .2 Axiomatic Formulation of Quantum Mechanics .3 Dirac Formalism of Quantum Mechanics .4 General Definition of Angular Momentum.
186 Questions and Problems. 187 CHAPTER 6 Particle in a Box .1 Particle in an Infinitely Deep Potential Well (Box) .2 Particle in a Two Dimensional Potential Well .3 Particle in a Three Dimensional Potential Well .5 Density of States .6 Spherically Symmetric Potential Well. 202 Questions and Problems .com xii Contents CHAPTER 7 Harmonic Oscillator. 205 Questions and Problems.
215 CHAPTER 8 Rigid Rotator. 218 Questions and Problems. 224 CHAPTER 9 Particle in a Central Force Field .1 Reduction of Two-body Problem in Two Equivalent One-body Problem in a Central Force .3 Most Probable Distance of Electron from Nucleus .4 Degeneracy of Hydrogen Energy Levels .5 Properties of Hydrogen Atom Wave Functions. 243 Questions and Problems.
245 UNIT III STATISTICAL MECHANICS CHAPTER 1 Preliminary Concepts .2 Maxwell-Boltzmann (M-B) Statistics .3 Bose-Einstein (B-E) Statistics .4 Fermi-Dirac (F-D) Statistics .5 Specification of the State of a System .6 Density of States. 258 CHAPTER 2 Phase Space .2 Density of States in Phase Space .3 Number of Quantum States of an N-particle System. 270 CHAPTER 3 Ensemble Formulation of Statistical Mechanics .com Contents xiii 3.2 Density of Distribution (Phase Points) in g-space .3 Principle of Equal a Priori Probability .9 Ensemble Formulation of Statistical Mechanics .11 Classical Ideal Gas in Microcanonical Ensemble Formulation .12 Canonical Ensemble and Canonical Distribution .13 The Equipartition Theorem .14 Entropy in Terms of Probability .15 Entropy in Terms of Single Particle Partition Function Z1. 291 CHAPTER 4 Distribution Functions .1 Maxwell-Boltzmann Distribution .2 Heat Capacity of an Ideal Gas .3 Maxwell’s Speed Distribution Function .4 Fermi-Dirac Statistics .5 Bose-Einstein Statistics.
305 CHAPTER 5 Applications of Quantum Statistics. 309–333 Fermi-Dirac Statistics 5.1 Sommerfeld’s Free Electron Theory of Metals .2 Electronic Heat Capacity .4 An Ideal Bose Gas .5 Degeneration of Ideal Bose Gas .6 Black Body Radiation: Planck’s Radiation Law .7 Validity Criterion for Classical Regime .8 Comparison of M-B, B-E and F-D Statistics. 331 CHAPTER 6 Partition Function .1 Canonical Partition Function .2 Classical Partition Function of a System Containing N Distinguishable Particles .3 Thermodynamic Functions of Monoatomic Gas .com xiv Contents 6.5 Indistinguishability of Particles and Symmetry of Wave Functions .6 Partition Function for Indistinguishable Particles .7 Molecular Partition Function .8 Partition Function and Thermodynamic Properties of Monoatomic Ideal Gas .9 Thermodynamic Functions in Terms of Partition Function .10 Rotational Partition Function .11 Vibrational Partition Function .12 Grand Canonical Ensemble and Grand Partition Function .13 Statistical Properties of a Thermodynamic System in Terms of Grand Partition Function .15 Ideal Gas from Grand Partition Function .16 Occupation Number of an Energy State from Grand Partition Function: Fermi-Dirac and Bose-Einstein Distribution. 356 CHAPTER 7 Application of Partition Function .1 Specific Heat of Solids .3 Planck’s Radiation Law: Partition Function Method.
367 Questions and Problems. 370 UNIT IV ATOMIC SPECTRA CHAPTER 1 Atomic Spectra–I .3 Rutherford Atomic Model .5 Bohr’s Theory of Hydrogenic Atoms (H, He+, Li++) .6 Origin of Spectral Series .7 Correction for Nuclear Motion .8 Determination of Electron-Proton Mass Ratio (m/MH) .9 Isotopic Shift: Discovery of Deuterium .11 Franck-Hertz Experiment .12 Bohr’s Correspondence Principle .com Contents xv 1.13 Sommerfeld Theory of Hydrogen Atom .14 Sommerfeld’s Relativistic Theory of Hydrogen Atom. 405 Questions and Problems. 409 CHAPTER 2 Atomic Spectra–II .2 Quantum Numbers and the State of an Electron in an Atom .3 Electronic Configuration of Atoms .4 Magnetic Moment of Atom .6 The Magnetic Moment and Lande g-factor for One Valence Electron Atom .7 Vector Model of Atom .8 Atomic State or Spectral Term Symbol .9 Ground State of Atoms with One Valence Electron (Hydrogen and Alkali Atoms) .10 Spectral Terms of Two Valence Electrons Systems (Helium and Alkaline-Earths) .11 Hund’s Rule for Determining the Ground State of an Atom .12 Lande g-factor in L-S Coupling .13 Lande g-factor in J-J Coupling .14 Energy of an Atom in Magnetic Field .15 Stern and Gerlach Experiment (Space Quantization): Experimental Confirmation for Electron Spin Concept .16 Spin Orbit Interaction Energy .17 Fine Structure of Energy Levels in Hydrogen Atom .18 Fine Structure of Hµ Line .19 Fine Structure of Sodium D Lines .20 Interaction Energy in L-S Coupling in Atom with Two Valence Electrons .21 Interaction Energy In J-J Coupling in Atom with Two Valence Electrons .22 Lande Interval Rule.
459 Questions and Problems. 467 CHAPTER 3 Atomic Spectra-III .1 Spectra of Alkali Metals .2 Energy Levels of Alkali Metals .3 Spectral Series of Alkali Atoms .4 Salient Features of Spectra of Alkali Atoms .5 Electron Spin and Fine Structure of Spectral Lines .6 Intensity of Spectral Lines.com xvi Contents 3.7 Spectra of Alkaline Earths .8 Transitions Between Triplet Energy States .10 The Great Calcium Triads .11 Spectrum of Helium Atom. 494 Questions and Problems. 497 CHAPTER 4 Magneto-optic and Electro-optic Phenomena .2 Anomalous Zeeman Effect .3 Paschen-back Effect.
514 Questions and Problems. 519 CHAPTER 5 X-Rays and X-Ray Spectra .