Introduction to Modern Physics: Volume 1, Second Edition

Preface to the Second Edition
......Page 6
Preface to the First Edition
......Page 8
Contents
......Page 10
Unit I Special Theory of Relativity
......Page 20
1.1 Introduction
......Page 22
1.2 Classical Principle of Relativity : Galilean Transformation Equations
......Page 23
1.3 Michelson-Morley Experiment (1881)
......Page 26
1.4 Einstein's Special Theory of Relativity
......Page 28
1.5 Lorentz Transformations
......Page 29
1.6 Velocity Transformation
......Page 32
1.8 Lorentz Contraction
......Page 34
1.9 Time Dilation
......Page 35
1.10 Experimental Verification of Length Contraction and Time Dilation
......Page 36
1.11 Interval
......Page 37
1.12 Doppler's Effect
......Page 38
1.14 Relativistic Expression for Momentum: Variation of Mass With Velocity
......Page 41
1.15 The Fundamental Law of Relativistic Dynamcis
......Page 43
1.16 Mass-Energy Equivalence
......Page 45
1.17 Relationship Between Energy and Momentum
......Page 46
1.19 Transformation of Momentum and Energy
......Page 47
1.20 Verification of Mass-Energy Equivalence Formula
......Page 49
Solved Examples
......Page 50
Questions
......Page 63
Problems
......Page 64
Unit II Quantum Mechanics
......Page 66
1.1 Introduction
......Page 68
1.2 Black Body Radiation
......Page 69
1.3 Spectral Distribution of Energy in Thermal Radiation
......Page 70
1.4 Classical Theories of  Black Body Radiation
......Page 71
1.5 Planck's Radiation Law
......Page 73
1.6 Deduction of Stefan's Law From Planck's Law
......Page 75
1.7 Deduction of Wien's Displacement Law
......Page 76
Solved Examples
......Page 77
1.8 Photoelectric Effect
......Page 79
Solved Examples
......Page 82
1.9 Compton's Effect
......Page 84
Solved Examples
......Page 87
1.10 Bremsstrahlung
......Page 89
1.11 Raman Effect
......Page 91
Solved Examples
......Page 93
1.12 The Dual Nature of Radiation
......Page 94
Questions and Problems
......Page 95
2.2 de Broglie Hypothesis
......Page 97
2.3 Experimental Verification of de Broglie Hypothesis
......Page 99
2.5 Historical Perspective
......Page 101
2.6 The Wave Packet
......Page 102
2.7 Particle Velocity and Group Velocity
......Page 105
2.8 Heisenberg's Uncertainty Principle or the Principle of Indeterminacy
......Page 106
Solved Examples
......Page 108
Questions and Problems
......Page 115
3.1 Introduction
......Page 116
3.2 Schrodinger Equation
......Page 117
3.3 Physical Significance of Wave Function
......Page 121
3.4 Interpretation of Wave Function in Terms of Probability Current Density
......Page 122
3.5 Schrodinger Equation in Spherical Polar Coordinates
......Page 124
3.6 Operators in Qunatum Mechanics
......Page 125
3.7 Eigen Value Equation
......Page 131
3.8 Orthogonality of Eigen Functions
......Page 132
3.9 Compatible and Incompatible Observables
......Page 134
3.10 Commutator
......Page 135
3.11 Commutation Relations for Ladder Operators
......Page 139
3.12 Expectation Value
......Page 140
3.13 Ehrenfest Theorem
......Page 141
3.14 Superposition of States (Expansion Theorem)
......Page 144
3.15 Adjoint of an Operator
......Page 146
3.17 Eigen Functions of Hermitian Operator Belonging to Different Eigen Values are Mutually Orthogonal
......Page 147
Solved Examples
......Page 148
Questions and Problems
......Page 163
4.1 Potential Step or Step Barrier
......Page 166
4.2 Potential Barrier (Tunnel Effect)
......Page 170
4.3 Particle in a One -Dimensional Potential Well of Finite Depth
......Page 178
4.4 Theory of Alpha Decay
......Page 182
Questions
......Page 186
5.1 Eigen Values and Eigen Functions of L2 and Lz
......Page 188
5.2 Axiomatic Formulation of Quantum  Mechanics
......Page 195
5.3 Dirac Formalism of Quantum Mechanics
......Page 197
5.4 General Definition of Angular Momentum
......Page 198
5.5 Parity
......Page 205
Questions and Problems
......Page 206
6.1 Particle in an Infinitely Deep Potential Well (Box)
......Page 208
6.2 Particle in a Two Dimensional Potential Well
......Page 211
6.3 Particle in a Three Dimensional Potential Well
......Page 214
6.4 Degeneracy
......Page 216
6.5 Density of States
......Page 217
6.6 Spherically Symmetric Potential Well
......Page 219
Solved Examples
......Page 221
Questions and Problems
......Page 223
7.1 Introduction
......Page 224
Questions and Problems
......Page 234
8.1 Introduction
......Page 237
Questions and Problems
......Page 243
9.1 Reduction of Two-Body Problem in Two Equivalent One-Body Problem in a Central Force
......Page 244
9.2 Hydrogen Atom
......Page 247
9.3 Most Probable Distance of Electron From Nucleus
......Page 257
9.5 Properties of Hydrogen Atom Wave Functions
......Page 260
Solved Examples
......Page 262
Questions and Problems
......Page 264
Unit III Statistical Mechanics
......Page 268
1.2 Maxwell-Boltzmann (M-B) Statistics
......Page 270
1.5 Specification of the State of a System
......Page 271
1.6 Density of States
......Page 273
1.8 Macroscopic (Macro) State
......Page 275
1.9 Microscopic (Micro) State
......Page 276
Solved Examples
......Page 277
2.1 Introduction
......Page 285
2.2 Density of States in Phase Space
......Page 287
2.3 Number of Quantum States of an N-Particle System
......Page 289
3.1 Ensemble
......Page 290
3.3 Principle of Equal a Priori Probability
......Page 291
3.5 Liouville's Theorem
......Page 292
3.6 Statistical Equilibrium
......Page 296
3.7 Entropy
......Page 297
3.8 Free Energy
......Page 298
3.9  Ensemble Formulation of Statistical Mechanics
......Page 299
3.10 Microcanonical Ensemble
......Page 300
3.11 Classical Ideal Gas in Microcanonical Ensemble Formulation
......Page 301
3.12 Canonical Ensemble and Canonical Distribution
......Page 303
3.13 The Equipartition Theorem
......Page 307
3.14 Entropy in Terms of Probability
......Page 309
3.15 Entropy in Terms of Single Particle Partition Function Z1
......Page 310
4.1 Maxwell-Boltzmann Distribution
......Page 311
4.2 Heat Capacity of An Ideal Gas
......Page 316
4.3 Maxwell's Speed Distribution Function
......Page 317
4.4 Fermi-Dirac Statistics
......Page 321
4.5 Bose-Einstein Statistics
......Page 324
5.1 Sommerfeld's Free Electron Theory of Metals
......Page 328
5.2 Electronic Heat Capacity
......Page 336
5.3 Thermionic Emission (Richardson-Dushmann Equation)
......Page 337
5.4 An Ideal Bose Gas
......Page 340
5.5 Degeneration of Ideal Bose Gas
......Page 343
5.6 Black Body Radiation: Planck's Radiation Law
......Page 347
5.7 Validity Criterion for Classical Regime
......Page 348
5.8 Comparison of M-B, B-E And F-D Statistics
......Page 350
6.1 Canonical Partition Function
......Page 353
6.2 Classical Partition Function of a System Containing N Distinguishable Particles
......Page 354
6.3 Thermodynamic Functions of Monoatomic Gas
......Page 356
6.4 Gibbs Paradox
......Page 357
6.5 Indistinguishability of Particles and Symmetry of Wave Functions
......Page 360
6.6 Partition Function for Indistinguishable Particles
......Page 361
6.8 Partition Function and Thermodynamic Properties of Monoatomic Ideal Gas
......Page 363
6.9 Thermodynamic Functions in Terms of Partition Function
......Page 365
6.10 Rotational Partition Function
......Page 366
6.11 Vibrational Partition Function
......Page 368
6.12 Grand Canonical Ensemble and Grand Partition Function
......Page 370
6.14 Grand Potential
......Page 373
6.15 Ideal Gas From Grand Partition Function
......Page 374
6.16 Occupation Number of an Energy State From Grand Partition Function Fermi-Dirac-and Bose-Einstein Distribution
......Page 375
7.1 Specific Heat of Solids
......Page 378
7.2 Phonon Concept
......Page 384
7.3 Planck's Radiation Law: Partition Function Method
......Page 386
Questions and Problems
......Page 388
Appendix-A
......Page 389
Unit IV Atomic Spectra
......Page 396
1.2 Thomson's Model
......Page 398
1.3 Rutherford Atomic Model
......Page 400
1.4 Atomic (Line) Spectrum
......Page 401
1.5 Bohr's Theory of Hydrogenic Atoms (H,HE+,Li++)
......Page 404
1.6 Origin of Spectral Series
......Page 408
1.7 Correction for Nuclear Motion
......Page 410
1.9 Isotopic Shift: Discovery of Deuterium
......Page 413
1.10 Atomic Excitation
......Page 414
1.11 Franck-Hertz Experiment
......Page 415
1.12 Bohr's Correspondence Principle
......Page 416
1.13 Sommerfeld Theory of Hydrogen Atom
......Page 417
1.14 Sommerfeld's Relativistic Theory of Hydrogen Atom
......Page 422
Solved Examples
......Page 424
Questions and Problems
......Page 428
2.2 Quantum Numbers and the State of An Electron in an Atom
......Page 431
2.3 Electronic Configuration of Atoms 
......Page 434
2.4 Magnetic Moment of Atom
......Page 435
2.5 Larmor Theorem
......Page 436
2.6 The Magnetic Moment and Lande g-Factor for one Valence Electron Atom
......Page 437
2.7 Vector Model of Atom
......Page 439
2.9 Ground State of Atom With One Valence Electron (Hydrogen and Alkali Atoms)
......Page 445
2.10 Spectral Terms of Two Valence Electrons Systems (Helium and Alkaline-Earths)
......Page 446
2.11 Hund's Rule for Determining the Ground State of an Atom
......Page 453
2.12 Lande g-Factor in L-S Coupling
......Page 454
2.13 Lande g-Factor in J-J Coupling
......Page 458
2.14 Energy of an Atom in Magnetic Field
......Page 459
2.15 Stern and Gerlach Experiment (Space Quantization): Experimental Confirmation for Electron Spin Concept
......Page 460
2.16 Spin Orbit Interaction Energy
......Page 462
2.17 Fine Structure of Energy Levels in Hydrogen Atom
......Page 465
2.18 Fine Structure of H Line
......Page 468
2.19 FIne Structure of Sodium D Lines
......Page 469
2.20 Interaction Energy in L-S Coupling in Atom With Two Valence Electrons
......Page 470
2.21 Interaction Energy in J-J Coupling in Atom With Two Valence Electrons
......Page 474
2.22 Lande Interval Rule
......Page 477
Solved Examples
......Page 478
Questions and Problems
......Page 486
3.2 Energy Levels of Alkali Metals
......Page 490
3.3 Spectral Series of Alkali Atoms
......Page 493
3.5 Electron Spin and Fine Structure of Spectral Lines
......Page 496
3.6 Intensity of Spectral Lines
......Page 500
Solved Examples
......Page 503
3.7 Spectra of Alkaline Earths
......Page 506
3.10 The Great Calcium Triads
......Page 512
3.11 Spectrum of Helium Atom
......Page 513
Questions and Problems
......Page 516
4.1 Zeeman Effect
......Page 518
4.2 Anomalous Zeeman Effect
......Page 522
4.3 Paschen-Back Effect
......Page 525
4.4 Stark Effect
......Page 531
Solved Examples
......Page 533
Questions and Problems
......Page 538
5.2 Laue Photograph
......Page 539
5.3 Continuous And Characteristic X-Rays
......Page 540
5.4 X-Ray Energy Levels And Characteristic X-Rays
......Page 542
5.5 Moseley's Law
......Page 545
5.6 Spin-Relativity Doublet or Regular Doublet
......Page 546
5.7 Screening (Irregular)Doublet
......Page 547
5.8 Absorption of X-Rays
......Page 548
5.9 Bragg's Law
......Page 551
Solved Examples
......Page 554
Questions and Problems
......Page 557
Unit V Molecular Spectra of Diatomic Molecules
......Page 558
1.1 Introduction
......Page 560
1.2 Rotational Spectra-Molecule as Rigid Rotator
......Page 562
1.3 Isotopic Shift
......Page 566
1.4 Intensities of Spectral Lines
......Page 567
2.1 Vibrational Spectra-Molecule as Harmonic Oscillator
......Page 568
2.2 Anharmonic Oscillator
......Page 569
2.3 Isotopic Shift of Vibrational Levels
......Page 572
3.1 Energy Levels of a Diatomic Molecule and Vibration-Rotation Spectra
......Page 574
3.2 Effect of Interaction (Coupling)of Vibrational and Rotational Energy on Vibration-Rotation Spectra
......Page 578
4.1 Electronic Spectra of Diatomic Molecules
......Page 581
4.2 Franck-Condon Principle: Absorption
......Page 592
4.3 Molecular States
......Page 598
Examples
......Page 600
5.1 Introduction
......Page 601
5.2 Classical Theory of Raman Effect
......Page 603
5.3 Quantum Theory of Raman Effect
......Page 605
Solved Examples
......Page 611
Questions and Problems
......Page 620
6.2 Stimulated Emission
......Page 622
6.3 Population Inversion
......Page 625
6.4 Three Level Laser
......Page 627
6.5 The Ruby Laser
......Page 628
6.6 Helium-Neon Laser
......Page 629
6.8 Characteristics of Laser
......Page 630
Questions and Problems
......Page 631
Index
......Page 632