1000 Solved Problems in Modern Physics (eBook)

The author obtained his Doctoral degree from University of Bristol, U.K. under the supervision of Emeritus Professor Dr.D.H. Perkins, FRS. The author has worked in high-energy physics for a number of years using photographic emulsions exposed at CERN. He has also used low-energy facilities at Nuclear Science Center at New Delhi. He was a postdoctoral fellow at the University of Ottawa, visitor to CERN, visiting professor at the University of Tebrez. He has published 40 research papers in International Journals and gave lectures on Nuclear physics, particle physics, quantum mechanics, classical mechanics, mathematical physics, atomic and molecular physics and relativity at undergraduate and graduate levels at various universities for several years. He was a Professor and Head of the Department of Physics and Chairman, Board of studies at the Osmania University.

Preface 6
Contents 9
1 Mathematical Physics 15
1.1 Basic Concepts and Formulae 15
1.2 Problems 35
1.2.1 Vector Calculus 35
1.2.2 Fourier Series and Fourier Transforms 36
1.2.3 Gamma and Beta Functions 37
1.2.4 Matrix Algebra 38
1.2.5 Maxima and Minima 38
1.2.6 Series 39
1.2.7 Integration 39
1.2.8 Ordinary Differential Equations 40
1.2.9 Laplace Transforms 43
1.2.10 Special Functions 43
1.2.11 Complex Variables 44
1.2.12 Calculus of Variation 45
1.2.13 Statistical Distributions 46
1.2.14 Numerical Integration 47
1.3 Solutions 47
1.3.1 Vector Calculus 47
1.3.2 Fourier Series and Fourier Transforms 53
1.3.3 Gamma and Beta Functions 56
1.3.4 Matrix Algebra 58
1.3.5 Maxima and Minima 62
1.3.6 Series 63
1.3.7 Integration 65
1.3.8 Ordinary Differential Equations 71
1.3.9 Laplace Transforms 81
1.3.10 Special Functions 82
1.3.11 Complex Variables 86
1.3.12 Calculus of Variation 88
1.3.13 Statistical Distribution 91
1.3.14 Numerical Integration 99
2 Quantum Mechanics -- I 101
2.1 Basic Concepts and Formulae 101
2.2 Problems 106
2.2.1 de Broglie Waves 106
2.2.2 Hydrogen Atom 106
2.2.3 X-rays 109
2.2.4 Spin and µ Quantum Numbers -- Stern--Gerlah's Experiment 110
2.2.5 Spectroscopy 111
2.2.6 Molecules 113
2.2.7 Commutators 114
2.2.8 Uncertainty Principle 115
2.3 Solutions 115
2.3.1 de Broglie Waves 115
2.3.2 Hydrogen Atom 117
2.3.3 X-rays 122
2.3.4 Spin and µ Quantum Numbers -- Stern--Gerlah's Experiment 125
2.3.5 Spectroscopy 129
2.3.6 Molecules 134
2.3.7 Commutators 137
2.3.8 Uncertainty Principle 142
3 Quantum Mechanics -- II 145
3.1 Basic Concepts and Formulae 145
3.2 Problems 151
3.2.1 Wave Function 151
3.2.2 Schrodinger Equation 152
3.2.3 Potential Wells and Barriers 154
3.2.4 Simple Harmonic Oscillator 160
3.2.5 Hydrogen Atom 161
3.2.6 Angular Momentum 163
3.2.7 Approximate Methods 166
3.2.8 Scattering (Phase-Shift Analysis) 167
3.2.9 Scattering (Born Approximation) 168
3.3 Solutions 170
3.3.1 Wave Function 170
3.3.2 Schrodinger Equation 176
3.3.3 Potential Wells and Barriers 182
3.3.4 Simple Harmonic Oscillator 213
3.3.5 Hydrogen Atom 223
3.3.6 Angular Momentum 229
3.3.7 Approximate Methods 243
3.3.8 Scattering (Phase Shift Analysis) 247
3.3.9 Scattering (Born Approximation) 254
4 Thermodynamics and Statistical Physics 261
4.1 Basic Concepts and Formulae 261
4.2 Problems 265
4.2.1 Kinetic Theory of Gases 265
4.2.2 Maxwell's Thermodynamic Relations 267
4.2.3 Statistical Distributions 269
4.2.4 Blackbody Radiation 270
4.3 Solutions 272
4.3.1 Kinetic Theory of Gases 272
4.3.2 Maxwell's Thermodynamic Relations 280
4.3.3 Statistical Distributions 293
4.3.4 Blackbody Radiation 299
5 Solid State Physics 305
5.1 Basic Concepts and Formulae 305
5.2 Problems 308
5.2.1 Crystal Structure 308
5.2.2 Crystal Properties 308
5.2.3 Metals 309
5.2.4 Semiconductors 311
5.2.5 Superconductor 312
5.3 Solutions 313
5.3.1 Crystal Structure 313
5.3.2 Crystal Properties 315
5.3.3 Metals 317
5.3.4 Semiconductors 323
5.3.5 Superconductor 325
6 Special Theory of Relativity 327
6.1 Basic Concepts and Formulae 327
6.2 Problems 333
6.2.1 Lorentz Transformations 333
6.2.2 Length, Time, Velocity 334
6.2.3 Mass, Momentum, Energy 337
6.2.4 Invariance Principle 340
6.2.5 Transformation of Angles and Doppler Effect 342
6.2.6 Threshold of Particle Production 344
6.3 Solutions 346
6.3.1 Lorentz Transformations 346
6.3.2 Length, Time, Velocity 352
6.3.3 Mass, Momentum, Energy 356
6.3.4 Invariance Principle 365
6.3.5 Transformation of Angles and Doppler Effect 369
6.3.6 Threshold of Particle Production 379
7 Nuclear Physics -- I 382
7.1 Basic Concepts and Formulae 382
7.2 Problems 395
7.2.1 Kinematics of Scattering 395
7.2.2 Rutherford Scattering 396
7.2.3 Ionization, Range and Straggling 398
7.2.4 Compton Scattering 400
7.2.5 Photoelectric Effect 401
7.2.6 Pair Production 403
7.2.7 Cerenkov Radiation 403
7.2.8 Nuclear Resonance 403
7.2.9 Radioactivity (General) 404
7.2.10 Alpha-Decay 406
7.2.11 Beta-Decay 406
7.3 Solutions 407
7.3.1 Kinematics of Scattering 407
7.3.2 Rutherford Scattering 412
7.3.3 Ionization, Range and Straggling 417
7.3.4 Compton Scattering 420
7.3.5 Photoelectric Effect 424
7.3.6 Pair Production 427
7.3.7 Cerenkov Radiation 428
7.3.8 Nuclear Resonance 429
7.3.9 Radioactivity (General) 430
7.3.10 Alpha-Decay 435
7.3.11 Beta-Decay 436
8 Nuclear Physics -- II 439
8.1 Basic Concepts and Formulae 439
8.2 Problems 446
8.2.1 Atomic Masses and Radii 446
8.2.2 Electric Potential and Energy 447
8.2.3 Nuclear Spin and Magnetic Moment 447
8.2.4 Electric Quadrupole Moment 447
8.2.5 Nuclear Stability 448
8.2.6 Fermi Gas Model 449
8.2.7 Shell Model 449
8.2.8 Liquid Drop Model 450
8.2.9 Optical Model 451
8.2.10 Nuclear Reactions (General) 452
8.2.11 Cross-sections 454
8.2.12 Nuclear Reactions via Compound Nucleus 455
8.2.13 Direct Reactions 455
8.2.14 Fission and Nuclear Reactors 456
8.2.15 Fusion 459
8.3 Solutions 459
8.3.1 Atomic Masses and Radii 459
8.3.2 Electric Potential and Energy 461
8.3.3 Nuclear Spin and Magnetic Moment 462
8.3.4 Electric Quadrupole Moment 463
8.3.5 Nuclear Stability 466
8.3.6 Fermi Gas Model 468
8.3.7 Shell Model 469
8.3.8 Liquid Drop Model 470
8.3.9 Optical Model 472
8.3.10 Nuclear Reactions (General) 474
8.3.11 Cross-sections 480
8.3.12 Nuclear Reactions via Compound Nucleus 481
8.3.13 Direct Reactions 482
8.3.14 Fission and Nuclear Reactors 483
8.3.15 Fusion 495
9 Particle Physics -- I 496
9.1 Basic Concepts and Formulae 496
9.2 Problems 499
9.2.1 System of Units 499
9.2.2 Production 500
9.2.3 Interaction 500
9.2.4 Decay 502
9.2.5 Ionization Chamber, GM Counter and Proportional Counters 504
9.2.6 Scintillation Counter 506
9.2.7 Cerenkov Counter 507
9.2.8 Solid State Detector 508
9.2.9 Emulsions 508
9.2.10 Motion of Charged Particles in Magnetic Field 508
9.2.11 Betatron 509
9.2.12 Cyclotron 510
9.2.13 Synchrotron 511
9.2.14 Linear Accelerator 512
9.2.15 Colliders 513
9.3 Solutions 514
9.3.1 System of Units 514
9.3.2 Production 515
9.3.3 Interaction 516
9.3.4 Decay 519
9.3.5 Ionization Chamber, GM Counter and Proportional Counters 523
9.3.6 Scintillation Counter 526
9.3.7 Cerenkov Counter 529
9.3.8 Solid State Detector 531
9.3.9 Emulsions 531
9.3.10 Motion of Charged Particles in Magnetic Field 532
9.3.11 Betatron 535
9.3.12 Cyclotron 535
9.3.13 Synchrotron 538
9.3.14 Linear Accelerator 541
9.3.15 Colliders 542
10 Particle Physics -- II 545
10.1 Basic Concepts and Formulae 545
10.2 Problems 554
10.2.1 Conservation Laws 554
10.2.2 Strong Interactions 556
10.2.3 Quarks 560
10.2.4 Electromagnetic Interactions 561
10.2.5 Weak Interactions 562
10.2.6 Electro-Weak Interactions 566
10.2.7 Feynman Diagrams 566
10.3 Solutions 568
10.3.1 Conservation Laws 568
10.3.2 Strong Interactions 573
10.3.3 Quarks 582
10.3.4 Electromagnetic Interactions 587
10.3.5 Weak Interactions 588
10.3.6 Electro-weak Interactions 600
10.3.7 Feynman Diagrams 602
Appendix: Problem Index 613
Index 642