1000 Solved Problems in Modern Physics / Edition 1

by Ahmad A. Kamal

Overview

This book is targeted mainly to the undergraduate students of USA, UK and other European countries, and the M. Sc of Asian countries, but will be found useful for the graduate students, Graduate Record Examination (GRE), Teachers and Tutors. This is a by-product of lectures given at the Osmania University, University of Ottawa and University of Tebrez over several years, and is intended to assist the students in their assignments and examinations. The book covers a wide spectrum of disciplines in Modern Physics, and is mainly based on the actual examination papers of UK and the Indian Universities. The selected problems display a large variety and conform to syllabi which are currently being used in various countries. The book is divided into ten chapters. Each chapter begins with basic concepts containing a set of formulae and explanatory notes for quick reference, followed by a number of problems and their detailed solutions. The problems are judiciously selected and are arranged section-wise. The so- tions are neither pedantic nor terse. The approach is straight forward and step— step solutions are elaborately provided. More importantly the relevant formulas used for solving the problems can be located in the beginning of each chapter. There are approximately 150 line diagrams for illustration. Basic quantum mechanics, elementary calculus, vector calculus and Algebra are the pre-requisites.

Product Details

ISBN-13:	9783642043321
Publisher:	Springer Berlin Heidelberg
Publication date:	07/01/2010
Edition description:	2010
Pages:	634
Product dimensions:	6.30(w) x 9.20(h) x 1.60(d)

About the Author

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.

Table of Contents

1 Mathematical Physics 1

1.1 Basic Concepts and Formulae 1

1.2 Problems 21

1.2.1 Vector Calculus 21

1.2.2 Fourier Series and Fourier Transforms 22

1.2.3 Gamma and Beta Functions 23

1.2.4 Matrix Algebra 24

1.2.5 Maxima and Minima 24

1.2.6 Series 25

1.2.7 Integration 25

1.2.8 Ordinary Differential Equations 26

1.2.9 Laplace Transforms 29

1.2.10 Special Functions 29

1.2.11 Complex Variables 30

1.2.12 Calculus of Variation 31

1.2.13 Statistical Distributions 32

1.2.14 Numerical Integration 33

1.3 Solutions 33

1.3.1 Vector Calculus 33

1.3.2 Fourier Series and Fourier Transforms 39

1.3.3 Gamma and Beta Functions 42

1.3.4 Matrix Algebra 44

1.3.5 Maxima and Minima 48

1.3.6 Series 49

1.3.7 Integration 51

1.3.8 Ordinary Differential Equations 57

1.3.9 Laplace Transforms 67

1.3.10 Special Functions 68

1.3.11 Complex Variables 72

1.3.12 Calculus of Variation 74

1.3.13 Statistical Distribution 77

1.3.14 Numerical Integration 85

2 Quantum Mechanics - I 87

2.1 Basic Concepts and Formulae 87

2.2 Problems 92

2.2.1 de Broglie Waves 92

2.2.2 Hydrogen Atom 92

2.2.3 X-rays 95

2.2.4 Spin and μ and Quantum Numbers - Stern-Gerlah's Experiment 96

2.2.5 Spectroscopy 97

2.2.6 Molecules 99

2.2.7 Commutators 100

2.2.8 Uncertainty Principle 101

2.3 Solutions 101

2.3.1 de Broglie Waves 101

2.3.2 Hydrogen Atom 103

2.3.3 X-rays 108

2.3.4 Spin and μ and Quantum Numbers - Stern-Gerlah's Experiment 111

2.3.5 Spectroscopy 115

2.3.6 Molecules 120

2.3.7 Commutators 123

2.3.8 Uncertainty Principle 128

3 Quantum Mechanics - II 131

3.1 Basic Concepts and Formulae 131

3.2 Problems 137

3.2.1 Wave Function 137

3.2.2 Schrodinger Equation 138

3.2.3 Potential Wells and Barriers 140

3.2.4 Simple Harmonic Oscillator 146

3.2.5 Hydrogen Atom 147

3.2.6 Angular Momentum 149

3.2.7 Approximate Methods 152

3.2.8 Scattering (Phase-Shift Analysis) 153

3.2.9 Scattering (Born Approximation) 154

3.3 Solutions 156

3.3.1 Wave Function 156

3.3.2 Schrodinger Equation 162

3.3.3 Potential Wells and Barriers 168

3.3.4 Simple Harmonic Oscillator 199

3.3.5 Hydrogen Atom 209

3.3.6 Angular Momentum 215

3.3.7 Approximate Methods 229

3.3.8 Scattering (Phase Shift Analysis) 233

3.3.9 Scattering (Born Approximation) 240

4 Thermodynamics and Statistical Physics 247

4.1 Basic Concepts and Formulae 247

4.2 Problems 251

4.2.1 Kinetic Theory of Gases 251

4.2.2 Maxwell's Thermodynamic Relations 253

4.2.3 Statistical Distributions 255

4.2.4 Blackbody Radiation 256

4.3 Solutions 258

4.3.1 Kinetic Theory of Gases 258

4.3.2 Maxwell's Thermodynamic Relations 266

4.3.3 Statistical Distributions 279

4.3.4 Blackbody Radiation 285

5 Solid State Physics 291

5.1 Basic Concepts and Formulae 291

5.2 Problems 294

5.2.1 Crystal Structure 294

5.2.2 Crystal Properties 294

5.2.3 Metals 295

5.2.4 Semiconductors 297

5.2.5 Superconductor 298

5.3 Solutions 299

5.3.1 Crystal Structure 299

5.3.2 Crystal Properties 301

5.3.3 Metals 303

5.3.4 Semiconductors 309

5.3.5 Superconductor 311

6 Special Theory of Relativity 313

6.1 Basic Concepts and Formulae 313

6.2 Problems 319

6.2.1 Lorentz Transformations 319

6.2.2 Length, Time, Velocity 320

6.2.3 Mass, Momentum, Energy 323

6.2.4 Invariance Principle 326

6.2.5 Transformation of Angles and Doppler Effect 328

6.2.6 Threshold of Particle Production 330

6.3 Solutions 332

6.3.1 Lorentz Transformations 332

6.3.2 Length, Time, Velocity 338

6.3.3 Mass, Momentum, Energy 342

6.3.4 Invariance Principle 351

6.3.5 Transformation of Angles and Doppler Effect 355

6.3.6 Threshold of Particle Production 365

7 Nuclear Physics - I 369

7.1 Basic Concepts and Formulae 369

7.2 Problems 382

7.2.1 Kinematics of Scattering 382

7.2.2 Rutherford Scattering 383

7.2.3 Ionization, Range and Straggling 385

7.2.4 Compton Scattering 387

7.2.5 Photoelectric Effect 388

7.2.6 Pair Production 390

7.2.7 Cerenkov Radiation 390

7.2.8 Nuclear Resonance 390

7.2.9 Radioactivity (General) 391

7.2.10 Alpha-Decay 393

7.2.11 Beta-Decay 393

7.3 Solutions 394

7.3.1 Kinematics of Scattering 394

7.3.2 Rutherford Scattering 399

7.3.3 Ionization, Range and Straggling 404

7.3.4 Compton Scattering 407

7.3.5 Photoelectric Effect 411

7.3.6 Pair Production 414

7.3.7 Cerenkov Radiation 415

7.3.8 Nuclear Resonance 416

7.3.9 Radioactivity (General) 417

7.3.10 Alpha-Decay 422

7.3.11 Beta-Decay 423

8 Nuclear Physics - II 427

8.1 Basic Concepts and Formulae 427

8.2 Problems 434

8.2.1 Atomic Masses and Radii 434

8.2.2 Electric Potential and Energy 435

8.2.3 Nuclear Spin and Magnetic Moment 435

8.2.4 Electric Quadrupole Moment 435

8.2.5 Nuclear Stability 436

8.2.6 Fermi Gas Model 437

8.2.7 Shell Model 437

8.2.8 Liquid Drop Model 438

8.2.9 Optical Model 439

8.2.10 Nuclear Reactions (General) 440

8.2.11 Cross-sections 442

8.2.12 Nuclear Reactions via Compound Nucleus 443

8.2.13 Direct Reactions 443

8.2.14 Fission and Nuclear Reactors 444

8.2.15 Fusion 447

8.3 Solutions 447

8.3.1 Atomic Masses and Radii 447

8.3.2 Electric Potential and Energy 449

8.3.3 Nuclear Spin and Magnetic Moment 450

8.3.4 Electric Quadrupole Moment 451

8.3.5 Nuclear Stability 454

8.3.6 Fermi Gas Model 456

8.3.7 Shell Model 457

8.3.8 Liquid Drop Model 458

8.3.9 Optical Model 460

8.3.10 Nuclear Reactions (General) 462

8.3.11 Cross-sections 468

8.3.12 Nuclear Reactions via Compound Nucleus 469

8.3.13 Direct Reactions 470

8.3.14 Fission and Nuclear Reactors 471

8.3.15 Fusion 483

9 Particle Physics - I 485

9.1 Basic Concepts and Formulae 485

9.2 Problems 488

9.2.1 System of Units 488

9.2.2 Production 489

9.2.3 Interaction 489

9.2.4 Decay 491

9.2.5 Ionization Chamber, GM Counter and Proportional Counters 493

9.2.6 Scintillation Counter 495

9.2.7 Cerenkov Counter 496

9.2.8 Solid State Detector 497

9.2.9 Emulsions 497

9.2.10 Motion of Charged Particles in Magnetic Field 497

9.2.11 Betatron 498

9.2.12 Cyclotron 499

9.2.13 Synchrotron 500

9.2.14 Linear Accelerator 501

9.2.15 Colliders 502

9.3 Solutions 503

9.3.1 System of Units 503

9.3.2 Production 504

9.3.3 Interaction 505

9.3.4 Decay 508

9.3.5 Ionization Chamber, GM Counter and Proportional Counters 512

9.3.6 Scintillation Counter 515

9.3.7 Cerenkov Counter 518

9.3.8 Solid State Detector 520

9.3.9 Emulsions 520

9.3.10 Motion of Charged Particles in Magnetic Field 521

9.3.11 Betatron 524

9.3.12 Cyclotron 524

9.3.13 Synchrotron 527

9.3.14 Linear Accelerator 530

9.3.15 Colliders 531

10 Particle Physics - II 535

10.1 Basic Concepts and Formulae 535

10.2 Problems 544

10.2.1 Conservation Laws 544

10.2.2 Strong Interactions 546

10.2.3 Quarks 550

10.2.4 Electromagnetic Interactions 551

10.2.5 Weak Interactions 552

10.2.6 Electro-Weak Interactions 556

10.2.7 Feynman Diagrams 556

10.3 Solutions 558

10.3.1 Conservation Laws 558

10.3.2 Strong Interactions 563

10.3.3 Quarks 572

10.3.4 Electromagnetic Interactions 577

10.3.5 Weak Interactions 578

10.3.6 Electro-weak Interactions 590

10.3.7 Feynman Diagrams 592

Appendix: Problem Index 603

Index 633

Editorial Reviews

From the reviews:

“The book provides a collection of problems and solutions in physics targeting mainly undergraduate students. … The book focuses mainly on basic problems in quantum mechanics, nuclear physics and particle physics. … the book could be a useful addition to problem and solution books in physics for undergraduate students.” (Willi-Hans Steeb, zbMATH, Vol. 1271, 2013)

“Kamal … has prepared an excellent resource for physics professors and students. … The solutions give enough detail to understand how to solve the problems without being pedantic. … The level of the material makes this a great book for upper-level undergraduates studying the topics for the first time, a very good resource for graduate students looking to review the material … and a good resource for professors seeking example problems or quiz/exam problems. Summing Up: Highly recommended. Academic libraries serving upper-division undergraduates through researchers/faculty.” (D. B. Mason, Choice, Vol. 48 (5), January, 2011)

From the Publisher