1000 Solved Problems In Modern Physics

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 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 solutions are neither pedantic nor terse. The approach is straight forward, and step-by-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.

The areas of Nuclear and Particle physics are emphasized as revolutionary developments have taken place both on the experimental and theoretical fronts in recent years. No book on problems can claim to exhaust the variety in the limited space. An attempt is made to include the important types of problems at the undergraduate level.

Chapter 1 is devoted to the methods of Mathematical physics and covers such topics which are relevant to subsequent chapters. Detailed solutions are given to problems under Vector Calculus, Fourier series and Fourier transforms, Gamma and Beta functions, Matrix Algebra, Taylor and Maclaurean series, Integration, Ordinary differential equations, Calculus of variation Laplace transforms, Special functions such as Hermite, Legendre, Bessel and Laguerre functions, complex variables, statistical distributions such as Binomial, Poisson, Normal and interval distributions and numerical integration.

Chapters 2 and 3 focus on quantum physics. Chapter 2 is basically concerned with the old quantum theory. Problems are solved under the topics of DE Broglie waves, Bohr’s theory of hydrogen atom and hydrogen-like atoms, positronium and mesic atoms, X-rays production and spectra, Moseley’s law and Duan–Hunt law, spectroscopy of atoms and molecules, which include various quantum numbers and selection rules, and optical Doppler effect.

Chapter 3 is concerned with the quantum mechanics of Schrodinger and Hasenberg. Problems are solved on the topics of normalization and orthogonality of wave functions, the separation of Schrodinger’s equation into radial and angular parts, 1-D potential wells and barriers, 3-D potential wells, Simple harmonic oscillator, Hydrogen-atom, spatial and momentum distribution of electron, Angular momentum, Clebsch–Gordon coefficients ladder operators, approximate methods, scattering theory-phase-shift analysis and Ramsuer effect, the Born approximation.

Chapter 4 deals with problems on Thermon–dynamic relations and their applications such a specific heat of gases, Joule–Thompson effect, Clausius–Clapeyron equation and Vander waal’s equation, the statistical distributions of Boltzmann and Fermi distributions, the distribution of rotational and vibrational states of gas molecules, the Black body radiation, the solar constant, the Planck’s law and Wein’s law.

Chapter 5 is basically related to Solid State physics and material science. Problems are covered under the headings, crystal structure, Lattice constant, Electrical properties of crystals, Madelung constant, Fermi energy in metals, drift velocity, the Hall effect, the Debye temperature, the intrinsic and extrinsic semiconductors, the junction diode, the superconductor and the BCS theory, and the Josephson effect.

Chapter 6 deals with the special theory of Relativity. Problems are solved under Lorentz transformations of length, time, velocity, momentum and energy, the invariance of four-momentum vector, transformation of angles and Doppler effect and threshold of particle production.

Chapters 7 and 8 are concerned with problems in low energy nuclear physics. Chapter 7 covers the interactions of charged particles with matter which include kinematics of collisions, Rutherford Scattering, Ionization, Range and Straggling, Interactions of radiation with matter which include Compton scattering, photoelectric effect, pair production and nuclear resonance fluorescence, general radioactivity which includes problems on chain decays, age of earth, Carbon dating, alpha decay, Beta decay and gamma decay.

Chapter 8 is devoted to the static properties of nuclei such as nuclear masses, nuclear spin and parity, magnetic moments and quadrupole moments, the nuclear models, the Fermi gas model, the shell model, the liquid drop model and the optical model, problems on fission and fusion and Nuclear Reactors. Chapters 9 and 10 are concerned with high energy physics.

Chapter 9 covers the problems on natural units, production, interactions and decays of high energy unstable particles, various types of detectors such as ionization chambers, proportional and G.M. counters, Accelerators which include Betatron, Cyclotron, Synchrocyclotron, proton and electron Synchrotron, Linear accelerator and Colliders.

Chapter 10 deals with the static and dynamic properties of elementary particles and resonances, their classification from the point of view of the Fermi–Dirac and Bose–Einstein statistics as well as the three types of interactions, strong, Electro-magnetic and weak, the conservation laws applicable to the three types of interactions, Gell-Mann’s formula, the properties of quarks and classification into supermultiples, the types of weak decays and Cabibbo’s theory, the neutrino oscillations, Electro–Weak interaction, the heavy bosons and the Standard model