1000 solved problems in modern physics copy

https://t.me/UPSC_Mains https://t.me/UPSC_Mains www.pdfgrip.com https://t.me/UPSC_Mains 1000 Solved Problems in Modern Physics https://t.me/UPSC_Mains www.pdfgrip.com https://t.me/UPSC_Mains https://t.me/UPSC_Mains www.pdfgrip.com https://t.me/UPSC_Mains Ahmad A Kamal 1000 Solved Problems in Modern Physics 123 https://t.me/UPSC_Mains www.pdfgrip.com https://t.me/UPSC_Mains Dr Ahmad A Kamal 425 Silversprings Lane Murphy, TX 75094, USA anwarakamal@yahoo.com ISBN 978-3-642-04332-1 e-ISBN 978-3-642-04333-8 DOI 10.1007/978-3-642-04333-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009943222 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Cover design: eStudio Calamar Steinen Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) https://t.me/UPSC_Mains www.pdfgrip.com https://t.me/UPSC_Mains Dedicated to my parents https://t.me/UPSC_Mains www.pdfgrip.com https://t.me/UPSC_Mains https://t.me/UPSC_Mains www.pdfgrip.com https://t.me/UPSC_Mains Preface 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-bystep 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 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 and focus on quantum physics Chapter is basically concerned with the old quantum theory Problems are solved under the topics of deBroglie https://t.me/UPSC_Mains www.pdfgrip.com vii viii https://t.me/UPSC_Mains Preface 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 is concerned with the quantum mechanics of Schrodinger and Hesenberg 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 deals with problems on Thermo–dynamic relations and their applications such a specific heats 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 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 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 and are concerned with problems in low energy Nuclear physics Chapter covers the interactions of charged particles with matter which include kinematics of collisions, Rutherford Scattering, Ionization, Range and Straggiling, 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 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 and 10 are concerned with high energy physics Chapter covers the problems on natural units, production, interactions and decays of high energy unstable particles, various types of detectors such as ionization chambers, proprortional 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- https://t.me/UPSC_Mains www.pdfgrip.com Preface https://t.me/UPSC_Mains ix magnetic and weak, the conservation laws applicable to the three types of interactions, Gell-mann’s formula, the properties of quarks and classification into supermultiplets, the types of weak decays and Cabibbo’s theory, the neutrino oscillations, Electro–Weak interaction, the heavy bosons and the Standard model Acknowledgements It is a pleasure to thank Javid for the bulk of typing and suggestions and Maryam for proof reading I am indebted to Muniba for the line drawings, to Suraiya, Maqsood and Zehra for typing and editing I am grateful to the Universities of UK and India for permitting me to use their question papers cited in the text to CERN photo service for the cover page to McGraw-Hill and Co: for a couple of diagrams from Quantum Mechanics, L.I Schiff, 1955, to Cambridge University Press for using some valuable information from Introduction to High Energy Physics, D.H Perkins and to Ginn and Co: and Pearson and Co: for access to Differential and Integral Calculus, William A Granville, 1911 My thanks are due to Springer-Verlag, in particular Claus Ascheron, Adelheid Duhm and Elke Sauer for constant encouragement Murphy, Texas February 2010 Ahmad A Kamal https://t.me/UPSC_Mains www.pdfgrip.com 620 https://t.me/UPSC_Mains Appendix: Problem Index σ (θ ) versus σ (θ ∗ ) dσ p /dE p σ (ϕ) Scattering from sphere 7.8 7.9 7.10 7.11 7.2.2 Rutherford Scattering σ (ϕ) N (600 − 900 )/N (900 − 1200 ) Scattering probability Field of force θ ∗ for b = R0 /2 Breakdown of Rutherford scattering N (θ > 900 )/N Scattering with L = Z from Rutherford scattering dσ/dW for electron σ = σg (1 − R0 /R) rmin for α scattering E to reach nucleus θ for b = R0 Scattering for θ < 300 Scattering from brass Scattering from gold Darwin’s formula 7.12 7.13 7.14, 20 7.15 7.16 7.17, 26 7.18 7.19 7.21 7.22 7.23 7.24, 28 7.25 7.27 7.29 7.30 7.31 7.32 7.2.3 Ionization, Range and Straggling Radiation loss of D and e Muon penetration Range-energy for D and P Range of P, D and α Range of α and P in Al and air Straggling of He and He Mass estimation from ranges Range of D and α dE/dx of α Stopping power of P and D Specific ionization of α and P Stopping power in air and Al Bragg–Kleeman rule Geiger’s rule Geiger–Nuttal law Production of ion pairs Energy loss of P and D Radiation energy loss of e Multiple scattering and angular distribution in radiation processes 7.33 7.34 7.35 7.36 7.37 7.38 7.39 7.40 7.41 7.42 7.43 7.44 7.45 7.46 7.47 7.48 7.49, 50 7.51 7.52 https://t.me/UPSC_Mains www.pdfgrip.com Appendix: Problem Index https://t.me/UPSC_Mains 621 7.2.4 Compton Scattering Kinematics of Compton scattering (Δν)max Recoil velocity of electron Ph.elec, Comp, Pair λ0 ΔE for various situations Attenuation of E γ (Δλ)max hν0 given hν & θ Range of E γ from annihilation radiation 7.53 7.54 7.55 7.56 7.57 7.58 7.59 7.60 7.61 7.62 7.2.5 Photoelectric Effect υe T and hν, given Br and BE V0 , given λ0 and λ Photo effect not possible with free electron Attenuation of γ rays Absorption edges h, λ0 and W μph and μc Photo effect from hydrogen h (Planck’s constant) Photoelectric current T and λe 7.63 7.64 7.65 7.66 7.67 7.68 7.69 7.70 7.71 7.72 7.73 7.74 7.2.6 Pair Production E γ (threshold) E γ from e+ e− annihilation γ → e+ e− , not possible in vacuum 7.75 7.76 7.77 7.2.7 Cerenkov Radiation Range of n KE of proton No of photons emitted 7.78 7.79 7.80 7.2.8 Nuclear Resonance Mosbauer experiment ΔW when M ∗ → M Thermal broadening Red shift 7.81 7.82 7.83 7.84 7.2.9 Radioactivity (General) T1 and T2 Heating effect Radioactive equilibrium https://t.me/UPSC_Mains www.pdfgrip.com 7.85 7.86 7.87, 92, 93, 95 622 https://t.me/UPSC_Mains Age of radioactive alloy Source strength Electricity generation Carbon dating Half life time of 55 Co Partial half lives of 242 Pu Chain decay Age of earth Activity in Curies Rad Diagnostic 7.2.10 Alpha-Decay Gamow’s formula Minimum α energy to force it into nucleus Gieger–Nuttal rule 7.2.11 Beta-Decay Beta-decay transitions Mean lifetime Evolution of heat Kurie plot Energy of e, ν & recoiling nucleus Beta ray spectrum Appendix: Problem Index 7.88 7.89 7.90 7.91 7.94 7.96 7.97 7.98 7.99 7.100 7.101 7.102, 105 7.103 7.104 7.106 7.107, 108 7.109 7.110 7.111 7.112 Chapter Nuclear Physics II 8.2.1 Atomic Masses and Radii Mass spectroscopy Mirror nuclei Uncertainty relation Mass of 14 O 8.1, 2, 8.4 8.5 8.6 8.2.2 Electric Potential and Energy Electrostatic energy of nucleus Potential (r