Cosmology and Particle Physics

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[...]... the second ionization energy of He, that is the energy required to remove the second electron after the first one is removed? (c) The energy levels of the n = 3 states of the valence electron of sodium (neglecting intrinsic spin) are shown in Fig 1.1 Why do the energies depend on the quantum number l? (SUNY, Buffalo) Fig 1.1 8 Problems and Solutions in Atomic, Nuclear and Particle Physics Solution: (a)... obtained, to a dimensionless constant, if we remember dσ ∼ dΩ sin θ 2 −4 , and assume that it depends also on ze, Ze and E = 1 mv 2 2 Let −4 dσ θ , = K(zZe2)x E y sin dΩ 2 where K is a dimensionless constant Dimensional analysis then gives [L]2 = (e2 )x E y As the above gives e2 = [E] , r 26 Problems and Solutions in Atomic, Nuclear and Particle Physics x = 2, y = −x = −2 (b) For the protons, β≡ v = c pc... the degeneracies of states 1 and 2, use having been made of the relation A12 = 1/τ and the uncertainty principle Γτ ≈ Then as Nω = Iω /c, c being the velocity of light in free space, we have Pω = π 2 c2 g1 · ΓIω ω 2 g2 14 Problems and Solutions in Atomic, Nuclear and Particle Physics Introducing the form factor g(ω) and considering ω and Iω as average values in the band of g(ω), we can write the... uncertainty principle ∆E · τ , which gives ∆E τ (e) Consider the free protons as an ideal gas in which the proton spins have two quantized directions: parallel to B with energy Ep = −µp B and 12 Problems and Solutions in Atomic, Nuclear and Particle Physics e 2mp −E exp( kTp ), antiparallel to B with energy Ep = µp B, where µp = is the magnetic moment of proton As the number density n ∝ we have exp exp µp... however, can result from atomic collisions which cause phase changes in the emitted radiation and consequently a spread in the energy 6 Problems and Solutions in Atomic, Nuclear and Particle Physics (b) Doppler broadening: The first order Doppler frequency shift is given v by ∆ν = ν0c x , taking the x-axis along the line of sight Maxwell’s velocity distribution law then gives dn ∝ exp − 2 M vx 2kT... bound electron (say an L electron) Atomic and Molecular Physics 9 may jump into the hole left by the ejected electron, emitting a photon If the process takes place without radiating a photon but, instead, a higherenergy shell (say L shell) is ionized by ejecting an electron, Cosmology and Particle Physics Cosmology and Particle Physics Bởi: OpenStaxCollege Look at the sky on some clear night when you are away from city lights There you will see thousands of individual stars and a faint glowing background of millions more The Milky Way, as it has been called since ancient times, is an arm of our galaxy of stars—the word galaxy coming from the Greek word galaxias, meaning milky We know a great deal about our Milky Way galaxy and of the billions of other galaxies beyond its fringes But they still provoke wonder and awe (see [link]) And there are still many questions to be answered Most remarkable when we view the universe on the large scale is that once again explanations of its character and evolution are tied to the very small scale Particle physics and the questions being asked about the very small scales may also have their answers in the very large scales Take a moment to contemplate these clusters of galaxies, photographed by the Hubble Space Telescope Trillions of stars linked by gravity in fantastic forms, glowing with light and showing evidence of undiscovered matter What are they like, these myriad stars? How did they evolve? What can they tell us of matter, energy, space, and time? (credit: NASA, ESA, K Sharon (Tel Aviv University) and E Ofek (Caltech)) As has been noted in numerous Things Great and Small vignettes, this is not the first time the large has been explained by the small and vice versa Newton realized that the nature of gravity on Earth that pulls an apple to the ground could explain the motion of the moon and planets so much farther away Minute atoms and molecules explain 1/18 Cosmology and Particle Physics the chemistry of substances on a much larger scale Decays of tiny nuclei explain the hot interior of the Earth Fusion of nuclei likewise explains the energy of stars Today, the patterns in particle physics seem to be explaining the evolution and character of the universe And the nature of the universe has implications for unexplored regions of particle physics Cosmology is the study of the character and evolution of the universe What are the major characteristics of the universe as we know them today? First, there are approximately 1011 galaxies in the observable part of the universe An average galaxy contains more than 1011 stars, with our Milky Way galaxy being larger than average, both in its number of stars and its dimensions Ours is a spiral-shaped galaxy with a diameter of about 100,000 light years and a thickness of about 2000 light years in the arms with a central bulge about 10,000 light years across The Sun lies about 30,000 light years from the center near the galactic plane There are significant clouds of gas, and there is a halo of less-dense regions of stars surrounding the main body (See [link].) Evidence strongly suggests the existence of a large amount of additional matter in galaxies that does not produce light—the mysterious dark matter we shall later discuss 2/18 Cosmology and Particle Physics The Milky Way galaxy is typical of large spiral galaxies in its size, its shape, and the presence of gas and dust We are fortunate to be in a location where we can see out of the galaxy and observe the vastly larger and fascinating universe around us (a) Side view (b) View from above (c) The Milky Way as seen from Earth (credits: (a) NASA, (b) Nick Risinger, (c) Andy) Distances are great even within our galaxy and are measured in light years (the distance traveled by light in one year) The average distance between galaxies is on the order of a million light years, but it varies greatly with galaxies forming clusters such as shown in [link] The Magellanic Clouds, for example, are small galaxies close to our own, some 160,000 light years from Earth The Andromeda galaxy is a large spiral galaxy like ours and lies million light years away It is just visible to the naked eye as an extended glow in the Andromeda constellation Andromeda is the closest large galaxy in our local group, and we can see some individual stars in it with our larger telescopes The most 3/18 Cosmology and Particle Physics distant known galaxy is 14 billion light years from Earth—a truly incredible distance (See [link].) (a) Andromeda is the closest large galaxy, at million light years distance, and is very similar to our Milky Way The blue regions harbor young and emerging stars, while dark streaks are vast clouds of gas and dust A smaller satellite galaxy is clearly visible (b) The box indicates what may be the most distant known galaxy, estimated to be 13 billion light years from us It exists in a much older part of the universe (credit: NASA, ESA, G Illingworth (University of California, Santa Cruz), R Bouwens (University of California, Santa Cruz and Leiden University), and the HUDF09 Team) Consider the fact that the light we receive from these vast distances has been on its way to us for a long time In fact, the time in years is the same as the distance in light years For ...Major American Universities Ph.D. Qualifying Questions and Solutions Problems and Solutions on Atomic, Nuclear and Particle Physics Compiled by The Physics Coaching Class University of Science and Technology of China Edited by Yung-Kuo Lim National University of Singapore World Scientific Singapore • New Jersey • London • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P 0 Box 128, Farrer Road, Singapore 912805 USA office: Suite lB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Major American Universities Ph.D. Qualifying Questions and Solutions PROBLEMS AND SOLUTIONS ON ATOMIC, NUCLEAR AND PARTICLE PHYSICS Copyright © 2000 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts, thereof may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-02-3917-3 981-02-3918-l (pbk) This book is printed on acid-free paper. Printed in Singapore by Uto-Print PREFACE This series of physics problems and solutions, which consists of seven volumes — Mechanics, Electromagnetism, Optics, Atomic, Nuclear and Particle Physics, Thermodynamics and Statistical Physics, Quantum Me- chanics, Solid State Physics and Relativity, contains a selection of 2550 problems from the graduate-school entrance and qualifying examination papers of seven U.S. universities — California University Berkeley Cam- pus, Columbia University, Chicago University, Massachusetts Institute of Technology, New York State University Buffalo Campus, Princeton Uni- versity, Wisconsin University — as well as the CUSPEA and C.C. Ting’s papers for selection of Chinese students for further studies in U.S.A., and their solutions which represent the effort of more than 70 Chinese physicists, plus some 20 more who checked the solutions. The series is remarkable for its comprehensive coverage. In each area the problems span a wide spectrum of topics, while many problems overlap several areas. The problems themselves are remarkable for their versatil- ity in applying the physical laws and principles, their uptodate realistic situations, and their scanty demand on mathematical skills. Many of the problems involve order-of-magnitude calculations which one often requires in an experimental situation for estimating a quantity from a simple model. In short, the exercises blend together the objectives of enhancement of one’s understanding of physical principles and ability of practical application. The solutions as presented generally just provide a guidance to solving the problems, rather than step-by-step manipulation, and leave much to the students to work out for themselves, of whom much is demanded of the basic knowledge in physics. Thus the series would provide an invaluable complement to the textbooks. The present volume consists of 483 [...]... of other authors The discussion of the Second Law and the arrow of time being nished, I will procede in the next part with the arrow of time in cosmology 3.2 Cosmology and information theory In an article in Scienti c American 25], David Layzer presents an unorthodox theory concerning the arrows of time in both thermodynamics and cosmology He identi es two phenomenological arrows of time that are in. .. points according to the fundamental postulate of statistical mechanics at every instant in time The use of the postulate in this manner must rst be shown to be legitimate and is in fact in contradiction with the deterministic character of the underlying laws of dynamics Thirdly, the reasoning involved in establishing the statistical interpretation of the H -theorem is perfectly time symmetrical The. .. strong cosmological principle and of a prevailing thermodynamical equilibrium at or near the initial singularity, the historical and thermodynamical arrows of time will follow Many aspects of the derivation of Layzer remain unclear to me The most crucial point is, in my opinion, the absence of the connection between the cosmological and thermodynamical arrows of time It is one thing to prove, or make it... leave the H -theorem and other dynamical theories? According to Price, these theories incorporate somewhere a time asymmetrical principle (otherwise they cannot generate time asymmetrical results) and are aimed at explaining the future and not the past Since the real problem is not the entropy state of the future but that of the past, these theories are misdirected The [...]... Magnetic resonance imaging Problems 9 Outstanding Questions and Future Prospects 9.1 267 270 273 278 278 282 290 294 297 Particle physics 9.1.1 The Higgs boson 9.1.2 Grand unification 9.1.3 Supersymmetry 9.1.4 Particle astrophysics Nuclear physics 9.2.1 The structure of hadrons and nuclei 9.2.2 Quark–gluon plasma, astrophysics and cosmology 9.2.3 Symmetries and the standard model 9.2.4 Nuclear medicine... that there is symmetry between particles and antiparticles, and it is a convention to call the electron the particle and the positron its antiparticle This reflects the fact that the normal matter contains electrons rather than positrons 1.3 Symmetries and Conservation Laws Symmetries and the invariance properties of the underlying interactions play an important role in physics Some lead to conservation... quantum number (spin is another) that characterizes a particle, whether it is elementary or composite (i.e a hadron) Many quantum numbers differ in sign for particle and antiparticle, and electric charge is an example of this We will meet others later When brought together, particle antiparticle pairs, each of mass m, can annihilate, releasing their combined rest energy 2mc2 as photons or other particles... photographic plates were being fogged by an unknown radiation emanating from uranium ores He had accidentally discovered radioactivity: the fact that some nuclei are unstable and spontaneously decay In the years that followed, the phenomenon was extensively investigated, notably by the husband and wife team of Pierre and Marie Curie and by Ernest Rutherford and his collaborators,2 and it was established that there... of nuclear physics, where I have chosen just three major areas to discuss Nuclear and particle physics have been, and still are, very important parts of the entire subject of physics and its practitioners have won an impressive number of Nobel Prizes For historical interest, I have noted in the footnotes many of the awards for work related to the field Some parts of the book dealing with particle physics. .. the basic theoretical tools needed to describe the phenomena of both nuclear and particle physics, starting with a key concept: antiparticles 1.2 Relativity and Antiparticles Elementary particle physics is also called high-energy physics One reason for this is that if we wish to produce new particles in a collision between two other particles, then because of the relativistic mass–energy relation E ¼... universal Familiar examples are translational invariance, leading to the conservation of linear momentum; and rotational invariance, leading to conservation of angular momentum The latter plays an important role in nuclear and particle physics as it leads to a scheme for the classification of states based, among other quantum 23 Carl Anderson shared the 1936 Nobel Prize in Physics for the discovery of the... called bosons There are three families of elementary particles in the standard model: two spin-1 families of 2 fermions called leptons and quarks; and one family of spin-1 bosons In addition, 13 Gell-Mann received the 1969 Nobel Prize in Physics for ‘contributions and discoveries concerning the classification of elementary particles and their interactions’ For the origin of the word ‘quark’, he cited the... quarks and nuclei are bound states of nucleons, the properties of nuclei should, in principle, be deducible from the properties of quarks and their [...]...x Nuclear and Particle Physics care and grace under pressure were vital to the ultimate success of our project We thank David Rocco and Ray Teng for the artwork, and Richard Hagen for pointing out several typos and possible sources of confusion in the first edition of this book We also thank Charles Baltay and Susan Cooper for their suggested revisions of content, and Mark Strikman... quantum theory in explaining atomic phenomena was mainly due to two reasons First, the interaction responsible for holding the atom together is the long-ranged electromagnetic force, whose properties were well understood in the classical domain, and whose principles carried over quite readily to the quantum regime Second, the strength of the electromagnetic l 2 Nuclear and Particle Physics coupling is weak... the experimental information, both in nuclear and particle physics, is derived from scattering measurements - similar, in principle, to those that Ernest Rutherford and his collaborators performed in discovering the nucleus In such experiments, beams of energetic particles are directed into a fixed target, or, alternately, two beams of energetic particles are made to collide In either case, the results... Ionization Detectors 7.2.1 Ionization Counters 7.2.2 Proportional Counters 7.2.3 Geiger-Miiller Counters Scintillation Detectors Time of Flight Cherenkov Detectors Semiconductor Detectors Calorimeters Layered Detection xiii 157 159 162 165 165 169 173 174 175 177 8 Accelerators 8.1 Introductory Remarks 8.2 Electrostatic Accelerators 8.2.1 Cockcroft-Walton Machines 8.2.2 Van de Graaff Accelerator 8.3 Resonance... from the right hand side we conclude that the motion of the a -particle and the target must be essentially along the incident direction In other words, in such a case, one would expect only small deviations in the trajectory of the a -particle On the other hand, if mt » ma, then the left hand side of Eq (1.3) is negative, which implies large angles between the trajectories of the a -particle and the recoiling... Eq (1.3) gives vt < 2m7^v"., and from Eq (1.2) we again obtain that va « VQ- Therefore, mtVt < 2mava ftj 2mavo This means that the nucleus can carry away up to twice the incident momentum, which implies that the a -particle can recoil backwards with a momentum essentially equal and opposite to its initial value Such large momentum 6 Nuclear and Particle Physics transfers to the nucleus can, therefore,... provide invaluable, and often the only attainable, information about subatomic systems Since the basic principles in most of these experiments are quite similar, we will next sketch the ideas behind the pioneering work of Rutherford and his colleagues that was carried out at the University of Manchester, England, around 1910 and which provided the foundation for nuclear and particle physics Rutherford... collision, both particles move with respective velocities va and vt- Assuming that the collision is ... Making Connections: Cosmology and Particle Physics There are many connections of cosmology by definition involving physics on the largest scale—with particle physics by definition physics on the smallest... patterns in particle physics seem to be explaining the evolution and character of the universe And the nature of the universe has implications for unexplored regions of particle physics Cosmology. .. infinitesimal point 10/18 Cosmology and Particle Physics The evolution of the universe from the Big Bang onward is intimately tied to the laws of physics, especially those of particle physics at the earliest