Introduction to modern physics vol i

www.pdfgrip.com This page intentionally left blank www.pdfgrip.com www.pdfgrip.com Copyright © 2009, 2002, New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher All inquiries should be emailed to rights@newagepublishers.com ISBN (13) : 978-81-224-2922-0 PUBLISHING FOR ONE WORLD NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com www.pdfgrip.com PREFACE TO THE SECOND EDITION The standard undergraduate programme in physics of all Indian Universities includes courses on Special Theory of Relativity, Quantum Mechanics, Statistical Mechanics, Atomic and Molecular Spectroscopy, Solid State Physics, Semiconductor Physics and Nuclear Physics To provide study material on such diverse topics is obviously a difficult task partly because of the huge amount of material and partly because of the different nature of concepts used in these branches of physics This book comprises of self-contained study materials on Special Theory of Relativity, Quantum Mechanics, Statistical Mechanics, Atomic and Molecular Spectroscopy In this book the author has made a modest attempt to provide standard material to undergraduate students at one place The author realizes that the way he has presented and explained the subject matter is not the only way; possibilities of better presentation and the way of better explanation of intrigue concepts are always there The author has been very careful in selecting the topics, laying their sequence and the style of presentation so that student may not be afraid of learning new concepts Realizing the mental state of undergraduate students, every attempt has been made to present the material in most elementary and digestible form The author feels that he cannot guess as to how far he has come up in his endeavour and to the expectations of esteemed readers They have to judge his work critically and pass their constructive criticism either to him or to the publishers so that they can be incorporated in further editions To err is human The author will be glad to receive comments on conceptual mistakes and misinterpretation if any that have escaped his attention A sufficiently large number of solved examples have been added at appropriate places to make the readers feel confident in applying the basic principles I wish to express my thanks to Mr Saumya Gupta (Managing Director), New Age International (P) Limited, Publishers, as well as the editorial department for their untiring effort to complete this project within a very short period In the end I await the response this book draws from students and learned teachers R.B Singh www.pdfgrip.com This page intentionally left blank www.pdfgrip.com PREFACE TO THE FIRST EDITION This book is designed to meet the requirements of undergraduate students preparing for bachelor's degree in physical sciences of Indian universities A decisive role in the development of the present work was played by constant active contact with students at lectures, exercises, consultations and examinations The author is of the view that it is impossible to write a book without being in contact with whom it is intended for The book presents in elementary form some of the most exciting concepts of modern physics that has been developed during the twentieth century To emphasize the enormous significance of these concepts, we have first pointed out the shortcomings and insufficiencies of classical concepts derived from our everyday experience with macroscopic system and then indicated the situations that led to make drastic changes in our conceptions of how a microscopic system is to be described The concepts of modern physics are quite foreign to general experience and hence for their better understanding, they have been presented against the background of classical physics The author does not claim originality of the subject matter of the text Books of Indian and foreign authors have been freely consulted during the preparation of the manuscript The author is thankful to all authors and publishers whose books have been used Although I have made my best effort while planning the lay-out of the text and the subject matter, I cannot guess as to how far I have come up to the expectations of esteemed readers I request them to judge my work critically and pass their constructive criticisms to me so that any conceptual mistakes and typographical errors, which might have escaped my attention, may be eliminated in the next edition I am thankful to my colleagues, family members and the publishers for their cooperation during the preparation of the text In the end, I await the response, which this book draws from the learned scholars and students R.B Singh www.pdfgrip.com This page intentionally left blank www.pdfgrip.com CONTENTS UNIT I SPECIAL THEORY OF RELATIVITY CHAPTER The Special Theory of Relativity 3–46 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 Introduction Classical Principle of Relativity: Galilean Transformation Equations Michelson-Morley Experiment (1881) Einstein’s Special Theory of Relativity Lorentz Transformations 10 Velocity Transformation 13 Simultaneity 15 Lorentz Contraction 15 Time Dilation 16 Experimental Verification of Length Contraction and Time Dilation 17 Interval 18 Doppler’s Effect 19 Relativistic Mechanics 22 Relativistic Expression for Momentum: Variation of Mass with Velocity 22 The Fundamental Law of Relativistic Dynamics 24 Mass-energy Equivalence 26 Relationship Between Energy and Momentum 27 Momentum of Photon 28 Transformation of Momentum and Energy 28 Verification of Mass-energy Equivalence Formula 30 Nuclear Binding Energy 31 Solved Examples 31 Questions 44 Problems 45 www.pdfgrip.com CHAPTER $ LASERS 6.1 AND MASERS INTRODUCTION The words MASER and LASER are acronyms for Microwave Amplification by Stimulated Emission of Radiation and Light Amplification by Stimulated Emission of Radiation respectively The working of these devices is based on the phenomenon of stimulated emission, which was first suggested by Einstein in 1917 In this process an assembly of atoms or molecules, initially in the excited state, are stimulated (induced) by radiation of appropriate frequency to drop to lower energy state thereby emitting radiation of the same frequency as that of the stimulating radiation In 1953, Soviet scientists N Basov and A Prokhorov and American scientists C Townes and J Weber independently developed MASERS In 1964 Basov, Prokhorov and Townes were awarded Nobel Prize for this work In 1955 Gordon, Zeiger and Townes fabricated ammonia maser Soon after this discovery the principle of maser was extended to optical range and in 1960 T Meiman (USA) developed the first maser in the optical range called LASER In 1961 A Javan operated the first gas laser, helium-neon gas laser Since then a large number of masers and lasers have been developed This chapter is devoted to an elementary account of basic principles of these devices 6.2 STIMULATED EMISSION The Einstein’s Coefficients Consider an assembly of identical atoms in equilibrium with radiation at temperature T Let E1 and E2 be two energy levels of the atoms The frequency w of radiation is such that ω= E2 − E1 h .(6.2.1) Prior to 1917, it was supposed that the thermal equilibrium of atomic system and radiation was determined by only two processes (i) stimulated (induced) absorption in which atoms are raised under the action of radiation from the lower energy level to the higher one www.pdfgrip.com 604 Introduction to Modern Physics (ii) spontaneous emission in which the atoms return of their own from higher energy level to the lower one In 1917, Einstein while investigating this problem realized that two processes mentioned earlier viz stimulated absorption and spontaneous emission alone are not sufficient to maintain the equilibrium of the atomic system and the radiation He introduced the concept of stimulated (induced) emission in which the external radiation persuades the excited atoms to jump from the higher energy level to the lower one by giving up energy Thus, according to Einstein the equilibrium of matter and radiation governed by three processes: (i) stimulated (induced) absorption (ii) spontaneous emission (iii) stimulated (induced) emission Let N1 and N2 be the number of atoms in the energy levels E1 and E2 respectively and u(w) be the density of external radiation The number of stimulated absorption per unit time per unit volume is proportional to the number of atoms in the initial state and the energy density of the radiation i.e., (6.2.2) R 12 = B12 N1 u (w) where B12 is proportionality constant The number of spontaneous emission per unit time/volume depends only on the number of atoms in the excited state i.e .(6.2.3) R 21 = A21 N2 where A21 is a constant Fig 6.1.1 Induced, spontaneous and stimulated transitions The number of stimulated emission per unit time/volume is proportional to the number of atoms in the excited state and the density of stimulating radiation i.e R * 21 = B21 N2 u (w) .(6.2.4) The coefficients A and B’s are called the Einstein’s coefficients In thermal equilibrium the number of upward transitions must be equal to the number of downward transitions i.e R 12 = R21 + R*21 B12 N1 u(w) = A21 N2 + B21 N2 u(w) www.pdfgrip.com Lasers and Masers  605 Whence u(ω) = A21 B21  B12 N1  − 1   B21 N2  .(6.2.5) According to Boltzmann equation N1 = c.e− E1/kT N2 = c.e− E2 /kT where c is a constant From these equations, we find N1 = e(E2 − E1 )/kT = ehω /kT N2 .(6.2.6) Making use of this result we can write eqn (6.2.5) as u(ω) = A21 B21 B12 hω/kT e −1 B21 .(6.2.7) According to Planck’s radiation law the energy density of a radiation, which is in equilibrium with matter, is given by u(ω) = hω3 π c e hω / kT −1 .(6.2.8) Comparison of (6.2.7) and (6.2.8) gives and A21 hω3 = B21 π c .(6.2.9) B 12 = B21 .(6.2.10) The Einstein’s coefficients represent the transition probabilities per unit time Eqn.(6.2.10) states that the stimulated absorption and stimulated emission are equally probable The ratio of number of spontaneous transitions to that of stimulated emissions is given by R 21 * R = 21 = A21 B21u(ω) hω3 ( u ω) π c = ehω /kT − www.pdfgrip.com .(6.2.11) 606 Introduction to Modern Physics In microwave region (l = 0.1m) at room temperature T = 300 K 12400 eV.Å hω ch = = = 4.96 × 10−4 ≈ × 10−4 kT λkT 10 Å (0.025eV ) ( ) ehω/kT ≈ whence R 21 R*21 ≈0 This means that in the microwave region the rate of stimulated emission is much higher than the spontaneous emission Also N2 = e− hω/kT ≈ N1 i.e., the energy levels E1 and E2 are nearly equally populated In the optical region (l = 5000 Å), we have 12400 eV Å ch hω = = ≈ 100 kT λ kT (5000 Å)(0.025 eV) \ R21 * R = e100 − ≈ a very large number 21 That is, the spontaneous emission is more predominant in the optical region The photons or the wave trains emitted in spontaneous emission move in random directions and have no definite phase relationship with each other In other words, the radiation is incoherent On the other hand, the photons or the wave trains emitted in stimulated emission have the same frequency, the same direction of propagation, the same phase and the same state of polarization i.e., the stimulating and stimulated radiation are strictly coherent This feature of stimulated emission underlies the action of a laser – a device in which the number of stimulated emissions predominate the spontaneous emission Since, the number of stimulated emissions is proportional to the number of atoms in the upper level, it is essential to increase the number of atoms in the upper level 6.3 POPULATION INVERSION When an atomic system is in thermodynamic equilibrium, Boltzmann’s law determines the distribution of atoms in different energy states Ni = C.e− Ei /kT .(6.3.1) where Ni is the number of atoms in energy state Ei and T is the temperature of the system It is evident from the above formula that the population in a state diminishes with increase in energy of www.pdfgrip.com Lasers and Masers  607 that state If an atomic system has two characteristic energy states E1 and E2 (> E1) with populations N1 and N2 respectively then N1 = e−(E1 −E2 )/kT N2 .(6.3.2) Fig 6.3.1 Population inversion Fig 6.3.2 A photon stimulates an excited atom causing it to emit a photon The incident and the emitted photons induce other exited atoms to emit photons This process rapidly multiplies and an intense laser beam builds up At equilibrium, the lower energy state will be more populated than the upper state Consequently in such system the absorption of radiation will predominate over the stimulated emission A light beam while passing through such medium will get attenuated A medium having this property is said to have positive absorption coefficient To obtain amplification of incident light, a condition has to be created in which stimulated emission predominates over the stimulated absorption Obviously this can be achieved if we can bring the system in a state with greater number of atoms in the upper state www.pdfgrip.com 608 Introduction to Modern Physics than that in the lower state A system having N2 > N1 is said to have inverse population From equation (6.3.2), we can see that the states of population inversion (N2 > N1, E2 > E1) correspond to negative value of temperature T and therefore such states are called states with negative temperature The population inversion is obtained by what is called optical pumping, which is a process of imparting energy to the working substance of a laser to transfer the atoms to excited states In a substance with inverse population the stimulated emission may exceed the absorption of light and hence a light beam while passing through the medium will be amplified Such a medium is called active medium Allowing the light beam to traverse the same active medium many times before it emerges may further enhance its amplification 6.4 THREE LEVEL LASER In case of two levels laser, the method of pumping fails to produce the desired population inversion because the excited atoms residing in the excited state for a very short time interval lose their energy through spontaneous emission and through collision with electrons and drop to the lower level To overcome this difficulty a three levels scheme was suggested by Basov, Prokhorov and Townes in 1955 and the ruby laser was developed in 1960 by T Meiman In order to understand the working principle of three-levels laser let us consider the energy level diagram of atom participating in lasing action Such an atom has three energy levels shown in the figure By means flash light of appropriate frequency the atoms are lifted from the ground state E1 to excited state E2 where their life time is extremely small (10–8sec) Some of the atoms spontaneously revert to the ground state whose probability is small But most of the atoms rapidly pass through non-radiative transition to the metastable state (E3) where their life time is considerable long (=105 times) and stay there for long Fig 6.4.1 Three level laser In this way the population in the level E3 increases and that in E1 decreases The state of population inversion is thus achieved The photon emitted in the spontaneous transition (E3 ® E1) although its probability is small but not zero, induces the atoms in the metastable state to drop to the ground state The photon emitted in this way further induces other excited atoms The stimulated emission builds up rapidly www.pdfgrip.com Lasers and Masers  6.5 609 THE RUBY LASER A ruby is aluminium oxide (Al2O3) crystal in which some of the aluminium atoms are substituted by chromium ions (Cr3+) In such a crystal, stimulated transitions occur in the chromium ions The chromium ion has two wide energy bands E2 and E3 very close to the ground level E1 and also a double level E4 and E5 Light tube, which produces light with a broad band of frequencies, is used to illuminate the chromium ions Under the action of this light the chromium ions are raised from the ground state to E2 and E3, which is a group of closely spaced energy levels In these energy states the life-time of ions is very small (=10–8 sec.) During this time some of the ions pass to the ground state (spontaneous emission) Most of the ions, however, pass to the metastable state E4 and E5 The probabilities of these transitions are much greater than the spontaneous transitions (E2 ® E1, E3 ® E1) The energy of non-radiative transitions (E2 ® E4, E3 ® E5) is transferred to the crystal lattice In the metastable states the life-times of ions is about 10–3 sec which is about 105 times greater than the life-time in ordinary excited state In this way the population of metastable state may exceed that of the ground state E1 In other words, the population of these two states will be inverted The population inversion is promoted still more by the low probability of the spontaneous transition of ions from metastable states to the ground state The probability of spontaneous emission from the metastable states to the ground state is small but not zero A photon emitted in spontaneous transition (E4 ® E1, E5 ® E1) may cause stimulated emission producing additional photons of wavelengths 6927 Å and 6943 Å, which subsequently further stimulate other excited ions to jump to the ground state This process repeats again and again and a cascade of photons is formed The photons whose direction is parallel to the axis of the ruby rod suffer multiple reflections at its ends In their way, these photons stimulate the excited ions to return to the ground state by emitting photons The process of formation of cascade results in increase in intensity of the beam Fig 6.5.1 Action of Ruby laser www.pdfgrip.com 610 6.6 Introduction to Modern Physics HELIUM-NEON LASER The Helium-Neon gas laser consists of a mixture Helium and Neon in the ratio of 7: The gaseous is kept at low pressure (1 mm of Hg) in a discharge tube of about 1m long At the both ends of the tube parallel mirrors are placed one of which is partly transparent The spacing of mirrors is equal to integral multiple of half-wavelength of the laser radiation An electric discharge is produced in the gas by connecting the electrodes to a high frequency a.c source The electrons from the discharge collide with helium atoms and the latter are excited to metastable states of energies 19.81 eV and 20.5 eV These excited states of helium are very close to the excited states of neon When excited helium atoms collide with neon atoms in the ground state, a resonant energy transfer takes place and the neon atoms are raised from their ground states to excited states If the rate of upward transitions is greater than the radiative decay of the excited atoms, the population in the excited state exceeds that in the ground state In this way, population inversion is achieved Thus, the purpose of helium atoms is to create population inversion in neon atoms The important LASER transitions in neon atoms are: 3s ® 3p l = 3.39 mm E4 ® E E ® E5 3s ® 2p l = 6328 Å E3 ® E5 2s ® 2p l = 1.15 mm Fig 6.6.1 Helium-Neon laser The wavelengths 3.39 µm and 1.15 µm are not in visible region Fig 6.6.2 Transitions in He-Ne Laser www.pdfgrip.com Lasers and Masers  6.7 611 AMMONIA MASER In 1955 Gordon, Zeiger and Townes first developed the ammonia maser The vibrational energy levels of ammonia molecule consist of pairs of energy levels with small separation compared to the separation of one pair from the other The lowest pair of energy levels, which has a separation of 10 – eV, is used in the fabrication of ammonia maser This energy difference corresponds to frequency 23870 MHz or wavelength 1.25 cm By heating the ammonia molecules in an oven a collimated beam of molecules is obtained The beam consists of molecules in the upper and the lower excited states In order to separate these two kinds of molecules, the beam is passed through an inhomogeneous electric field produced by four metallic rods placed symmetrically around the beam and connected to a d.c source of 15 kV This arrangement acts as a focuser and separator both Due to different electric properties (polarizabilities) the two kinds of molecules behave differently in the inhomogeneous electric field The polarizabilities of molecules in the lower and the upper states are opposite in sign Therefore, the molecules in the upper state are repelled away and those in the lower state are attracted towards the electrodes Thus the molecules in the lower state are dispersed and those in the upper state proceed undeviated along the axis and enter a cavity All the molecules in the cavity are in the upper state A signal of frequency 23870 MHz is fed to the cavity that triggers the stimulated emission The amplified radiation comes from another aperture of the cavity Fig 6.7.1 Ammonia maser 6.8 CHARACTERISTICS OF LASER The most striking features in which laser differs from conventional sources are following: Directionality: The light from a conventional source spreads in all direction whereas the radiation from a laser travels in one direction only Owing to this property the light from a laser can be transmitted over a very long distance without appreciable spread Intensity: Due to diverging nature of ordinary light, its intensity falls rapidly with distance whereas the intensity of laser radiation remains almost unaltered after traversing a very long distance www.pdfgrip.com 612 Introduction to Modern Physics Monochromatic nature of radiation: The photons emitted in stimulated emission have essentially the same frequency and is therefore is strictly monochromatic The wave trains emitted during stimulated emission possesses definite phase relationship with each other and hence the laser light is highly coherent Applications The directional and the coherence properties of laser light allows it to be used where tremendous spatial concentration of power is required The extremely concentrated power may be used in constructive and destructive both ways In constructive way, it may be used in cutting hard material, drilling metal plates, producing high temperature for nuclear fusion reaction, etc In destructive ways it may be used to destroy enemy installations, planes, war-heads missiles, etc In medicine laser light is used as a very useful surgical tool In communication it is used to transmit information more conveniently than radio and microwaves In fact laser has revolutionized the field of communication In scientific research it offers as an extraordinary light source for investigating molecular structure (Raman effect) QUESTIONS AND PROBLEMS Explain the terms: induced absorption, spontaneous emission and stimulated emission Obtain expressions for Einstein’s A and B coefficients and discuss their physical significance Distinguish between spontaneous and stimulated emission of radiation Obtain a relation between the transition probabilities of two emissions Explain population inversion and optical pumping with suitable examples Explain what you understand by meta-stable states and population inversion? How is the population inversion achieved and why is it necessary for producing laser beam? Describe briefly the characteristics of Laser What is the principle of three level laser? Describe the principle, construction and working of three level Ruby laser Describe the principle and working of Helium-Neon laser with suitable diagrams Describe the principle and working of ammonia maser giving appropriate diagrams www.pdfgrip.com INDEX Aberration of light 21 Absolute activity 322 Active medium 608 Alpha decay 163 Alpha-particle scattering experiment 379 Angular momentum 179 Anharmonicity constants 551 Anti-stokes frequency 586 Anti-stokes lines 582 Antistokes’ frequencies 72 Aufbau’s principle 415 Balmer formula 388 Balmer series 384, 389 Band head 560, 569 Band origin 570 Band system 565 Basis functions 112 Black body radiation 50, 328 Bohr magneton 417 Bohr orbit 386 Bohr’s theory of hydrogenic atoms 385 Bose gas 321 Bose-Einstein condensation 324 Bose-Einstein distribution function 358 Bose-Einstein statistics 251, 305 Bosons 252, 305 Bracket series 384, 389 Bragg’s spectrometer 534 Braking radiation 70 Breit’s scheme 427 Bremsstrahlung 70 Bremsstrahlung process 523 Burger-Dorgello-Ornstein sum rule 482 C.J davisson 80 Calcium triads 493 Canonical distribution 284 Canonical ensemble 284 Central force 225 Characteristic radiation 71 Characteristic temperature 365 Characteristic X-rays 521 Chemical potential 279, 305, 321 Classical principle of relativity Compound doublet 476 Compound triplet 491 Compton shift 65 Compton wavelength 66 Compton’s effect 65 Condensation temperature 324 Condon parabola 577 Continuous 521 Correspondence principle 397 Critical temperature 323 Cut-off frequency 62 Cut-off potential 60 Debye model 362 Debye T3 law 364 Degeneracy 197, 309 www.pdfgrip.com 614 Introduction to Modern Physics Degeneracy temperature 324 Degenerate 112, 252, 253, 257, 312, 324 Degenerate states 309 Degeneration of fermi gas 313 Degree of degeneracy 112, 257 Density function 271 Density of states 198, 309 Deslandre table 565 Diffuse series 471 Dirac formalism 178 Doppler’s effect 19 Dual nature of radiation 75 Duane and Hunt law 523 Dulong-Petits law 361 Effect or screening effect 527 Einstein frequency 359 Einstein temperature 361 Einstein’s coefficients 603 Electronic spectra 562 Ensemble average 273 Enthalpy 279 Equipartition theorem 288 Equivalent electrons 431 Ergodic hypothesis 273 Ergodic surface 281 Exchange interaction 420 Expectation value 113, 121 Fermi energy 310 Fermi gas 309 Fermi level 305, 311 Fermi-Dirac distribution 358 Fermi-Dirac statistics 251, 302 Fermions 252, 302 Fine structure 443 Fine structure constant 387, 404 Fine-structure 477 Fine-structure levels 427 First overtone 552 Fitzgerald contraction 15 Fluorescence 591 Fortrat diagram 571 Fourier’s transform 85 Frame of reference Franck and Hertz experiment 396 Franck-Condon principle 573 Fugacity (absolute activity) 322 Fundamental (Bergmann) series 471 Fundamental band 552 Galilean transformation G-factor spectroscopic splitting factor 437 Gibb’s free energy 279 Gibbs canonical probability distribution 284 Gibbs paradox 283, 338 Grand canonical ensemble 351 Grand partition function 351 Grand potential 354 Group velocity 84, 86 C-space 268, 271 Gyromagnetic ratio 417 Hamilton’s equations 268 Heat capacity 297 Heisenberg’s uncertainty principle or the principle of indeterminacy 87 Heliocentric frame Helmholtz free energy 279, 280, 346 Hermite polynomials 210 Homogeneity Hot bands 552 Hund’s rule 416, 434 Incoherent scattering 65 Inertial frames Interaction energy in J-J coupling 455 www.pdfgrip.com Index Interaction energy in L-S coupling 451 Internal energy 279 Interval 18 Inverse photoelectric effect 523 Inverse population 608 Isotopic shift 394, 547, 553 Isotropy Morse potential 551 µ-space 268 Multiplet 427 Multiplets 477 Muonic (mesic) atom 393 Negative temperature 608 Non-degenerate 112, 253, 312 Non-equivalent electrons 427 Non-inertial frame Nuclear motion 391 Number space 255 J-J coupling 425 L.H Germer 80 Ladder operators 120, 180, 184 Lamb shift 446 Lande Interval rule 459, 491 Laser 603 Linear absorption coefficient 529 Lorentz contraction 15 Lorentz number 501 Lorentz transformation equations 10 Lorentz transformations 10 Lowering operator 181 L-S coupling 420 Lyman series 383, 389 Operators 106 Optical pumping 608 Orbital 414 Orbital (azimuthal) quantum number 413 Orbital g-factor 417 Orthohelium 495 Overlap integral 578 Macroscopic state 256 Magnetic quantum number (ml) 413 Magnetic sub-levels 500 Maser 603 Mass-energy equivalence 26 Maxwell-Boltzmann or classical statistics 251 Meson 305 Metastable state 608, 496 Michelson-Morley experiment Microscopic state 257 Modified radiation 65 Momentum of photon 28 Monoatomic gas 337 Monoatomic ideal gas 344 Pair production 30 Parahelium 494 Parity 186 Particle velocity 86 Partition function 286 Paschen series 384, 389 Pauli exclusion principle 342 Pauli principle 414 Pauli’s exclusion principle 309, 416 P-branch 568 Periodic boundary conditions 199 Pfund series 384, 389 Phase point 266 Photoelectric effect 60, 523 Photons 305 Planck’s radiation law 328, 367, 54 Polarizability 584 www.pdfgrip.com 615 616 Introduction to Modern Physics Positronium atom 392 Postulate of equal a priori probability 272 Potential well 189 Principal quantum number 412 Principal series 471 Probability amplitude 102 Probability density 102 Probability current density 103 Progression 565 Q-branch 568 Quantization of phase space 269 Quantum defect 471 Radiant emittance 50 Raising operator 181 Raman effect 72, 582 Rayleigh (or elastic) scattering 582 Rayleigh and Jeans law 52 R-branch 560, 568 Regular doublet 527 Relativistic dynamics 24 Representative point 266 Resonance scattering 157 Retarding potential 60 Rotational characteristic temperature 348 Rotational constant 544 Rotational raman spectrum 588 Rotational spectra 543 Ruby laser 608, 609 Runge’s law 477, 491 Russell-Saunders coupling 420 Rydberg constant 388 Rydberg-Schuster law 477, 491 Sackur-Tetrode 283 Sackur-Tetrode equation 347 Satellite 476 Second overtone 552 Sequence 565 Shading off 570 Sharp series 471 Shell 414 Simultaneity 15 Singlet 478, 487 Sommerfeld’s free electron theory 309 Space quantization 413, 441 Spectral distribution of energy 51 Spectral series of hydrogen atom 383 Spectral terms 427 Spin g-factor 417 Spin orbit interaction energy 443 Spin quantum number (ms) 413 Spin-orbit interaction 420, 425, 443, 478 Spin-relativity doublet 527 Spontaneous emission 604 Stationary state 100 Statistical weight 258 Stefan’s law 56 Step barrier 147 Stern and gerlach experiment 441 Stimulated (induced) absorption 603 Stimulated (induced) emission 604 Stokes frequency 586 Stokes lines 582 Stokes’ frequencies 72 Sub-shell 414 Thermionic emission 318 Thermodynamic probability 258, 278 Thomas precession 444 Three dimensional potential well 195 Threshold 62 Threshold frequency 60 Threshold wavelength 60, 62 Time averaged value 273 Time dilation 16 Transformation of acceleration www.pdfgrip.com Index Transformation of length Transformation of momentum and energy 28 Transformation of velocity Triplet 487 Two-body problem 225 Unmodified radiation 65 Variation of mass with velocity 22 Vector model 420 Vibrational characteristic temperature 350 Vibrational constant 549 Vibrational raman scattering 587 Vibrational spectra 549 Wave function 98, 102 Wein’s law 52 White radiation 71, 521 Wien’s displacement law 57 Work function 61 X-rays 520 Zeeman levels 500 Zero-point energy 210, 550 www.pdfgrip.com 617 ... www.pdfgrip.com .(1.5.9) 12 Introduction to Modern Physics Fig 1.5.2 (iii) Instead of mechanical particle, let the observers see photon or light wave front According to the second postulate (the constancy... Valence Electron Atom 418 Vector Model of Atom 420 Atomic State or Spectral Term Symbol 426 Ground State of Atoms with One Valence Electron (Hydrogen and Alkali Atoms) 426... expansion have been omitted www.pdfgrip.com .(1.3.1) Introduction to Modern Physics For an observer stationed in ether frame the beam to return to the plate P after suffering reflection at the mirror