Physics Galaxy Optics & Modern Physics - Study Guide PDF

Study Physics Galaxy with www.puucho.com Volun1e1V Optics 8 Modern Physics 'Physics Galaxy' iOS and Android Application 'Physics Galaxy' Mobile Application is a quick way to access World's Largest Video Encyclop...

Study Physics Galaxy with www.puucho.com Volun1e1V Optics 8 Modern Physics 'Physics Galaxy' iOS and Android Application 'Physics Galaxy' Mobile Application is a quick way to access World's Largest Video Encyclopedia of Online Video Lectures by Ash1sh Arora Sir on High School Physics to prepare for JEE(Mains), NEET, and BITSAT. For JEE(Advance) and AIIMS more than 700 advance concept video illustrations will help students to Excel 1n their conceptApplicabons. Download the Application on your device with many more content and features. www.puucho.com Study Physics Galaxy with www.puucho.com Students of IX to XI I for '1arious competiti'1e exams includin9 JEE-MAIN I JEE-ADVANCE BITSAT I NEET I AIIMS I NTSE & KVPY PG Streaming Classes Courses Live & On-Demand Streaming - PG Classes (No internet required) 7000+ Video Lectures Junior, Middle & High School Physics PG on Youtube Largest channel on high school physics Discussion Panel Get your queries solved 8000+ Online MCQs Junior, Middle & High School Physics www.puucho.com Study Physics Galaxy with www.puucho.com Physics Gala Volume IV Optics & Modern Physics Ashish Arora Mentor & Founder PHYSICSGALAXY.COM Worlds largest encyclopedia ofon line video lectures on Higl, School Physics ~ G K Publications (P) Ltd www.puucho.com  Study Physics Galaxy with www.puucho.com CL MEDIA (P) L,TD. First Edition 2000 · Revised Edition 2017 · Edition 2019-20 © AUTHOR Administrative:and Production Offices No part ofthis book may be reproduced in a retrieval syst.em Published by : CL Media (P) Ltd. · or transmitted, in any form or by any means, electronics, A-41, Lower Ground Floor, inechanical, photocopying, recording, scanning and or Espire Building, without the written.pernrission of the author/publisher. Mohan Cooperative Industrial Area, Main Mathura Road, New Delhi - 110044 Marketed by : G.K. Publications (P) Ltd. A-41, Lower Ground-Floor, Esplre Building, ISBN 978-93-87444-70-6 Mohan Cooperative Industrial Area, Main Mathura Road, Typeset by : CL Media DTP Unit ·. New Delhi - 110044 For product information : Visit www.gkpublications.com or email to gkp@gkpublications.?om www.puucho.com  Study Physics Galaxy with www.puucho.com ,-------- - - - - - - - - - - - - - - - --------- Dedicated to My Parents, Son, Daughter. and My belo.ved wife ----------- ------ ___ _, www.puucho.com  Study Physics Galaxy with www.puucho.com In his teaching career since 1992 Ashish Arora personally mentored more than I 0000 IITians and students who reached global heights in various career and profession chosen. It is his helping attitude toward students with which all his students remember him in life for his contribution in their success and keep connections with him live. Below is the list of some of the successful students in International Olympiad personally taught by him. NAVNEET LOIWAL International GOLD Medal in /Ph0-2000 at LONDON, Also secured AIR-4 in IIT JEE 2000 PROUD FOR INDIA : Navncet Loiwal was the first Indian Student who won first International GOLD Medal for our country in International Physics Olympiad. DUNGRA RAM CHOUDHARY AIR-I in IIT JEE 2002 HARSHIT CHOPRA National Gold Medal in INPh0-2002 and got AIR-2 in IIT JEE-2002· KUNTAL WYA A Girl Student got position AIR-8 in IIT JEE 2002 LUVKUMAR National Gold Medal in· INPb0-2003 and got AIR-3 in IIT JEE-2003 RAJHANS SAMDANI National Gold Medal in JNPh0-2003 and got AIR-5 in IIT JEE-2003 SHANTANU BHARDWAJ International SILVER Medal in IPh0-2002 at INDONESIA SHALEEN HARLALKA lntern'ational GOLD Medal in IPb0-2003 at CHINA and got AIR46 in IIT JEE-2003 TARUN GUPTA National GOLD Medal in INPb0-2005 APEKSHA KHANDELWAL National GOLD Medal in INPb0-2005 ABHINAV SINHA Hon'ble Mt.nsion Award in APb0-2006 at KAZAKHSTAN RAMAN SHARMA International GOLD Medal in IPb0-2007 at /RAN and got AIR-20 in IIT JEE-2007 PRATYUSH PANDEY lntt.rnational SILVER Mt.dal in IPb0-2007 at IRAN and got AIR-85 in 11.T JEE-2007 GARVIT JUNIWAL. International GOL_D Mt.dal it1 /Pb0-2008 at VIETNAM and got AIR-10 in IIT JEE-2008 ANKIT PARASHAR National GOLD Mt.dal in INPb0-2008 HEMANT NOVAL National GOLD Medal in INPb0-2008 and got AIR-25 in IIT JEE-2008 ABHISHEK MITRUKA National GOLD Medal in INPb0-2009 SARTHAK KALANI National GOLD Medal in !NPh0-20~9 ASTHA AGARWAL /ntt.rnational SILVER Medal in IJS0-2009 at AZERBAIJAN RAHUL GURNANI International SILVER Medal in IJS0-2009 at AZERBAIJAN AYUSH SINGHAL Intt.rnational SILVER Medal in IJS0-2009 at AZERBAIJAN MEHULKUMAR lntt.rnational SILVER Mida/ in /Pb0-2010 at CROATIA and got AIR-19 in IIT JEE-2010 ABHIROOP BHATNAGAR National GOW Medal in INPb0-2010 AYUSH SHARMA International Double GOLD Medal i11 IJS0-2010 at !'JIGERIA MSTHA AGRAWAL Hon'ble Mension Award in APh0-2011 at ISRAEL and got AIR-93 in IIT JEE 2011 ABHISHEK BANSAL !Jational GOW Medal in INPb0-2011 SAMYAKDAGA National GOW Medal in INPh0-2011 SHREY GOYAL. Nationai GOW Medal in INPb0-2012 and secured AIR-24 in IIT JEE 2012 RAHUL GURNANI National GOLD Medal in INPb0-2012 JASPREET SINGH JHEETA National GOLD Medal in /NPh0-2012 DIVYANSHU MUND National GOW Medal in INPb0-2012 SHESHANSH AGARWAL International SILVER Medal in IA0-2012 at KOREA SWATI GUPTA International SILVER Medal in IJS0-2012 at IRAN PRATYUSH RAJPUT /nternationa~ SILVER Medal in IJS0-2012 at IRAN SHESHANSH AGARWAL International BRONZE Medal in IOAA-2013 at GREECE SHESHANSH AGARWAL International GOLD Medal in /OAA-2014 at ROMAN/A, SHESHANSH AGARWAL International SILVER Medal in /Pb0-2015 at INDIA and secured AIR-58 in JEE(Advanccd}-2015 VIDUSHI VARSHNEY International SILVER Medal in IJS0-2015 to he held at SOUTH KOREA AMAN BANSAL AIR-1 in JEE Advanced 2016 KUNAL GOYAL AIR-3 in JEE Advanced 2016 GOURAV DIDWANIA AIR-9 in JEE Advanced 2016 DIVYANSH GARG International SILVER Medal in IPb0-2016 at SWITZERLAND www.puucho.com  Study Physics Galaxy with www.puucho.com ABOUT THE AUTHOR The complexities of Physics have given nightmares to many, but the homegrown genius ofJaipur- Ashish Arora has helped several students to live their dreams by decoding it. Newton Law of Gravitation and Faraday's Magnetic force of attraction apply perfectly well with this unassuming genius. A Pied Piper of students, his webportal https://www.physicsgalaxy.com, The world's largest encyclopedia ofvideo lectures on high school Physics possesses strong gravitational pull and magnetic attraction for stJdents who want to make it big in life. Ashish Arora, gifted with rare ability to train masterminds, has mentored over 10,000 I!Tians in his past 24 years of teaching sojourn including lots of students made it to Top 100 in IIT-JEE/JEE(Advance) includingAIR-1 and many in Top-I 0. Apart from that, he has also groomed hundreds of students for cracking International Physics Olympiad. No wonder his student Navneet Loiwal brought laurel to the country by becoming the first Indian to win a Gold medal at the 2000 - International Physics Olympiad in London (UK). His special ability to simplify the toughest of the Physics theorems and applications rates him as one among the best Physics teachers in the world. With this, Arora simply defies the logic that perfection comes with age. Even at 18 when he started teaching _ Physics while pursuing engineering, he was as engaging as be is now. Experience, besides graying his hair, has just widened his horizon. · Now after encountering all tribes of students - some brilliant and some not-so-intelligent - this celebrated teacher has embarked upon a noble mission to make the entire galaxy of Physics inform of his webportal PHYSICSGALAXY.COM to serve and help global students in the subject. Today students from 221 countries are connected·with this webportal. On any topic of physics students can post their queries in INTERACT tab of the webportal on which many global experts with Ashish Arora reply to several queries posted online by students. Dedicated to global students of middle and high school level, his website www.physicsgalaxy.com also has teaching sessions dubbed in American accent and subtitles in 87 languages. For students in India preparing for JEE & NEET, his on line courses will be available soon on PHYSICSGALAXY.COM. www.puucho.com  Study Physics Galaxy with www.puucho.com FOREWORD It has been pleasure for me to follow the progress Er. Ashish Arora has made in teaching and professional career. In the last about two decades he has actively contributed in developing several new techniques for teaching & learning of Physics and driven important contribution to Science domain through nurturing young students and budding scientists. Physics Galaxy is one such example of numerous efforts he has undertaken. The 2nd edition of Physics Galaxy provides a good coverage of various topics of Mechanics, Thermodynamics and Waves, Optics & Modern Physics and Electricity & Magnetism through dedicated volumes. It would be an important resource for students appearing in competitive examination for seeking admission in engineering and medical streams. "E-version" of the book is also being launched to allow easy access to all. The structure of book is logical and the presentation is innovative. Importantly the book covers some ofthe concepts on the basis ofrealistic experiments and examples. The book has been written in an informal style to help students learn faster and more interactively with better diagrams and visual appeal of the content. Each chapter has variety of theoretical and numerical problems to test the knowledge acquired by students. The book also includes solution to all practice exercises with several new illustrations and problems for deeper learning. I am sure the book will widen the horizons of knowledge in Physics and will be found very useful by the students for developing in-depth understanding of the subject. May 13, 2017 Prof. Sandeep Sancheti Ph.D. (U.K.), B.Tech. FIETE, MIEEE President Manipal University Jaipur www.puucho.com  Study Physics Galaxy with www.puucho.com PREFACE For a science student, Physics is the most important subject, unlike to other subjects it requires logical reasoning and high imagination of brain. Without improving the level ofphysics it is very difficult to achieve a goal in the present age of competitions. To score better, one does not require hard working at least in physics. Ii just requires a simple understanding and approach to think a physical situation, Actually physics is the surrounding of our everyday life. All the six parts of general physics-Mechanics, Heat, Sound, Light, Electromagnetism and Modern Physics are the constituents of our surroundings. If you wish to make the concepts of physics strong, you should try to understand core concepts of physics in practical approach rather than theoretical. Whenever you try to solve a physics problem, first create a hypothetical approach rather than theoretical. Whenever you try to solve a physics problem, first create a hypothetical world in your imagfnation about the problem and try to think psychologically, whatthe next step should be, the best answer would be given by your brain psychology. For making physics strong in all respects and you should try to merge and understand all the concepts with the brain psychologically. The book PHYSICS GALAXY is designed in a totally different and friendly approach to develop the physics concepts psychologically. The book is presented in four volumes, which covers almost all the core branches of general physics. First volume covers Mechanics. It is the most important part of physics. The things you will learn in this book will form a major foundation for understanding of other sections of physics as mechanics is used in all other branches of physics as a core fundamental. In this book every part of mechanics is explained in a simple and interactive experimental way. The book is divided in seven major chapters, covering the complete kinematics and dynamics of bodies with both translational and rotational motion then gravitation and complete fluid statics and dynamics is covered with several applications. The. best way of understanding physics is'·the experiments and this methodology I am using in my lectures and I found that it helps students a lot in concept visualization. In this book I have tried to translate the things as I used in lectures. After every important section there are several solved examples included with simple and interactive explanations. It might help a student in a way that the student does not require to consult any thing with the teacher. Everything is self explanatory and in simple language. One important factor in preparation of physics I wish to highlight that most of the student after reading the theory of a concept start working out the numerical problems. This is not the efficient way of developing concepts in brain. To get the maximum benefit of the book students should read carefully the whole chapter at least three or four times with all the illustrative examples and with more stress on some illustrative examples include.din the chapter. Practice exercises included after every theory section in each chapter is for the purpose of in-depth understanding of the applications of concepts covered. Illustrative examples are a explaining some theoretical concept in the form of an example. After thorough reading of the chapter students can start thinking on discussion questions and start working on numerical problems. Exercises given at the end of each chapter are for circulation of all the concepts in mind. There are two sections, first is the discussion questions, which are theoretical and help in understanding the concepts at root level. Second section is of conceptual MCQs which helps in enhancing the theoretical thinking of students and building logical skills in the chapter. Third section of numerical MCQs helps in the developing scientific and analytical application of concepts. Fourth section of advance MCQs with one or more options correct type questions is for developing advance and comprehensive thoughts. Last section is the Unsolved Numerical Problems which includes some simple problems and some tough problems which require the building fundamentals of physics from basics to advance level problems which are useful in preparation ofNSEP, INPhO or IPhO. In this second edition of the book I have included the solutions to all practice exercises, conceptual, numerical and advance MCQs to support students who are dependent on their self study and not getting access to teachers for their preparation. This book has taken a shape just because of motivational inspiration by my mother 20 years ago when I just thought to write something for my_ students. She always motivated and was on my side whenever I thought to develop some new learning methodology for my students. www.puucho.com  Study Physics Galaxy with www.puucho.com '·don't have words for my best friend my wife Anuja for always·being together with me to complete this book in the unique style and format. · I would like to pay my gratitude to Sh. Dayashankar Prajapati in assisting me to complete the task in Desigu Labs of PHYSICSGALAXY.COM and presenting the book in totally new format of.second edition. At last but the most ill!portant person, my father who has devoted his valuable time to finally present the book in such a format and a simple language, thanks is a very small word for his dedication in this book. In this second edition I have tried my best to make this book error free but owing to the nature of work, inadvertently, there is possibilityoferrors left untouched. I shall be grateful to the readers, ifthey point out me regarding errors and oblige me by giving their valuable and constructive suggestions via emails for further improvement of the book. Date: May, 2017 Ashish Arora PHYSICSGALAXY.COM B-80, Model Town, Malviya Nagar. Jaipur-302017 e-mails: [email protected] ashashl [email protected] www.puucho.com  Study Physics Galaxy with www.puucho.com CONTENTS ---------- ------- -------·· ·-- -- Chapter I Atomic Physics __ __ _ 1-481 -- -- _ 1 1.1 A Brief History to Alomic Physics 2 1.2 Thomson S Alomic Model 2 1.3 Ruthorford's Atomic Model 3 1.4 Bohr's Model ofan Atom 3 1.4.1 First Poslulate 4 1.4.2 Second Pos/Ulate 4 1.4.3 Third Postulate 4 1.5 Properties of Electron in Bohr's Atomic Model 5 1.5.1 Radius of nth Orbit in Bohr Model 5 1.5.2 Velocity of Electron in nth Bohr's Orbit 5 1.5.3 Angular Velocity of Electron in nth Bohr's Orbit 5 1.5.4 Frequency of Electron in nth Bohr's Orbrt 6 1.5.5 Time period of Electron in nth Bohr's Orbit 6 1.5.6. Current in nth Bohr's Orbit 6 1.5.7 Magnetic Induction at the Nucleus Due to nth Orbit 6 1.5.8 Magnelic Moment of the nth Bohr's Orbit 6 1.5.9 Energy of Electron in nth Orbit 6 1.5.10 Energies of Differenl Energy Level in Hydrogenic Atoms 7 1.6 Excitation and Ionization of an Atom 9 1.6.! Frequency and Wavelength of Emitted Radiation 11 1.6.2 Number of Lines Emitted During, de-excitation of an Atom 12 1. 7 The Hydrogen Spectrum 12 1. 7. 1 Spectral Series of Hydrogen Atom 12 1.8 Effect of Mass of Nucleus on Bohr Model 21 1.9 Use of Bohr Model to Define Hypothetical Atomic Energy levels 25 I.IO Atomic Collisions 26 · DISCUSSION QUESTION 33 CONCEPTUAL MCQs SINGLE OP110N CORRECT 35 NUMERICAL MCQs SINGLE OPTIONS CORRECT 38 ADVANCE MCQs WITH ONE OR MORE OPTIONS CORRECT 42 UNSOLVED NUMERICAL PROBLEMS FOR PREPARATION OF NSEP. INPhO & IPhO 45 ---- -- --- -,- I Chapter2 Photo Electric Effect & Matter Waves 49-98: ---- ------------·- ---- ----- - ---- -- 2.1 Electron Emission Processes 50 2.1.1 Thermionic Emission 50 2./.2 Photoelectric Emission 50 2.1.3 Secondary Emission 50 2./.4 Field Emission 50 2.2 Photoelectric Effect 51 l.2./ Fundamental Laws of Photoelectric Effect 51 2.3 Experimental Study of Photo Electric ~jfect 55 2.3./ Kinetic Energies of Electrons Reaching Anode _ 56 2.3.2 Reversed Potential Across Discharge Tube 57 2.3.3 Cut off Potential or Stopping Potential 57 2.3.4· Effect of Change in Frequency of Light on Stopping Potential 58 2.4 No. of Photon £milled by Source Per second 62 www.puucho.com  Study Physics Galaxy with www.puucho.com 2.5 Intensity of Light due lo o Light Source 62 2.5.l Photon Flux in o light Beam 63 2.5.2 Photon Density in· o Light Beam 63 2.6 Wave Particle Dualily 70 2.6.l Momentum of a Photon 70 2.7 De-Broglie's Hypothesis 70 2. 7.1 Explanation of Bohr S Second Postulate 71 2.8 Radiation Pressure 72 2.8.1 Force Exerted by a Light Beam on a Surface 72 2.8.2 Force Exerted on any Object in the Palh of a Light Beam 72 2.8.3 Force Exerted by a Light Beam al Oblique Incidence 73 2.8.4 Recoiling of on Atom Due to Electron Transition 75 2.8.5 Variation in Wavelength of Emitted Photon with Stale of Motion of an Atom 75 2.8.6 Variation in Wavelength of Photon During Reflection 75 DISCUSSION QUESTION 80 CONCEPTUAL MCQ, SINGLE OPTION CORRECT 82 NUMERICAL MCQ, SINGLE OPTIONS CORRECT 86 ADVANCE MCQ, WITH ONE OR MORE OPTIONS CORRECT 92 UNSOLVED NUMERICAL PROBLEMS FOR PREPARATION OF NSEP, /NPhO & IPhO 95 --------, hapter3 X-Rays 99-116: - -- -- - --- - -- ·- - -- -- 3.1 lnlroduction lo X-Rays 100 3.1.1 Types of X-rays 100, 3.2 Production Mechanlsm of X-rays 100 3.2.l Conlinuous X-rays 100 3.2.2 Production of Conlinuous X-rays 100 3.2.3 Characteristic X-rays 102 3.2.4 Production of Charac/eristic X-rays 102 3.3 Moseley S Law 103 3.4 Applications of X-rays 103 DISCUSSION QUESTION 107 CONCEPTUAL MCQ, SINGLE OPTION CORRECT 108 NUMERICAL MCQ, SINGLE OPTIONS CORRECT Ill ADVANCE MCQ, WITH ONE OR MORE OPTIONS CORRECT 113 UNSOLVED NUMERICAL PROBLEMS FOR PREPARATION OF NSEP, INPhO & IPhO 115 ------------- -- -·7 hapter4 ___ ·-.. ___ _ _1_17-~_!!_6J 4.1 Composition and Structure of The Nucleus 118 4./.l Size of a-Nucleus 118 4.1.2 S1rong Nuclear Force and S/ability of Nucleus 118 4.2 Nuclear Binding Energy 119 4.2.l Mass Energy Equivalence 124 4.2.2 Binding Energy Per Nucleon 124 4.2.3 Variation of Binding Energy per Nucleon with Mass Number 124 4.3 Radioactivity 127 4.3.l Measurem,mt of Radioactivity 127 4.3.2 Fundamental Laws of Radioactivity 128 4.3.3 Rodioac_tive Decay Law 128 4.3.4 Half Life Time 129 4.3.5 Alternale form of Decay Equation in terms of Half Life Time 129 4.3.6 Mean Life Time 130 4.3. 7 Calculation of Mean Life Time. For a Radioactive Element 130 www.puucho.com  Study Physics Galaxy with www.puucho.com 4.4 Radioactive Series 135 4.4.1 Radioactive Equilibrium 136 4.4.2 Simultaneous Decaj, Modes of a Radioactive Element 136 4.4.3 Accumulation of a Radioactive Element in Radioactive Series 136 4.5 Nuclear Reactions 140 4.5_.J Q-M:ilue of Nuclear Reaction 141 4.6 Nuclear Fission 141 4.6.1 Fission of Uranium Isotopes and Chain Reaction 142 4.6.2 Liquid Drop Model 143 4.7 Nuclear Fusion 143 4.8 Properties of Radioactive Radiations 152 4.8.1 Alpha Decay 153 4.8.2 Beta Decay 153. 4.8.3 Apparent "Violation of Conservation LaWS in b-decay 154 4.8.4 Pauli's Neutrino Hypothesis 155 4.8.5 Mass Defect Calculation For b-decay 155 4.8.6 Gamma Decay 156 DISCUSSION QUESTION 161 CONCEPTUAL MCQs SINGLE OPTION CORRECT 164 NUMERICAL MCQs SINGLE OPTIONS CORRECT 168 ADVANCE MCQs WITH ONE OR MORE OPTIONS CORRECT 174 UNSOLVED NUMERICAL PROBLEMS FOR PREPARATION OF NSEP, INPhO & IPhO 177 -· ---------~·"------.--- - - - - - - - - - - - - ··-· I Chapter 5 _ Geometrical_ Optics __ _ -- __ 187-340! 5./ Understanding a Light Ray and Light Beams 188 5.1.J Different ·Types of Light Rays 188, 5.1.2 Different Types of Light Beams 189 5.2 Reflection of Light 189 5.2.1 Regular or Specular Reflection 190 5.2.2 !rreglJ[ar or Diffused Reflection 190 5.2.3 How we see an object in our surrounding 190 5.2.4 Laws of Reflection _191 5.2.5 Vector Analysis of Laws of Reflection 191 5.3 Understanding Object and Image in Geo":etrical Optics 192 5.3.1 Object in Geometrical Optics 192 5.3.2 Image in Geometrical Optics 193 5.4 Reflection and Image formation by a Plane Mirror 194 5.5 Field of new for image formed by a Plane Mirror 195 5.5.1 Field of "View of an image 195 5.5.2 Field of J'iew of a Mirror for an observer 195 5.6 Characteristics of Image formed by a Plane Mirror 196 5.6.1 Characteristic-I of Image formation by a Plane Mirror 196 5.6.2 Characteristic-2 of Image formation by a Plane Mirror 196 5.6.3 Characteristic-3 of Image formation by a Plane Mirror 197 5.6.4 Characterislic-4 of Image formation by a Plane Mirror 198 5.6.5' Characteristic-5 of Image formation by a Plane Mirror 198 5.6.6 Characteristic-6 of Image formation by a Plane Mirror 198 5.6. 7 Characterislic-7 of Image formation by a Plane Mirror 198 5.6.8 Characteristic-8 of Image formation by a Plane Mirror 199 5.6.9 Characteristic-9 of Image formation by a Plane Mirror 200 5.6.10 Characteristic-JO of Image formation by a Plane Mirror 200 5.6.11 Characteristic-11 of Image formation by a Plane Mirror 201 www.puucho.com Study Physics Galaxy with www.puucho.com 5.7 Understanding Shadow Formation 201 5.7.1 Umbra·and Penumbra Regions 202 5.7.2 Antumbra Region 203 5.8 Spherical Mirrors 206 5.8.1 Standard terms related to Spherical lef.i"ors 207 5.8.2 Focal Length of a Spherical Mirror 207 i8.3 Image Formation by a Spherical Mirror using Paraxial Rays 208 5.8.4 Standard Reflected Light Rays for Image Formation by Spherical Mirrors 208 5.8.5 Relation in focal length and Radius of Curvature of a Spherical Mirror 209 5.8.6 Image formation by Concave Mirrors 2 IO 5.8.7 Imageformatfon by Convex Mirrors 21 I 5.8.8 How an observer sees image of an extended objecl in a spherical mi"or 2 I2 5.8.9 How image produced by a spherical mi"or can be obtained on a screen 212 5.8.10 Sign Convention 213 5.9 Analysis of Image formation by Spherical Mirrors 214 5.9. 1 Mirror Formula for Location of Image 214 5.9.2 Analyzing Nature of Image Produced by a Spherical Mirror 215 5.9.3 Magnificalion Formula for· Size and Orientation of Image 215 5.9.4 Relalion in Nature and Orientation of Image 216 5.9.5 Longitudinal Magnification of Image 216 5.9.6 Superficial Magnification by a Spherical Mirror 217 5.9.7 Variation Curves of Image Distance vs Object Distance 218 5.9.8 Effect of Moving Object and Spherical Mirror on Image 221 5.9.9 Effect of shifting Principal Axis ofa_Mi"or 223 5.9.10 Image formation of distant Objects by Spherical Mirrors 224 5.9.J 1 Concepl of Reversibility of Light 224 5.10 Refraction of Light 226 5.10.J Absolute Refractive Index of a Medium 226 5.10.2 Relative Refractive Index of a Medium 226 5.10.3 Laws of Refraclion 227 5.10.4 Veclor form of Snell's Law of Refraction 227 5./0.5 Image Formation due to Refraction at a Plane Surface 228 5. 10.6 An Object placed in a Denser Medium is seen from Air 228 5.10.7 An Object placed in Air and see,i from a Denser Medium 229 5.10.8 'Shift of image due to Refraction of Light by a Glass Slab 23-1 5.10.9 Shift due to Refraction of Light by a Hollow thin walled Glass Box pla~ed inside a Denser Medium 232" 5.10.10 Lateral Displacement of Light Ray by a Glass Slab 232 5.10.JJ Lateral Displacement of a Light Ray due to Re.fraction by Multiple Glass Slabs 233 5.10.12 Concept of Reflection by a Thick Mirror 233 5.11 Refraction of Light by Spherical Surfaces 23 9 5.11.1 Analysis of Image formation by Spherical Surfaces 240 5.11.2 La/era/ Magnification of Image by Refraction 243 5./1.3 Longitudinal Magnification of Image 243 5.11.4 Effect "of mot.ion of Object or Refracting Surface on Image 243 5.12 Total fnteriial Reflection 247 5.12.1 Refraction of Light ~ysfrom a Source in a Denser Medium to Air 248 5.12.2 Cases of G_razing Incidence of Light on a Media lnterface 249 5.12.3 Refraction by a Transparent Medium of varying Refractive Index 249 5./2.4 Total Internal Reflection in a Medium of varying Refractive Index 250 5./2.5 Equation of Trajectory ofa Light Ray in a Medium· of varying Refractive Index 250 5. J 3 Prism 254 5.13.J Refraction of Light through a Trihedral Prism 2S5 5./3.2 Deviation Produced by a Small Angled Prism 2S6 5.13.3 Maximum Deviation of Light Ray by a Prism 256 5.13.4 Cqndition of a Light Ray to pass through a Prism 257 www.puucho.com Study Physics Galaxy with www.puucho.com 5.14 Thin Lenses 263 5.14,1 Conv1:rging and Diverging Behaviour of Lenses 264 5.14.2 Primary and Secondary Focus of a Lens. 264 5.14.3 Standard Reflected Light Rays for Image Formation by Thin Lenses 265 5.14.4 Image Formation by Convex Lenses 266 5.14.5 Image formation by Concave Lenses 267 5.14.6 Focal length of a thin lens 268 5.14. 7 Focal lengJh of differe'?t types of standard thin lenses 268 5.15 Analysis of Image Fqrmation by Thin Lenses 269 5. 15: I Lateral MagnificaJion in Image Formation by a Thin Lens 269 5.15.2 Longitudinal Magnification by a Thin Lens 270 5.15.3 Variation Curves of Image Distance vs Object Distance for a Thin Lens 270 5.15.4 Effect of motion of Object and Lens on Image 271 5.16 Optical Power of a Thin Lens or a Spherical Mirror 278 5.16.1 Combination of Thin Lenses 279 5.16.2 Combination of Thin Lenses and Mirrors 280 5.16.3 Deviation in a Lig~I Ray due to Refraction through a Thin Lens 283 5.16.4 Combination of Two Thin Lenses at some Separation 283 5.16.5 Multiple images produced by a Lens made up of different materials 284 5.17 Lens and Mirrors submerged in a Transparent Medium 285 5.18 Displacement MeJhod Experiment to measure focal length ofa Convex Lens 285 5.18.1 Condition of formation of Real Image by a Thin Convex Lens 286 5.18.2 pisplacement Method Experiment 286 5.19 Dispersion of Light 291 5.19.1.Dispersion of White Light through a Glass Slab 292 5.19.2 Dispersion of White Light through a Glass Prism 292 5.19.3 Dispersive Power of a Prism Material 293 5.19.4 Dispersion Analysis for a Small Angled Prism 293 5.19.5 Achromatic Prism Combination 294 5.19.6 'Direct Vision Prism Combination 294 5.20 Optical Aberrations in Lenses and Mirrors 295 5.20.1 Spherical AberraJions 295 5.20.2 Methods to Reduce Spherical Aberrations 295 5.20.3 Chromatic Aberration in a Lens 296 5.20.4 Achromatic Combination of Lenses 297 5.21 Optical Instrumenls 301 5.21.1 The Human Eye 301 5.21.2 Camera 302 5.21.3 Angular Size of Objects and Images 302 5.21.4 Simple Microscope 302 5.21.5 Magnification of Simple Microscope ·303 5.21.6 Compound Microscope 303 5.21.7 Magnifying Power ofComP0und Microscope 304 5.21.8 Tube Length of a Compound Microscope 304 5.21.9 Refracting Astronomical Telescope 304 5.21.10 Magnifying Power of a Refracting Telescope 305 5.21.11 Thbe Lenglh of a Refracting Telescope 305. 5.21.12 Reflecting Telescope 306 5.21.13 Terrestrial Telescope 306 5.21.14 Galilean Telescope 306 DISCUSSION QUESTION 31 l CONCEPTUAL MCQs SINGLE OPTION CORRECT 312 NUMERICAL MCQs SINGLE OPTIONS CORRECT 319 ADVANCE MCQs WITH ONE OR MORE OPTIONS CORRECT 325 UNSOLVED NUMERICAL PROBLEMS FOR PREPARATION OF NSEP, INPhO & IPhO 330 www.puucho.com  Study Physics Galaxy with www.puucho.com Iv·-·.;:! Chapter 6 W'!!'e_!!ptic!_______________________________ ________3_4_1_-4_0_8! 6.1 Wave Theory 342 6.1.J Dual Nature of Light 342 6. 1.2 Wavefront of a Light Wave 342 6.1.3 Huygen's Wave Theory 343 6.2 Interference of Light 343 6.2.J Coherent Sources of light and Condition of Coherence 344 6.2.2 Theory of Interference of Two Waves 344 6.2.3 Interference of hvo Coherent Waves of Same Amplitude 345 6.2.4 Intensity of Light at the Point of Interference 345 6.2.5 Condition of Path Difference for Interference 346 6.3 Young's'Double Slit Experiment (YDSE) 349 6.3.1 Analysis of Interference Pallern in YDSE 349 6.3.2 Position of Bright and Dark Fringes in YDSE Interference Pattern 350 6.3.3 Lighl Intensity on Screen in YDSE Setup 350 6.3.4 Fringe Width in YDSE Interference Pallern 351 6.~ Modifications in YDSE Setup 353 6.4.1 Effect of Changing lhe direction of Incident Light in YDSE 353 6.4.2 Effect of Submerging YDSE Setup in a Transparent Medium 354 6.4.3 Path difference between two parallel waves due lo a denser medium in path of one beam 354 6.4.4 Effect of Placing a Thin Transparent Film in front of on: of the slits in YDSE Setup 354 6.4.5 Concept of z-value in Interference Pattern of YDSE 355 6.4.6 Use of White Light in YDSE 357 6.4.7 Effect of Changing Slit Widlh in YDSE Settlp 357 6.4.8 Fresnel's Biprism as a Limiling case of YDSE 358 6.4. 9 Lloyd's Mirror as a limiting case of YDSE 359 6.4./0 Billet Split lens as a limiting case of YDSE 360 6.4.11 Interference of1ko Converging Coherent Parallel Beams of Light 360 6.5 Interference by Thin Fj/ms 366 6.5./ Interference due to Thin Film in Reflected light al Near Normal Incidence 367 6.5.2 Interference due to Thin Film in Transmitted lighl a Near Normal Incidence 368 6.5.3 Inter:ference due to a Thin Liquid Film on Glass 368 6.5.4 Interference in Reflected Light by a Very Thin Film in Air 368 6.5.5 Interference in Reflected Light from a Thin Film for Oblique Incidence 368 6.5.6 Interference in Transmilted Light from a Thin Film for Oblique Incidence 369 6.5.7 Interference in Reflected Li'ght due lo Thin Wedge shaped Film 370 6.5.8 Interference by an Air Wedge 371 6.5.9 Shape of Interference Fringes in Reflected Light from different Air Wedges 371 6.5.10 Shape of Interference Fringes due to different types of Sources 371 6. 6 Diffraction of Light 375 6.6.I Explanalion of Diffraction by Huygen's Wave !71eory 375 6.6.2 Types of Diffracti_on of Light 376 6.6.3 Dijfraclion of Lighl by a Single Slil 376 6.6.4 Analysis of DiffracJion of Light by a Single Slit 377 6.6.5 Diffraction Minima due to Single Slit 378 6.6.6 Diffraction Miiiima due to Single Slit 378 6.6.7 Observing Single Slit Diffraction Pattern on a Sc,:,een 379 6.6.8 P,ifference between Double Slit lnlerference and Single Slit Diffraclion Patlerns 379 6.6.9 Illumination Pattern due to Diffraction by a Single Slit 380 6.6."JO Diffraclion by a Small Circular Aperture 380 6. 7 Polarization of light 382 6.7.J Representation of Unpolarized Ond Polarized Light 383 6.7.2 Circularly and Elliptically Polarized Light 384 www.puucho.com  Study Physics Galaxy with www.puucho.com 6.8 Methods of Polarizing an Ordinary Light 384 6.8. I Polarization by Rejleclion 384 6.8.2 Brewster's Law 385 6.8.3 Polarizalion by Refraclion 385 6.8.4 Polarization by Double Refraction 385 6.8.5 Polarization by Dichroism 386 6.8.6 Polarization by Scallering 386 6.8.7 Malus' Law 387 6.8.8 Intensity of Polarized light through a Polaroid (Polarizer) 387 6.8.9 Optical Activity of Substances 388 DISCUSSION QUESTION 391 CONCEPTUAL MCQs SINGLE OPTION CORRECT 392 NUMERICAL MCQs SINGLE OPTIONS CORRECT 395 ADVANCE MCQs WITH ONE OR MORE OPTIONS CORRECT 399 UNSOLVED NUMERICAL PROBLEMS FOR PREPARATION OF NSEP, INPhO & IPhO 401 ANSWE~ & SOLUTIONS Chapter 1 Atomic Phys_ics 409 - 420 Chapter2 Photo Electric Effect & Matter Waves 421 - 434 Chapter3 X-Rays 435 - 440 Chapter4 Nuclear Physics aud Radioactivity 441 - 454 Chapter 5 Geometrical Optics 455 - 504 Chapter6.. WaveOpµcs sos·: 524 www.puucho.com  Study Physics Galaxy with www.puucho.com / / Atomic Physics: \ 1 FEW WORDS FOR STUDENTS.. /11 your previous classes from several we hte studied about existence ofatoms and 1111clei. However most of IS ca1111ot cite much ,, experimental evidence from them. 111 this_ cha ter we will discuss ' '' the experiments that form the basis/or our lt11owledge of atoi11s. ' ' '' Now, we examine many f1111dame11tal facts of6tolllic structures and ''' ' '' '' ' our reasons for believing in them. Th us in_ this cflpter we are going '' '' ' '' to frame our gro1111d1v_ork for further disc11ssi(?11 of afomic physics '' ' in the followi11g chapters. '' ' '' -------- ---- - - --.... ::-.___ CHAPTER CONTENTS 1.1 A BriefHistory to Atomic Physics j.6 Excitation anti /011izatio11 of a11 Atom 1.2 Thomson~ Atomic Model 1.7 The Hydrogen Spectrum 1.3 Ruthorford'sAtomic Model 1.8 Effect ofMass ofNucleus 011 Bohr Model 1.4 Bohr's Model ofa11Atom / 1.9 Use ofBohr Model to Define Hypothetical Atomic' 1.5 Energy Levels Properties ofElectron i11 i l ' s Atomic Model \ 1.10 ' ,Atomic Collisions COVER APPLICATION / /, / ,/ Alpha Pa M 13 = 12.09 eV n = 2 and n = 3 as shown in figure-1.9, which is not permissible for an electron. Thus when in ground state electron can absorb Similarly ifwe find the difference in energies of staten = I and only those photons which have energies equal to the difference n=4, we get_ in energies of the stable energy levels with ground state. If a M =E4 -E1 photon beam incident on H-atoms having photon energy not 14 equal to the difference of energy levels of H-atoms such as tiE 14 =(-0.85)-(- 13.6)eV 11 eV, the beam will just be transmitted. without any absorption tiE 14 = 12.75 eV by the H-atoms. Thus when a photon of energy 12.75 eV incidents on a hydrogen Thus to excite an electron from lower energy level to higher atom, the electron may be excited ton= 4 level ifit absorbs this levels by photons, it is necessary that the photon must be of energy equal to the difference in energies of the two energy photon. In the same fashion, the energy ofa photon required to excite the electron ofa hydrogen atom from ground state (n = I) levels involved in the transition. to next higher level (n = 2) which we call first excited state is As we know that for higher energy levels, energy of electrons given as is less. When an electron is moved away from the nucleus to M 12 =E2 -E 1 ooth energy level or at n = oo, the energy becomes O or the electron becomes free from the attraction of nucleus or it is => !iE 12 =(-3.4)-(-13.6) eV removed from the atom. Infect when an electron is in an atom, => M 12 =10.2eV its total energy is negative ( E" = - !;6 1 Z 2 ). This n~gative Here we have seen that in the ground state of a hydrogen atom sign shows that electron is under the influence of attractive electron can absorbs photons ofenergies 10.2 eV, 12.09 eV and forces ofnucleus. When energy equal in magnitude to the total 12.75 eV to get excited ton= 2, n = 3 and n =4 levels. energy of an electron in a particular energy level is given externally, its total energy becomes zero or we can say that Now we'll see what will happen when a photon of energy equal electron gets excited to oolh energy level or the electron is to 11 eV incident on this atom. From the above calculation of removed from the atom and atom is said to be ionized. energy differences of different energy levels we can say that if the electron in ground state absorbs this photon it will jump to We know that removal of electron from an atom is called a state somewhere between energy levels n = 2 and n = 3 as ionization. In other words, ionization is the excitation of an shown in figure-1.9. When electron in ground state absorbs a electron ton= oo level. The energy required to ionize an atom is photon of 11 eV energy, its total energy becomes called ionization energy ofatom for the particular energy level E=E 1 + 11 from which the electron is removed. In hydrogenic atoms, the. ionization energy for nth state can be given as E=-13.6+ 11 eV E=-2.6eV www.puucho.com  Study Physics Galaxy with www.puucho.com..-::-- -- --·---- - ,Atomic PhJ_S}cs _ _____J_1J This energy can be converted.to e Vby dividing this energy by l!.En-->«> =o-( 13.6 Z n2 2 JeV ·- the electronic charge e, as ifwavelength is given in A, the energy irt e V can be given as he (" V) l!.E = 1'.e me... (1.36) Substituting the values of h, e and e we get 1.6.1 Frequency and Wavelength ofEmitted Radiation (6.63x l0-34 )x(3 x 108 ) When an electron absorbs a monochromatic radiation from an l!.E = =-'--'----'-'--'--"------'-'....!.. eV 1'.x(l.6xl0-19)x 10-10 external energy source then it makes a transition from a lower energy level to a higher level. But this state of the electron is l!.E= 12431 eV not a stable one. Electron can remain in this excited state for a ,_... (1.37) very small internal at most of the order ofl o-s second. The time Here in above equation-(1.37), lambda is in A units. period for which this excited state_ofthe electron exists is called the lifetime ofthat excited state. After the life time of the excited This equation is the most importantin numerical calculations, state the electron must radiate energy and it will jump to the as it will beveryfrequentlyused. From equation-(1.34) & (1_.36) ground state. Say ifit was in fifth energy level then it may come we have to the ground state by following the path as 5 ~ 3 ~ 1 or it may follow 5 ~4 ~2 ~ l or in somanyways, and in each transition it will emit a photon ofenergy equal to the energy difference of -he =-13.6Z ,_.. -l - - 2( 1 ) eV n2 n2 the two corresponding orbits according to Bohr's Third I 2 Postulate. Let us assume that the electron is initially in n2 state and it will 1 I=- 13.6Z he 2 (-1 __ n2 l n2 Jev. I 2 jump to a lower state n 1 then it_ will emit a photon of energy equal to the energy difference of the two states n 1 and n2 as l!.E=En2 -En1 v = _I_ =-Rz2 ,_ (-1 __l ) n2 I n2 2... (1.38) Where l!.E is the energy ofthe emitted photon. Now substituting the values of E., and E., in above equation, we get (As Rydberg Constant R = 13.6/he eV) 2 2 2 4 2 2 2 4 l!.E=- 21t K Z e m + 21t K Z e m 2 Here v is called wave number of the emitted radiation and is nih nfh 2 defined as number of waves per unit length and the above relation is used to find the wavelength of emitted radiation when an electron makes a transition from higher level n2 io lower level n I is called Rydberg formula. But students are advised to use equation-(1.37) in numerical _calculations to find the -M' = 13.6 Z2 (J,.c~J n1 n2 eV _-_. (1.34) wavelength of emitted radiation using the energy difference in electron volt. If can be rearranged as Here 13.6 2 2 can be used as ionization energyforn= l state for 12431 A a hydrogenic atom thus the energy of emitted photon can also l!.E(in eV)... (1.39) be written as Above relation you can use directly for fast calculations in numerical problems. For example if we wish to find the... (1.35) wavelength of radiation emitted when an electron makes a transition from n = 4 to n = l in a hydrogen atom, we use the Equation-(1.34) can also be used to find the energy of emitted relation in equation-(l.39). As we koow the energy released in radiation when an electron jumps from a higher orbit n2 to a above transition is lower orbit n 1. If1'. be the wavelength of the emitted radiation l!.E=E4 -E1 then M'=(-0.85)-(3.6)eV M'=l2.75eV www.puucho.com  Study Physics Galaxy with www.puucho.com L_E ___ _ Thus the wavelength of radiation emitted can be given by atoms in the discharge tube get excited due to the high potenfial,. equations-( 1.39) as and there are so many infinite number ofatoms in the tube and different atoms are excited to different excited states and when 1,.= 12431 A they again jump to their ground state after life time ofthe excited 12.75 states, so many radiations are emitted from the discharge tube. 1,.=975A These radiation are allowed to pass through the spectrometer and the radiation spectrum of these radiations is obtained on a 1.6.2 Number of Lines Emitted During, de-excitation of an fluorescent screen. It looks like the photograph shown in Atom figure- I. 10. Wavelength. A When an electron is in some excited state of an atom, after its ·, life time ofexcitation it will make a transition to lower states and CE -C E C E = E C E C ~ ' CN -N ~ ~ 0 N ~ ~ emits electromagnetic radiations which when passed through a ~- ~ M I :2 ~ spectrometer, different lines are plotted in the corresponding spectrum for each radiation emitted. We know that for an electron in nth state of a hydrogenic atom, it can make a transition to lower states in different possible ways and ultimately it comes Lyman Ill 1111 Balmer series Paschen series I series back to ground state by following different possible paths. Figure 1;10 When electron makes transition to lower state then it emits a photon corresponding to each transition until it reaches In the above H-spectrum, we can si.:e. that there are several ground state. Thus from nth state an electron can have "C2 group oflines between which there is a blank band in which no different possible ways to make a transition before it comes to wavelength is emitted by h-atom. These groups we call spectral ground state. Thus for a g·as containing several atoms/ions all series of Hydrogen atom. In next section we'll discuss these excited to nth state when start making transition to ground state spectral series in detail. the number of maximum possible lines obtained in the resulting I I spectrum are 1. 7.1 Spectral Series of Hydrogen Atom N="C = n(n-1) The wavelength of the lines of every spectral series can be... (1.40) 2 2 calculated using the formula given by equation-(1.37). When an electron makes a transition from nth state to ground Five spectral series are observed in the Hydrol,len Spectrum state then the electron during its transition to ground state it corresponding to the five energy levels of the Hydrogen atom will emit a minimum one photon when it will directly transit from · and these five series are named as on the names of their n ~ I and will emit maximum (n- I) photon when it will follow inventors. These series are \ the path n~(n- l)~(n-2)~....... 3 ~2 ~I.Thus maximum ' number of photons emitted by a.single electron from state n are (I) Lyman Series \ (2) Balmer Series (3) Paschen Series (4) Breckel! Series N=n-1... (1.41) (5) Pfund Series 1. 7 The Hydrogen Spectrum These spectral series are shown in figure-I. I I n=8 E-O It is clear that the energy of outer orbits is greater than the n=1 11 energy of inner orbits. When external radiation is given to the n=6 111 n=5 I E --0.54eV hydrogen atom then the electron in ground state jumps to a E --0.85 eV 11 P'.und Series higher energy state and the atom is called now in excited state. n=4 Any excited state is an unstable state and the maxim\nn lifetime n=3 1 Brackett Series E =- 1.51 eV Paschen Series ofan excited state is of the order of 10-s seconds, and after )he n=2 1 E --3.4eV lifetime of the excited state the electron jumps to the ground Balmer Series state again directly or indirectly by emitting one or more n=l I E - 13.6 eV electromagnetic radiations. It may have so many paths to come Lyman Senes to ground state. Figure 1.11 When Hydrogen gas is discharged in a discharge tube (at High (l) Lyman Series: The series consists of wavelengths of the potential difference ?fthe order of 104 volts), the Hydrngen radiations which are einitted when electronjuinps from a higher ' www.puucho.com  Study Physics Galaxy with www.puucho.com Atomic Physics 13 energy level to n = I orbit. The wavelengths constituting this series lie in the Ultra Violet region of the electromagnetic... (I.42) spectrum. For the first member of Lyman series For Lyman Series II I= I v= R[~- 2\]= 3 :... (1.43) and n 2 =2,3,4...... Dividing equation-(!.42) by equation-( 1.43), we get First line of Lyman series is the line corresponding to the !:,_ 5 5 transition 112 = 2 to n 1 = I, similarly second line of the Lyman '-1 27 or ½= 27 '-, series is the line corresponding to the transition 112 =3 ton 1= I. ,· = 5 x 6563 = 1215 37 A => "2 27.. (2) Balmer Series: The series consists of wavelengths of the radiations which are emitted when electron jumps from a higher energy level ton = 2 orbit. The wavelengths consisting this # Illustrative Example 1.8 series lie in the visible region of the electromagnetic spectrum. ----------,------------- Find the ratio ofionization energy of Bohr's hydrogen atom and (3) Paschen Series : The series consists of wavelengths of hydrogen-like lithium atom. the radiations which are emitted when electron jumps from a higher energy level ton= 3 orbit. The wavelengths constituting Solutiou this series lie in the Near Infra Red region of the electromagnetic spectrum. Energy ofan electron in ground state of Bohr's hydrogen-like atom is given _by, (4) Brackett Series : The series consists of wavelengths of 2 the radiations which are emitted when electron jumps from a £=- 13.6Z eV ,,2 higher energy level to 11 = 4 orbit. The wavelengths constituting this series lie in the Infra Red region of the electromagnetic Where Z = atomic number of the atom. spectrum. The ionization energy of this atom is equal in magnitude to (5) Pfund Series: The series consists ofwavelengths·ofthe energy of ground state= £ 00 = 13.6 Z2 radiations which are emitted when electron jumps from a higher energy level ton= 5 orbit. The wavelengths constituting this => series lie in the Deep Infra Red region of the electromagnetic spectrum. => 9 We can find out the wavelengths corresponding to the first line and the last line for remaining four spectral series as mentioned in the case ofLyman Series. #Il111strative Example 1.9 Lets discuss the transition ofelectron between different orbits Electrons of energies I 0.20 eVand 12.09 eV can cause radiation in detail with the help of some examples. to be emitted from hydrogen atoms. Calculate in each case, the principal quantum number of the orbit to which electron in the # Il/11strative Example I. 7 hydrogen atom is raised and the wavelength of the radiation emitted ifit drops back to the ground state. The wavelength of the first member of the Balmer series in hydrogen spectrum is 6563 A. Find the wavelength of first So/11iio11 member of Lyman series in the same spectrum. We know the orbital energy of an electron revolving in nth orbit Solution is given by For the first member of the Balmer series www.puucho.com  Study Physics Galaxy with www.puucho.com QC. ·_ -~ Atomic Physics I Where n is the principal quantum number.· Soflltion When n=IE 1=-13.6eV We know for transition n = 2 ton= I, the energy released is n=2E2 =-3.4eV b.£21 = E2 -E1 n=3E3 =-l.51eV b.£21 =(-3.4eV)-(-13.6 eV) b.£21 =10;2eV Here we can see that The wavelength _corresponding to this transition can be given 10.0eV=E2 -E 1 as and 12.09eV = E3 -E 1 ;\,= t _~ 1 1 = 1218.7 A Thus by absorbing a radiation photon of 10.2 eV electron will This radiations is in ultraviolet region. make a transition to n = 2 state and by absorbing 12.09 eV photon electron will make a transition ton= 3 state. Now after_ # Illllstrative Example I.II the lire time of excited states, the electron inn= 2 and n = 3 will - - - - - - - - - - - - - - - - - - - - - make transitions to lower states and ultimately come back to Hydrogen atom in its ground state is excited by means of ground state. In this process the possibilities of reverse monochromatic radiation of wavelength 975 A. How many 'transition are different lines are possible in the resulting spectrum? Calculate the longest wavelength amongst them. You may assume the n=3 to n=2 ionization energy for hydrogen atom as 13.6 eV. n=3 to n=I n=2 to n=I Sol11tion In above three transitions the amount of energy released will be When an electron of hydrogen atom absorbs a wavelength 975 A. The energy in eV, it absorbs is given by Af_,32 =(-1.51 eV)-(--3.4 eV) 12431 =l.89eV E=975 b.£31 =(-1.51 eV)-(-13.6eV) E=l2.75eV =12.09eV As discussed earlier that 12.75 eV is the energy difference of b.£21 =(-3.4eV)-(-13.6 eV) n = I and n = 4. Thus electron will make a transition from ground state ton= 4 orbit. From n = 4 when electron will start reverse =I0'.2eV transitions and ultimately comes back to ground state then the Thus wavelengths of radiations of corresponding transition number of possible transitions are are N="C = n(n-1) 2 2 12431 ;\,32 = 1.89 =6577.2A N= nx3 =I, 2 - 12431. These are also shown in figure-l:12 "-11 = 12.09 = 1028.2 A n=4 E4 =-0.85 eV "-ii= 12431 _ = 1218.7 A n=3 ! E3 =-1.51 eV 10 2 n=2 l E, ~-3.4 eV #Ill11strative Example I.JO