S. Chand’s

ENGINEERING PHYSICS(For the B.E. First Semester Students of RTM Nagpur University, Nagpur

as per New Syllabus)

Dr. M. N. AVADHANULUM.Sc., Ph.D.

Ex-Principal, Om College of Engineering, WardhaFormer Professor and Head Department of PhysicsKavikuluguru Institute of Technology and Science

Dr. SHILPA A. PANDE Dr. ARTI R. GOLHARAssociate Professor Assistant Professor

Department of Applied Physics Department of PhysicsLaxminarayan Institute of Technology Priyadarshini Bhagwati College of Engineering

R.T.M. Nagpur University, Nagpur. Umred Road, Nagpur.

M.Sc., Ph.D. M.Sc., Ph.D.

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© 2016, Dr. M.N. Avadhanulu and othersAll rights reserved. No part of this publication may be reproduced or copied in any material form (including photo copying or storing it in any medium in form of graphics, electronic or mechanical means and whether or not transient or incidental to some other use of this publication) without written permission of the copyright owner. Any breach of this will entail legal action and prosecution without further notice.Jurisdiction : All disputes with respect to this publication shall be subject to the jurisdiction of the Courts, tribunals and forums of New Delhi, India only.

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PREFACE

Physics is a mandatory for all engineering students, where almost all the importantelements of the subject are covered. Finally, these evolve as different branches of theEngineering course. The book entitled “Engineering Physics” has been written keeping inmind the need of undergraduate students from various engineering and science colleges ofRTM Nagpur University.

In view of limited time, the students can devote to Physics, an attempt is made tofocus on essetial points and the details that are not of immediate relevance are dropped.

The aim of writing this book has been to present the material in a concise and verysimple way, so that even very weak students can grasp the fundamentals.

In view of this, every chapter starts with a simple introduction and then relatedtopic are covered with a detailed description alongwith the help of figures. The requirementsof the students are given priority and the material is molded in a more student friendly style.

The manuscript contains four chapters, which have been prepared as per the syllabustaught in various colleges and institutions. The fundamental concepts are emphasized ineach chapter and the details are developed in an easy to follow style. Each chapter isdivided into small parts and sub-headings are provided to make the reading a pleasentjourney from one interesting topic to another. The manuscript has been organized such thatit provides a link between different topics of the chapter. In order to make it simpler all thenecessary mathamatical steps have been given and the physical feature of the mathamaticalequation is discussed as and when required.

Enough care has been taken to eliminate printing mistakes. However, some mistakesmight have crept in inadvertantly. The author appeals to the readers to point out such leftout mistakes.

The authors are indebted to the teachers in various engineering institutions, who hasbeen extending unstinted support to the book. They are also greatful to their colleagues,who rendered assistances at various stages of the preparation of this book. They are alsothankful to Mr. Rajendra V. Yelchalwar (Raj Art & Computers, Nagpur) for the carefulpreparation of the book.

Authors express their sincere thanks to the members of their respective management,Dr. R. B. Mankar, Director L.I.T, Nagpur and Dr. N. K. Choudhari, Principal, PBCOE,Nagpur for their indulgence and encouragement.

Authors are thankful to their families and parents for their coperation through outthis endevour.

Authors also offer special thanks to Shri Vijay Shribas, Branch Manager (Sales),Management Team and the Editorial department of S. Chand & Co. Pvt. Ltd., New Delhifor all help and support in publication of this book.

Dr. M. N. AVADHANULUmna2005@rediffmail.com

Dr. S. A. PANDEsap7001@rediffmail.com

Dr. A. R. GOLHARartigolhar@gmail.com

Unit - I: Quantum MechanicsPlank s Hypothesis, Properties of Photons, Compton Effect ,Wave –particle duality, De-Broglie Hypothesis, Matter Waves ,Davisson -Germer Experiment; Bohr s Quantization condition.

Unit - II: Wave Packet & Wave EquationsConcept of Group and phase velocities, Wave packet, Heisenberg suncertainty principle, Thought experiment on single slit electrondiffraction, Wave function and its probability interpretation,Schrödingers Time dependent & time independent equations, Solutionof Schrödinger s equation for one dimensional infinite potential well,Barrier Tunneling.

Unit - III: Crystal StructureCrystal structure, Meaning of lattice and basis, Unit cell: primitive andnon primitive unit cell; Cubic crystal structure: Body and Face centeredcubic structures, SC, BCC and FCC unit cells. Unit cell characteristics:Effective number of atoms per unit cell, atomic radius, nearestneighbour distance, coordination number, atomic packing fraction, voidspace, density; Crystal planes and Miller indices, Inter-planar distancebetween adjacent planes, Bragg’s law of X-ray diffraction, Tetrahedraland octahedral voids.

Unit - IV: Semiconductor PhysicsQualitative idea on the formation of electron energy bands in solids,Band-theory based classification of sol ids into insulators,semiconductors and conductors, Fermi-Dirac distribution Function,Intrinsic semiconductors: Germanium and silicon; Fermi- energy,Typical energy band diagram of an intrinsic semi-conductor, Dopingand Extrinsic semiconductors, Current conduction in semiconductors.PN- junction diode; Unbiased, Forward baised & Reverse biased modewith Energy band diagram reference, Diode rectifier equation, BipolarTransistor action, Hall effect, Hall coefficient & Hall Angle, V-Icharacteristics of i) Tunnel diode, ii) Zener diode iii) LED.

Roadmap to1st Semester Syllabus

Contents

Chapters Page Nos.

Unit – 1 QUANTUM MECHANICS 1 - 261.1.Wave picture of Radiation, 1.2. Planck’s Quantum Hypothesis,

1.3.Particle Picture of Radiation, 1.4. The Photon,1.5. Energy – MomentumRelation,1.6. Compton Effect,1.6.1. Failure of classical theory,1.6.2.Compton’s Explanation on the basis of quantum theory, 1.6.3.Existence of modified and unmodified radiation1.6.4.Intensity of Modifiedand Unmodified radiation in light and heavy elements, 1.6.5.Why free electroncannot absorb a photon, 1.6.6. Compton Effect is not detectable for visibleradiation,1.7. De Broglie Hypothesis,1.7.1.De Broglie waves areinsignificant in case of macro bodies,1.8. Properties of Matter Waves,1.9.Davisson Germer experiment,1.10. Application of de Broglie WavesWorked out problems & University Question Bank.Unit – II WAVE PACKET & WAVE EQUATIONS 27 - 532.1. Wave Packet2.1.1. Relation between Phase Velocity and Group Velocity,2.2. Heisenberg Uncertainty Principle, 2.2.1 Uncertainty principle is notsignificant in case of macro bodies, 2.3. Thought Experiment, 2.4 Applicationof Uncertainty Principle, 2.5. Wave Function, 2.5.1. Normalization condition2.6. Schrodinger Wave Equation, 2.6.1. Schrodinger time-independent waveequation, 2.7. Application of the Schrodinger Equation, 2.7.1. Energy Levels2.7.2. Probability of locating the particle, 2.7.3. Dependence of quantizationon the width of the well, 2.8 Tunnel Effect, 2.8.1. Finite potential Barrier2.8.2 Application of Tunneling.Worked out problems & University Question Bank.

Unit- III : CRYSTAL STRUCTURES 55 - 803.1. Space lattice, 3.2. Space Lattice and its Relationship to CrystalStructure, 3.3. Unit Cell, 3.4. Cubic System,3.5. Calculation of parametersof a cubic lattice, 3.5.1. Simple Cubic (SC) Cell, 3.5.2. Body Centered cubic(BCC) Cell, 3.5.3. Face Centered Cubic (FCC) Cell 3.6. Miler Indices 3.6.1.Drawing a lattice place,3.7.Interplanar Distance in a cubic lattice,3.8.Voids,3.9. Braggs LawWorked out problems & University Question Bank.

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Chapters Page Nos.

UNIT 4 : SEMICONDUCTOR PHYSICS 81 - 1554.1 Band Theory of Solids, 4.1.1Energy Level, 4.1.2 Energy Bands, 4.2Splitting of Energy Levels, 4.2.1 Group IV, 4.3 Classification of Solids, 4.4Fermi Dirac Distributions function, 4.5 Effective Mass, 4.6 Semiconductors4.7 Intrinsic Semiconductors, 4.7.1 At 0K and intrinsic semiconductorsbehaves as a perfect insulator, 4.7.2Mechanism of conduction in an intrinsicsemiconductor, 4.7.3 Intrinsic Conductivity, 4.8 Variation of carrierconcentration with temperature, 4.8.1The fraction of electrons in theconduction band, 4.9 Fermi Level in Intrinsic Semiconductor, 4.9.1 Variationof Fermi Level with temperature in an intrinsic Semiconductor, 4.10 ExtrinsicSemiconductor, 4.11 N Type Semiconductor, 4.12 p-Type Semiconductor4.13 Band Diagrams of Extrinsic semiconductor at 0K and 300K,4.14 CarrierConcentration in Extrinsic Semiconductors, 4.15 Charge Neutrality condition,4.16 Extrinsic Conductivity, 4.17 Fermi Level in extrinsic Semiconductor,4.18 Drift & diffusion currents, 4.19 Hall Effect, 4.19.1 Importance of HallEffect, 4.19.2 Experimental Arrangement,4.19.3 Hall Coefficient, 4.19.4Carrier Concentration, 4.19.5 Hall Mobity, 4.19.6 Hall Angle, 4.19.7 FactorsAffecting Hall Voltage, 4.19.8 Variation of Hall Coefficient with Temperture,4.20 P-N Junction Diode, 4.21 P-N Junction Diode at Equilibrium, 4.21.1Diffusion of majority carriers and formation of internal potential barrier, 4.21.2Drift of minority carriers, 4.21.3 Thermal equilibrium condition, 4.21.4 Energyband diagram, 4.21.5 Circuit symbol and Bias, 4.22 P-N Junction underforward Bias, 4.22.1 Energy Band Diagram, 4.22.2 The rectifier equation,4.23 P-N Junction under reverse Bias, 4.23.1 Energy Band Diagram, 4.23.2Current Equation for Reverse Bias, 4.24 The rectifier equation, 4.25 ReverseSaturation Current, 4.26 V-I Characteristics, 4.27 Reverse breakdown, 4.27.1Avalanche Breakdown, 4.28 Zener Diode, 4.28.1 Zener Breakdown, 4.29Light Emitting Diode (LED), 4.30 Tunnel Diode, 4.30.1 Tunneling Effect,4.30.2 V-I Characteristics of Tunnel Diode, 4.31 Bipolar Junction Transistor,4.31.1 Circuit Configuration, 4.31.2 Energy Band Diagram of an unbiasedtransistor, 4.32 Transistor Action, 4.32.1 Current in CB configuration, 4.33Energy Band Diagram of a transistor biased in normal modeWorked out problems & University Question Bank.

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Chapters Page Nos.

EXPERIMENTS IN ENGINEERING PHYSICS 157 - 1921. Band gap of semiconductor.2. Transistor in common emitter mode.3. Light emitting diode. (LED)4. p-n junction diode as rectifier.5. Study of hall effect.6. Study of p-n junction diode.7. Study of Zener diode.8. Transistor in common base mode.

UNIVERSITY PAPER SOLUTION 193 - 220

1. Winter - 20122. Summer - 20133. Winter - 20134. Summer - 2014

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Unit – I

Quantum Mechanics

.

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CLASSICAL PHYSICS :

The three laws of conservation, namely conservation of linear momentum, angularmomentum and energy formed the basis for classical Mechanics. The Classical (Newtonian)Mechanics, Maxwell’s electromagnetic theory and thermodynamics were the major theoriesof 19th century physics which came to be known as classical physics.

Classical physics was developed assuming that particles are localized and we canobserve them without appreciably disturbing them.

Classical physics successfully explains the behavior of macroscopic (visible) bodies.

QUANTUM PHYSICS :

Classical theory of physics could not explain a number of fundamental discoverieswhich were reported at about turn of 20th century. The inadequacy of classical theorieswas noticed first when they were applied to explain the black body radiation emitted by abody hotter than its surroundings. To explain the blackbody radiation, Max Planck putforward a revolutionary hypothesis that the molecules in a source emit energy not continuouslybut in small discrete packets called quanta. Other experimental results also showed thatthe classical concepts were entirely inadequate to explain the behavior of atoms andsubatomic particles. A new body of ideas based on Planck’s work was developed, andthe new theory came to known as quantum theory or quantum physics.

Quantum physics explains the behavior of matter and radiation at the microscopic(atomic) level.

Quantum Mechanics describes the laws applicable in the microscopic worldcomprising of atoms and subatomic particles.

Planck’s hypothesis of energy quanta, Einstein’s ideas on photons, de Broglie’svisualization of the wave properties of micro-particles and the Heisenberg’suncertainty principle provides the basis for the development of quantum mechanics.

CHAPTER

1 Quantum Mechanics

4 Engineering Physics

1.1 WAVE-PICTURE OF RADIATION- Energy flow is continuous

The propagation of electromagnetic waves and their interaction with matter can beexplained with the help of Maxwell’s electromagnetic theory.

Maxwell’s theory treated the emission of radiation by a source as a continuousprocess. A heated body may be assumed to be capable of giving out energythat travels in the form of waves of all possible wavelengths.

The radiation incident on a body was thought to be absorbed at all possiblewavelengths. The intensity of radiation is given by

I = |E|2 ........ (1.1)where E is the amplitude of the electromagnetic wave.

It is expected that wave nature of radiation would explain the experimentalobservation made on thermal (heat) radiation emitted by a blackbody. Various effortswere made to calculate theoretically the frequency distribution of thermal radiation emittedby a blackbody. By using classical theories Rayleigh and Jeans derived an equation but itwas unable to explain the frequency spectrum of black body. The failure of Rayleigh andJeans theory brought to focus the inadequacy of classical theories.

1.2 PLANCK’S QUANTUM HYPOTHESIS – Energy is quantized

In 1900, Max Planck’s proposed an empirical formula which explained thefrequency distribution of thermal radiation correctly. Planck’s theory was a radical departurefrom classical concepts. He postulated the following assumption in his theory.

(i) The atomic oscillator in a body cannot have any arbitrary amount of energy.They could have only discrete units of energy given by

E = nh ........ (1.2)

where n is any positive integer (n = 1,2,3,...........); is the frequency ofoscillation and h is a constant now known as Planck’s constant which is

given by h = 6.62× 10-34J.s.

(ii) The atomic oscillator cannot absorb or emit energy of any arbitrary amount.They absorb or emit energy in indivisible discrete units. The amount of radiantenergy in each unit is called a quantum of energy. Each quantum carries anenergy.

E = h ........ (1.3)

The hypothesis that radiant energy is emitted or absorbed basically in adiscontinuous manner and in the form of quanta is known as the Planck’s quantum

Quantum Mechanics 5

hypothesis. Planck’s hypothesis states that radiant energy is quantized and implies that anatom exists in certain discrete energy states. Such states are called quantum states.

1.3 PARTICLE PICTURE OF RADIATION – Radiation is a stream of photons

Einstein gave a more concrete shape to Planck’s quantum hypothesis. Hesuccessfully explained the experimental results of photoelectric effect. In the process ofexplaining photoelectric effect, Einstein extended Planck’s hypothesis as follows.

Einstein named the energy quanta as photons.

He asserted that radiation energy propagated through space in the form of photons.Each photon represented a packet of energy h.

The higher the frequency of the electromagnetic wave, the higher is the energyof each photon. Thus, x-ray and x-ray photons are more energeticcompared to optical photons while the photons of r.f. frequencies are the feeblest.

The intensity of a monochromatic light beam, I, is related to the concentration ofphotons, N, present in the beam.

I = N h ........ (1.4)

1.4 THE PHOTON

We now sum up the particle properties attributed to the photon.1. Energy : The energy of a photon is given by E = h2. Velocity : Photons always travel with the velocity of light ‘c’.3. Rest Mass : The rest mass of photon mo= 0 since a photon can never

be at rest.4. Relativistic Mass : As photons travel with the velocity of light, they

will have relativistic mass, m = 2

Ec = 2

hvc .

5. Linear Momentum : p =Ec =

hvc =

h

........ (1.5)

As the wave vector k = 2

, p = 2h k

= k. ........ (1.6)

6. Angular Momentum : 1

7. Electric Charge : Photons are electrically neutral and cannot beinfluenced by any electric or magnetic fields. Theycannot ionize matter.

6 Engineering Physics

1.5 ENERGY-MOMENTUM RELATION :

The energy-momentum relationship for an atomic particle can be obtained asfollows:

The relativistic mass m of an atomic particle moving with a velocity v is given by

02 2

m =1 /

mc

........ (1.7)

where mo is the rest mass of the particle. Squaring on both sides of (1.7) andrearranging the terms, we get

2 2 2 2 2 2om c m m c

Multiplying the above equation by c2 on both sides, we get

2 4 2 2 2 2 4om c m c m c

Writing mc2 = E and m = p, we get

2 2 2 2 4oE p c m c ;

2 2 2oE c p m c ........ (1.8)

1.6 COMPTON EFFECT :

Arthur H. Compton carried out investigations on the scattering of x-rays bymaterials of low atomic number.

(a) (b)

Fig 1.1 (a) Compton’s apparatus for the study of scattered x-rays(b) Unmodified and modified compontents

l

(A)

Path of Spectrometer

Scatteringsubstance

Unscatteredx-ray

Bragg x-rayspectrometer

Scat

tere

dx-

rayL2L1

i f

Engineering Physics

Publisher : SChand Publications ISBN : 9789352531035Author : Dr. M. N.Avadhanulu, Dr. Shilpa A.Pande, Dr. Arti R. Golhar

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