## Physics

## Science (Regular)

## Overview

**Establishment:**The college was established in the year 1957.**Buildings:**The department in functioning in new science block of the B.J.B.(Autonomous) college.**Classroom:**The department has adequate number of well-furnished classrooms for UG and PG.**Laboratory:**The department has a well-furnished laboratory for UG, a computer laboratory, a general physics laboratory, electronics laboratory and laboratory for PG is under process. One lab is provided with a projector and sound system.**Library:**The department has a seminar library having a good number of books and the books are issued to the students for study.**Vision & Mission:**The department of B.J.B.(Auto.) college has earned name and fame across in our country and globally well recognised for creating outstanding graduates and imparting knowledge and new technology to the students.

To shape ourselves into a learning community where we work, listen, and respect each other. To encourage each other, facilitate faculty-student to work synergistically across discipline boundaries. To develop and pursue curricula to those students are dynamic flexible and holistically designed to facilitate creativity and cognitive thinking.

**Sanctioned Posts:**07**Sanctioned Student Strength:**UG[48(3^{RD}YR)+48(2^{ND}YR)+64(1^{ST}YR)]+ PG[32(1^{ST}YR)+32(2^{ND}YR)]

- Department have classrooms equipped with LCD projectors and screens to enable teaching through power point presentations, in addition to black/white boards.
- The college provides facilities to computer aided teaching materials like computer lab, audio visual aids, microphones, LCD projectors, scanners, and LCD televisions.
- The department has computer centre with internet facilities. The computer centre has BSNL lease line server, 12 desktops, 3 laptops, 24 switch points, 100mbps WIFI system. The SCILAB software, python software also available at computer centre.
- The faculty members and students able to access the EBSCO portal which provides e-books, journals, research papers related to physics.
- The faculty members and the students have access to SWAYAM online courses and e-PG Pathsala, which provides high quality curriculum based, interactive e-content for post graduate disciplines of social sciences, arts, fine arts and humanities, natural, physical, and biological sciences.

**UG (Physics)****PG (Physics)**

**UG**

**PHYSICS**

**+3 FIRST YEAR FIRST SEMESTER**

**Core Paper – 1**

**MATHEMATICAL PHYSICS – I**

Time : **3 Hrs**. End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

The emphasis of course is on applications in solving problems of interest to physicists. The

students are to be examined entirely on the basis of problems, seen and unseen.

**UNIT – I :**

Calculus – I : Plotting of functions, Intuitive ideas of continuous, differentiable functions and

plotting of curves. Approximation: Taylor and binomial series (statements only). First Order

Differential Equations and Integrating Factor. Second Order Differential equations: Homogeneous Equations with constant coefficients, Wronskian and general solution, Statement of existence and Uniqueness Theorem for Initial Value Problems, Particular Integral.

**UNIT-II**

Calculus – II : Calculus of functions of more than one variable: Partial derivatives, exact and

inexact differentials. Integrating factor, with simple illustration, Constrained Maximization using Lagrange Multipliers.

Vector algebra : Recapitulation of vectors: Properties of vectors under rotations. Scalar product and its invariance under rotations, Vector product, Scalar triple product and their interpretation in terms of area and volume respectively, Scalar and Vector fields.

**UNIT-III**

Orthogonal Curvilinear Coordinates : Orthogonal Curvilinear Coordinates, Derivation of

Gradient, Divergence, Curl, and Laplacian in Cartesian, Spherical and Cylindrical Coordinate

Systems, Comparison of velocity and acceleration in cylindrical and spherical coordinate system

Dirac Delta function and its properties : Definition of Dirac delta function. Representation as limit of a Gaussian function and rectangular Function, Properties of Dirac delta function.

**UNIT-IV**

Vector Differentiation : Directional derivatives and normal derivative. Gradient of a scalar field and its geometrical interpretation, Divergence and curl of a vector field, Del, and Laplacian operators, Vector identities

Vector Integration : Ordinary Integrals of Vectors, Multiple integrals. Jacobian, Notion of

infinitesimal line, surface and volume elements, Line, surface, and volume integrals of Vector

fields, Flux of a vector field, Gauss’ divergence theorem, Green’s, and Stokes Theorems and

their applications (no rigorous proofs)

Textbooks:

- Mathematical Methods for Physicists, G. B. Arfken, H. J. Weber. F. E. Harris (2013, 7th Edn.,

Elsevier)

- Advanced Engineering Mathematics, Erwin Kreyszig (Wiley India)

Reference books:

- Mathematical Physics C. Harper (Prentice Hall India)
- Complex Variable: Schaum’s Outlines Series M. Spiegel (2nd Edition, Mc-Graw Hill Education)
- Complex variables and applications, J. W. Brown, and R.V.Churchill Mathematical Physics, SatyaPrakash (Sultan Chand)
- Mathematical Physics, B. D. Gupta (4th edition, Vikas Publication) Mathematical Physics and

Special Relativity, M. Das, P.K. Jena, and B. K. .Dash (Srikrishna Prakashan).

- Mathematical Physics-H.K. Dass, Dr. Rama Verma (S. Chand Publishing).

**CORE – 1 – LAB**

Credit : **02(25 Marks**)

The aim of this Lab is not just to teach computer programming and numerical analysis but to

emphasize its role in solving problems in Physics.

- Highlights the use of computational methods to solve physical problems.
- The course will consist of lectures (both theory and practical) in the Lab.
- Evaluation done not on the programming but on the basis of formulating the problem.
- Aim at teaching students to construct the computational problem to be solved.
- Students can use any one operating system Linux or Microsoft Windows.

Introduction and Overview:

Computer architecture and organization, memory, and Input output devices.

Basics of scientific computing:

Binary and decimal arithmetic, Floating point numbers, algorithms. Sequence. Selection and

Repetition, single and double precision arithmetic, underflow, and overflow emphasize the

importance of making equations in terms of dimension less variables, Iterative methods Algorithm.

Errors and error Analysis:

Truncation and round off errors, Absolute and relative errors. Floating point computations.

Systematic and Random Errors, Propagation of Errors, Normal Law of Errors. Standard and

Probable Error.

Review of C and C++ Programming :

Introduction to Programming, constants, variables and Fundamentals data types, operators

and Expressions. I/O statements, scan f and print f, c in and c out. Manipulators for data formatting, Control statements (decision making and looping statements) (If Statement. If else

Statement, Nested-lf structure, Else-lf Statement. Ternar-if operator. Go to Statement. Switch

Statement. Unconditional and Conditional Looping. While Loop. Do-While Loop. FOR Loop.

Break and Continue Statements. Nested Loops), Arrays (1D and 2D) and strings, user defined

functions, Structures and Unions, Idea of classes and objects.

Programs:

Sum and average of a list of numbers, largest of a given list of numbers and its location in the

list, sorting of numbers in ascending descending order, Binary search

Random number generation:

Area of circle, area of square, volume of sphere, value of π.

Reference Books:

- Introduction to Numerical Analysis, S.S. Sastry, 5th Edn., 2012, PHI Learning Pvt. Ltd.
- Schaum’s outline of Programming with C++ J. Hubbard, 2000, McGraw-Hill Pub.
- Numerical Recipes in C: The Art of Scientific Computing. W.H. Press et al, 3rd Edn. 2007,

Cambridge University Press.

- A first course in Numerical Methods, U.M. Ascher and C. Greif. 2012, PHI Learning.
- Elementary Numerical Analysis, K.E. Atkinson, 3rd Edn., 2007, Wiley India Edition.
- Numerical Methods for Scientists and Engineers, R.W. Hamming. 1973, Courier Dover Pub.
- An Introduction to computational Physics, T. Pang, 2nd Edn. 2006. Cambridge Univ. Press.

**Core Paper – 2**

**MECHANICS**

Time **: 3 Hrs. **End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT – I**

Rotational Dynamics: Centre of Mass, Motion of COM, Centre of Mass and Laboratory frames, Angular momentum of a particle and system of particles, Principle of conservation of angular momentum, Rotation about a fixed axis, Moment of Inertia, Perpendicular and Parallel Axis Theorems, Routh Rule, calculation of moment of inertia for cylindrical and spherical bodies. Kinetic energy of rotation, Eulers Equations of Rigid Body motion, Motion involving both translation and rotation. Moment of Inertia of a Flywheel.

Non-Inertial Systems : Non-inertial frames and fictitious forces, Uniformly rotating frame, Laws of physics in rotating coordinate systems, Centrifugal force, Coriolis force and its applications.

**UNIT – II**

Elasticity : Relation between Elastic constants, Twisting torque on a Cylinder or Wire, Bending of beams, External bending moment, Flexural rigidity, Single and double cantilever

Fluid Motion: Kinematics of Moving Fluids: Poiseuille’s Equation for Flow of a Liquid through a Capillary Tube. Surface tension, Gravity waves and ripple.

Viscosity: Poiseuille’s Equation for Flow of a Liquid with corrections.

**UNIT-III**

Gravitation and Central Force Motion: Law of gravitation. Gravitational potential energy, Inertial and gravitational mass, Potential and field due to spherical shell and solid sphere. Motion of a particle under a central force field. Two-body problem and its reduction to one-body problem and its solution, Differential Equation of motion with central force and its solution. The first Integrals (two), Concept of power Law Potentials, Kepler’s Laws of Planetary motion, Satellites: Geosynchronous orbits. Weightlessness, Basic idea of global positioning system (GPS), Physiological effects on astronauts.

**UNIT-IV**

Oscillations: Simple Harmonic Oscillations. Kinetic energy, potential energy, total energy and

their time-average values. Damped oscillation. Equation of motion and solution(cases of

oscillatory, critically damped, and overdamped) Forced oscillations: Transient and steady states; Resonance sharpness of resonance; power dissipation and Quality Factor, Bar Pendulurn, Kater’s Pendulum.

Special Theory of Relativity: Michelson-Morley Experiment and its out-come. Postulates of

Special Theory of Relativity, Lorentz Transformations. Simultaneity and order of events,

Lorentz contraction, Time dilation, Relativistic transformation of velocity, Frequency and wave number, Relativistic addition of velocities. Variation of mass with velocity, Massless Particles, Mass-energy Equivalence, Relativistic Doppler effect Relativistic Kinematics, Transformation of Energy and Momentum.

Text Books:

- Mechanics, D.S.Mathur(S. Chand Publishing)
- Introduction to Special Relativity, R. Resnick (John Wiley)

Reference Books:

- Introduction to Mechanics Daniel Klapnner and Robert Kolenkow. McGraw Hill.
- Mechanics by K.R Simon
- Mechanics. Berkeley Physics, vol. 1, C.Kittel, W. Knight, et al (Tata McGraw- Hill)

204 Syllabus-Science

- Physics. Resnick. Halliday and Walker (8/e.2008,Wiley) Theoretical Mechanics-M.R. Spiegel

(Tata McGraw Hill).

- Feynman Lectures. Vol. I. R.P.Feynman, R. B. Leighton, M. Sands (Pearson)
- Mechanics-M. Das. P. K. Jena and R.N. Mishra (Srikrishna Publications)

**CORE – 2 – LAB**

Credit : **02 (25 Marks)**

- To study surface tension by capillary rise method.
- To determine the height of a building using a Sextant.
- To study the Motion of Spring and calculate (a) Spring constant, (b) g and (c) Modulus of rigidity.
- To determine the Moment of Inertia of a Flywheel.
- To determine Coefficient of Viscosity of water by Capillary Flow Method (Poiseuilles method).
- To determine the Modulus of Rigidity of a Wire by Maxwell’s needle.
- To determine the value of g using Bar Pendulum.
- To determine the value of g using Kater’s Pendulum.

Reference Books:

- Advanced Practical Physics for students, B. L. Flint and H.T. Worsnop, 1971, Asia Publishing House.
- Advanced level Physics Practicals, Michael Nelson, and Jon M. Ogborn, 4th Edition, reprinted

1985, Heinemann Educational Publishers.

- A Text Book of Practical Physics, I. Prakash, and Ramakrishna. 11th Edn, 2011, Kitab Mahal.

**+3 FIRST YEAR SECOND SEMESTER**

**Core Paper – 3**

**ELECTRICITY AND MAGNETISM**

Time : **3 Hrs**. End Semester Theory : **60 Marks**

Credit :** 04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Electric Field and Electric Potential:

Electric field: Electric field lines, Electric flux, Gauss Law with applications to charge distributions with cylindrical and planar symmetry, Conservative nature of Electrostatic Field. Electrostatic Potential, Potential and Electric Field of a dipole, Force and Torque on a dipole, Potential calculation in different simple cases, Laplace’s, and Poisson equations. The Uniqueness Theorem, Method of Images, and its application to (1) Plane Infinite Sheet and (2) Sphere. Electrostatic energy of system of charges, Electrostatic energy of a charged sphere,

Conductors in an electrostatic Field, Surface charge and force on a conductor.

**UNIT-II**

Magnetic Field: Magnetic Force, Lorentz Force, Biot-Savarts Law, Current in a Loop as a

Magnetic Dipole and its Dipole Moment (analogy with Electric Dipole). Amperes Circuital Law and its application to (1) Solenoid (2) Toroid (3) Helmholtz coil, Properties of B: curl and divergence. Vector Potential, Ballistic Galvanometer: Torque on a current Loop, Current and Charge Sensitivity, Electromagnetic damping, Logarithmic decrement, CDR.

**UNIT-III**

Dielectric Properties of Matter: Electric Field in matter. Polarization, Polarization Charges,

Electrical Susceptibility and Dielectric Constant, Capacitor (parallel plate, spherical, cylindrical) filled with dielectric, Displacement vector D, Relations between E, P and D, Gauss Law in dielectrics.

Magnetic Properties of Matter: Magnetization vector (M), Magnetic Intensity (H),

Magnetic Susceptibility and permeability, Relation between B, H. M, Ferromagnetism, B-H curve, and hysteresis.

Electromagnetic Induction: Faradays Law, Lenz’s Law. Self-Inductance and Mutual Inductance, Reciprocity Theorem, Energy stored in a Magnetic Field, Introduction to Maxwell’s Equations

**UNIT-IV**

Electrical Circuits: AC Circuits: Kirchhoff’s laws for AC circuits. Complex Reactance and

Impedance, Series LCR Circuit: (1) Resonance (2) Power Dissipation (3) Quality Factor. (4)

Band Width, Parallel LCR Circuit.

Network theorems: Ideal Constant-voltage and Constant-current Sources, Network Theorems: Thevenin theorem. Norton theorem, Superposition theorem, Reciprocity theorem, Maximum Power Transfer theorem. Applications to DC circuits. Transient Currents Growth and decay of current in RC and LR circuits.

Text Books:

- Introduction to Electrodynamics – D. J. Griffiths (Pearson, 4th edition. 2015)
- Foundations of Electromagnetic Theory-Ritz and Milford (Pearson)

Reference Books:

- Classical Electrodynamics, J. D. Jackson (Wiley).
- Electricity and Magnetism D. C. Tayal (Himalaya Publishing house)
- Electricity, Magnetism and Electromagnetic Theory- S. Mahajan and Choudhury (Tata McGraw Hill)
- Feynman Lectures Vol.2, R. P. Feynman, R. B. Leighton. M. Sands (Pearson)
- Electricity and Magnetism, J. H. Fewkes and J. Yarwood. Vol. I (Oxford Univ. Press)

206 Syllabus-Science

**CORE – 3 – LAB**

Credit : **02 (25 Marks)**

Use a Multimeter for measuring (a) Resistances, (b) AC and DC Voltages, (c) DC Current, (d)

Capacitances, and (e) Checking electrical fuses.

- To study the characteristics of a series RC Circuit.
- To determine an unknown Low Resistance using Potentiometer.
- To determine an unknown Low Resistance using Carey Fosters Bridge. To compare capacitances

using De-Sauty’s bridge.

- Measurement of field strength B and its variation in a solenoid (determine dB/dx)
- To verify the Thevenin and Norton theorems.
- To determine self-inductance of a coil by Andersons bridge.
- To study response curve of a Series LCR circuit and determine its (a) Resonant frequency, (b)Impedance at resonance, (c) Quality factor Q, and (d) Band width.
- To study the response curve of a parallel LCR circuit and determine its (a) Antiresonance

frequency and (b) Quality factor Q.

Reference Books:

- Advanced Practical Physics for students, B.L. Flint and H.T. Worsnop, 1971, Asia Publishing

House.

- A Text book of Practical Physics, I.Prakash and Ramakrishna, 11th Ed., 2011, Kitab Mahal.
- Advanced level Physics Practicals, Michael Nelson and Jon M. Ogborn, 4th Edition, reprinted

1985, Heinemann Educational Publishers.

- A Laboratory Manual of Physics for undergraduate classes, D.P.Khandelwal, 1985, Vani Pub.

**Core Paper – 4**

**WAVES AND OPTICS**

Time **: 3 Hrs**. End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Geometrical optics: Fermat’s principle, reflection and refraction at plane interface, Matrix

formulation of geometrical Optics, Cardinal points and Cardinal planes of an optical system.

Idea of dispersion, Application to thick Lens and thin Lens, Ramsden, and Huygens eyepiece.

Wave Optics: Electromagnetic nature of light. Definition and properties of wave front, Huygen’s Principle. Temporal and Spatial Coherence.

**UNIT – II**

Wave Motion : Plane and Spherical Waves, Longitudinal and Transverse Waves, Plane

Progressive (Traveling) Waves. Wave Equation, Particle and Wave Velocities, Differential

Equation, Pressure of a Longitudinal Wave, Energy Transport, Intensity of Wave. Super position of two perpendicular Harmonic Oscillations : Graphical and Analytical Methods, Lissajous Figures (1:1 and 1:2) and their uses, Super position of N harmonic waves.

**UNIT- III**

Interference : Division of amplitude and wave front, Young’s double slit experiment, Lloyds

Mirror and Fresnel’s Bi-prism. Phase change on reflection: Stoke’s treatment. Interference in

Thin Films: parallel and wedge-shaped films. Fringes of equal inclination (Haidinger Fringes).

Fringes of equal thickness (Fizeau Fringes), Newtons Rings: Measurement of wavelength and

refractive index. Interferometer: Michelson’s Interferometer-(1) Idea of form of fringes (No theory required), (2) Determination of Wavelength, (3) Wavelength Difference, (4) Refractive Index, and (5) Visibility of Fringes, Fabry-Perot interferometer.

**UNIT – IV**

Fraunhofer diffraction: Single slit, Circular aperture, Resolving Power of a telescope, Double

slit, N multiple slits. Diffraction grating, Resolving power of grating. Fresnel Diffraction: Fresnel’s Assumptions, Fresnel’s Half-Period Zones for Plane Wave, Explanation of Rectilinear Propagation of Light, Theory of a Zone Plate: Multiple Foci of a Zone Plate, Fresnel’s Integral, Fresnel diffraction pattern of a straight edge, a slit and a wire.

Text Books:

- A text book of Optics N. Subrahmanyam and Brij Lal (S.Chand Publishing)
- Optics – Ajoy Ghatak (McGraw Hill)

Reference Books:

- Optics-E. Hecht(Pearson)
- Fundamentals of Optics – F.A. Jenkins and H.E. White(McGraw-Hill)
- Geometrical and Physical Optics R.S. Longhurst (Orient Black swan)
- The Physics of Vibrations and Waves-HJ. Pain (John Wiley)
- Optics P.K. Chakrabarty.
- Principles of Optics-Max Bom and Emil Wolf (Pergamon Press)
- The Physics of Waves and Oscillations – N.K. Bajaj (McGraw Hill)

**CORE – 4 – LAB**

Credit : **02 (25 Marks)**

- To determine frequency of an electric tuning fork by “Meldls” experiment and verify λ2 -T law.
- To plot the I-D curve and to determine the refractive index of a prism.
- To determine refractive index of the Material of a prism using sodium source.
- To determine the dispersive power and Cauchy constants of the material of a prism using

mercury source.

- To determine wavelength of sodium light using Newtons Rings.
- To determine wavelength of (1) Na source and (2) spectral lines of Hg source using plane

diffraction grating.

- To determine dispersive power and resolving power of a plane diffraction grating.

Reference Books:

- Advanced Practical Physics for students, B.L. Flint and H.T. Worsnop, 1971, Asia Publishing

House.

- Book of Practical Physics, I. Prakash and Ramakrishna, 11th Ed.,2011, Kitab Mahal.
- Advanced level Physics Practicals, Michael Nelson, and Jon M. Ogborn, 4th Edition, reprinted

1985, Heinemann Educational Publishers

- A Laboratory Manual of Physics for undergraduate classes. D. P. Khandelwal, 1985, Vani.

**+3 SECOND YEAR THIRD SEMESTER**

**Core Paper – 5**

**MATHEMATICAL PHYSICS-II**

Time : **3 Hrs**. End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

The emphasis of the course is on applications in solving problems of interest to physicists.

Students are to be examined on the basis of problems, seen and unseen.

**UNIT-I**

Fourier Series-I: Periodic functions, Orthogonality of sine and cosine functions, Dirichlet

Conditions (Statement only), Expansion of periodic functions in a series of sine and cosine

functions and determination of Fourier coefficients. Complex representation of Fourier series,

Expansion of functions with arbitrary period, Expansion of non-periodic functions over an interval, Even and odd functions and their Fourier expansions and Application, Summing of Infinite Series, Term-by-Term differentiation and integration of Fourier Series, Parseval Identity.

**UNIT-II**

Frobenius Method and Special Functions: Singular Points of Second Order Linear

Differential Equations and their importance, Singularities of Bessel’s and Laguerre Equations,

Frobenius method and its applications to differential equations: Legendre and Hermite

Differential Equations, Legendre, and Hermite Polynomials: Rodrigues Formula, Generating

Function, Orthogonality.

**UNIT-III**

Polynomials: Simple recurrence relations of Legendre and Hermite Polynomials, Expansion

of function in a series of Legendre Polynomials, Associated Legendre Differential Equation,

Associated Legendre polynomials, Spherical Harmonics.

Some Special Integrals: Beta and Gamma Functions and relation between them, Expression

of Integrals in terms of Gamma Functions, Error Function (Probability Integral).

**UNIT-IV**

Partial Differential Equations: Solutions to partial differential equations using separation of

variables: Laplace’s Equation in problems of rectangular, cylindrical, and spherical symmetry.

Conducting and dielectric sphere in an external uniform electric field. Wave equation and its

solution for vibrational modes of a stretched string.

Text Books:

- Mathematical Methods for Physicists, G. B. Arfken, H. J. Weber, F. E. Harris (2013, 7th Edn., Elsevier)
- Advanced Engineering Mathematics, Envin Kreyszig (Wiley India)

Reference Books:

- Mathematical Physics and Special Relativity, M. Das, P.K. Jena and B.K. Dash (Srikrishna

Prakashan).

- Mathematical Physics-H. K. Dass, Dr. Rama Verma (S. Chand Publishing).
- Mathematical Physics C. Harper (Prentice Halllndiaj Complex Variable)
- Schaum’s Outlines Series M. Spiegel (2nd Edition, McGraw Hill Education)
- Complex variables and applications J.W.Brown and R.V.Churchill
- Mathematical Physics, Satya Prakash (Sultan Chand)
- Mathematical Physics B.D.Gupta (4th edition, Vikas Publication)

**CORE – 5 – LAB**

Credit : **02 (25 Marks)**

The aim of this Lab is to use the computational methods to solve physical problems.

Course will consist of lectures (both theory and practical) in the Lab. Evaluation done not on the

programming but on the basis of formulating the problem.

Topics Introduction to Numerical Computation Software Scilab: Introduction to Scilab,

Advantages, disadvantages, Scilab computation software, Scilab environment Command window, Edit window, Figure window, Variables and arrays, Initialising variables in Scilab. Multidimensional arrays, Subarray, Special. Values Displaying output data, data file, Scalar and array operations. Hierarchy of operations, Built in Scilab . Introduction to plotting, 2D and 3D plotting (2), Branching Statements and program design, Relational and logical perators, the while loop, for loop, details of loop operations, break and continue statements, nested loops, logical arrays and vectorization (2) User defined functions, Introduction to Scilab functions, Variables Passing in Scilab, optional arguments, preserving data between calls to a function,

Complex and Character string function, Multidimensional arrays (2) an introduction to Scilab file processing, file opening and closing, Binary I/o functions, comparing binary and formatted functions, Numerical methods and developing the skills of writing a program(2).

Curve fitting, Least square fit Goodness of fit. standard constant Deviation: Ohms law to

calculate, R. Hookes law to calculate spring constant.

Solution of Linear system of equations by Gauss elimination Solution method and Gauss

Seidal method. Diagonalization matrices, Inverse of a matrix, Eigenvectors, problems:

Solutions of meshi equations of electric circuits (3 meshes), Solution of coupled spring mass

systems (3 masses)

Solution of ODE First order Differential equadon Euler, modifted Euler Runge-Kutta second

methods Second order differential equation. Fixed difference method: First order

differential equation

- Radioactive decay
- Current in RC, LC circuits with DC source
- Newtons law of cooling
- Classical equations of motion

Second order DifferentialEquation

- Harmonic oscillator (no friction)
- Damped Harmonicoscillator
- Overdamped
- Criticaldamped
- Oscillatory
- Forced Harmonicoscillator
- Transient and Steady statesolution
- Apply above to LCR circuitsalso

Reference Books:

- Mathematical Methods for Physics and Engineers, K.F. Riley, M.P. Hobson and S. J.20 Bence, 3rd

ed., 2006, Cambridge University Press.

- Complex Variables, A.S. Fokas and M.J. Ablowitz, 8th Ed., 2011. Cambridge Univ. Press.
- First course in complex analysis with applications. D.GZill and P.D. Shana – han, 1940, Jones

and Bartlett.

- Simulation of ODE/PDE Models with MATLAB, OCTAVE and SCILAB: Scientific and Engineering

Applications: A.V. Wouwer, P. Saucez, C.V. Fern- ndez. 2014 Springer

Syllabus-Science 211

- Scilab by example: M.Affouf 2012, ISBN: 978-1479203444
- Scilab ( A free software to Matlab) : H.Ramchandran, A.S.Nair.2011 S.Chand and Company

Scilab Image Processing: Lambert M. Surhone. 2010 Betascript Publishing.

**Core Paper – 6**

**THERMAL PHYSICS**

Time : **3 Hrs**. End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Introduction to Thermodynamics :Recapitulation of Zeroth and First law of thermodynamics, Second Law of Thermodynamics: Reversible and Irreversible process with examples, Kelvin and Clausius Statements and their Equivalence, Carnot’s Theorem, Applications of Second Law of Thermodynamics. Thermodynamic Scale of Temperature and its Equivalence to Perfect Gas Scale.

Entropy: Concept of Entropy, Clausius Theorem. Clausius Inequality, Second Law of

Thermodynamics in terms of Entropy, Entropy of a perfect gas, Principle of increase of Entropy, Entropy Changes in Reversible and Irreversible processes with examples, Entropy of the Principle of Increase of Entropy, Temperature Entropy Diagram for Carnot’s Cycle, Third Law of Thermodynamics, Unattainability of Absolute Zero.

**UNIT-II**

Thermodynamic Potentials: Extensive and Intensive Thermodynamic Variables,

Thermodynamic Potentials: Internal Energy, Enthalpy, Helmholtz Free Energy, Gibbs Free

Energy, their definitions, Properties and Applications, Surface Films and Variation of Surface

Tension with Temperature, Magnetic Work, Cooling due to adiabatic demagnetization.

Phase Transitions: First and second order Phase Transitions with examples, Clausius Clapeyron Equation and Ehrenfest equations.

Maxwells Thermodynamic Relations: Derivations and applications of Maxwells Relations,

Maxwells Relations: (1) Clausius Clapeyron equation (2) Relation between Cp and Cv (3)TdS

Equations,(4)Joule-Kelvin coefficient for Ideal and Van der Waal Gases (5) Energy equations

(6) Change of Temperature during Adiabatic Process.

**UNIT-III**

Kinetic Theory of Gases

Distribution of Velocities: Maxwell-Boltzmann Law of Distribution of Velocities in an Ideal

Gas and its Experimental Verification, Sterns Experiment, Mean. RMS and Most Probable Speeds, Degrees of Freedom, Law of Equipartition of Energy (No proof required). Specific heats of Gases.

Molecular Collisions: Mean Free Path, Collision Probability, Estimates of Mean Free Path.

Transport Phenomenon in Ideal Gases: (1) Viscosity, (2) Thermal Conductivity and (3)

Diffusion. Brownian Motion and its Significance.

**UNIT-IV**

Real Gases: Behavior of Real Gases: Deviations from the Ideal Gas Equation, The Virial

Equation, Andrews Experiments on CO2 Gas. Critical Constants, Continuity of Liquid and Gaseous State. Vapour and Gas, Boyle Temperature, Vander Waals Equation of State for Real Gases, Values of Critical Constants, Law of Corresponding States, Comparison with Experimental Curves, P-V Diagrams, Joules Experiment, Free Adiabatic Expansion of a Perfect Gas, Joule- Thomson Porous Plug Experiment, Joule- Thomson Effect for Real and Van der Waal Gases, Temperature of Inversion, Joule-Thomson Cooling.

Text Books:

- Thermal Physics, A. B. Gupta (Books and allied Ltd)
- Heat and Thermodynamics, M.W. Zemansky, Richard Dittman (McGraw- Hill)

Reference Books:

- Theory and experiments on thermal Physics, P.K. Chakrabarty (New central book agency limited)
- Thermodynamics, Kinetic Theory and Statistical Thermodynamics-Sears and Salinger(Narosa)
- A Treatise on Heat- Meghnad Saha and B.N. Srivastava (The Indian Press) Heat,

Thermodynamics and Statistical Physics, N. Subrahmanyam and Brij Lal (S. Chand Publishing)

- Thermal and Statistical Physics M. Das, P.K. Jena, S. Mishra, R.N. Mishra (Shri Krishna

Publication)

**CORE PAPER – 6 – LAB**

(Minimum 5 experiments to be done)

Credit : **02 (25 Marks)**

- To determine Mechanical Equivalent of Heat, J, by Callender and Barnes constant flow method.
- To determine the Coefficient of Thermal Conductivity of a bad conductor by Lee and Charlton’s disc method.
- To determine the Temperature Coefficient of Resistance by Platinum Resistance Thermometer

(PRT). I

- To study the variation of Thermo-Emf of a Thermocouple with Difference of Temperature of its

Two Junctions.

- To determine J by Caloriemeter.
- To determine the specific heat of liquid by the method of cooling.

Syllabus-Science 213

- To determine the specific heat of solid by applying radiation of correction.

Reference Books:

- Advanced Practical Physics for students, B. L. Flint and H.T. Worsnop, 1971, Asia Publishing

House.

- A Text Book of Practical Physics, I.Prakash and Ramakrishna. 11 th Ed., 2011, Kitab Mahal.
- Advanced level Physics Practicals, Michael Nelson and Jon M. Ogbora, 4th Edition, reprinted

1985, Heinemann Educational Publishers.

- A Laboratory Manual of Physics for undergraduate classes,D.PKhandelwal,1985, Vani Pub.

**+3 SECOND YEAR THIRD SEMESTER**

**Core Paper – 7**

**ANALOG SYSTEMS AND APPLICATIONS**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Semiconductor Diodes: P and N type semiconductors, energy level diagram, conductivity

and mobility, Concept of Drift velocity, PN junction fabrication (simple idea), Barrier formation in PN Junction diode. Static and Dynamic Resistance, Current flow mechanism in Forward and Reverse Biased Diode, Drift velocity derivation for Barrier Potential, Barrier Width, and current Step Junction.

Two terminal device and their applications: (1) Rectifier Diode: Half- wave Rectifiers

Center tapped and bridge type Full-wave Rectifiers, Calculation of Ripple Factor and Rectification Efficiency, L and C Filters (1) Zener Diode and Voltage Regulation, Principle and structure of LEDS, (2) Photo diode(3) Solar Cell.

**UNIT – II**

Bipolar Junction Transistors: n-p-n and p-n-p transistors. Characteristics of CB,CE and CC

Configurations, Current gains α and β, Relation between α and β. Load line analysis of

Transistors, DC Load line and Q-point, Physical mechanism of current flow, Active, Cut-off and

Saturation Regions.

Transistors Biasing: Transistor Biasing and Stabilization circuits, Fixed Bias, and Voltage Divider Bias.

Amplifiers: Transistors as 2-port network h-parameter Equivalent Circuit, Analysis of a single

stage CE amplifier using Hybrid Model, Input and Output impedance. Current, Voltage and

Power Gains, Classification of class A, B and C amplifiers, Push-pull amplifier (class B).

**UNIT – III**

Coupled Amplifier: RC-coupled amplifier and its frequency response.

Feedback in Amplifiers: Effect of Positive and Negative Feedback on Input Impedance, Output Impedance, Gain Stability, Distortion and Noise. Sinusoidal Oscillations, Barkhausen’s Criterion for self-sustained oscillator. RC Phase shift oscillator, determination of Frequency, Hartley and Colpitts oscillators.

**UNIT-IV**

Operational Amplifiers (Black Box approach): Characteristics of an Ideal and Practical OPAMP (IC741). Open-loop and Closed loop Gain. Frequency Response. CMRR, Slew Rate and concept of virtual ground.

Application of Op-Amps: (1) Inverting and non-inverting amplifiers (2) Adder (3) Subtractor

(4) Differentiator, (5) Integrator (6) Log amplifier, (7) Zero crossing detector (8) Wein

Bridge oscillator.

Text Books:

- Foundations of Electronics-Raskhit and Chattopadhyay (New age International Publication)
- Concept of Electronics- D.C.Tayal (HimalayPublication)

Reference Books:

- Electronic devices and circuits R.L. Boylstad (Pearson lndia)
- Electronic Principles-A.P. Malvino (Tata McGraw Hill)
- Principles of Electronics- V. K. Mehta and Rohit Mehta (S. Chand Publication)
- OP-Amps and Linear Integrated Circuit-R. A. Gayakwad (Prentice Hall)
- Physics of Semiconductor devices, Donald A Neamen (Prentice Hall)

**CORE – PAPER – 7 – LAB**

(Minimum 5 experiments to be done)

Credit : **02 (25 Marks)**

- To study the V-I characterstics of a Zener diode and its use as voltage regulator.
- Study of V-I and power curves of solar cells, and find maximum power point and efficieny.
- To study the characterstics of a Bipolar Junction Transistor in CE configuration and draw load

line.

- To study the various biasing configurations of BJT for normal class A operation.
- To study the frequency response of voltage gain of a RC – coupled transistor amplifier.
- To design and study OP Amp-IC (741/351) as inverting and non-inverting amplifier.
- To design and study OP AMP-IC (741/351) as integrator and differentiation and study frequency

response.

- To design and study OP AMP – IC (741/351) as adder and subtractor.
- To design a wien bridge oscillator for given frequency using a OP-amp.
- To design a phase shipft oscillator of given specifications using BJT.

Syllabus-Science 215

Reference Books:

- Modern Digital Electronics, R.P. Jain, 4th Edition, 2010, Tata McGraw Hill.
- Basic Electronics: A text lab manual, P.B. Zbar, A.P. Malvino, M.A. Miller, 1994, Mc-Graw Hill.
- Microprocessor Architecture Programming and applications with 8085, R.S. Goankar, 2002,

Prentice Hall.

- Microprocessor 8085: Architecture, Programming and interfacing, A. Wadhwa, 2010, PHI

Learning.

**+3 SECOND YEAR FOURTH SEMESTER**

**Core Paper – 8**

**MATHEMATICAL PHYSICS – III**

Time : **3 Hrs**. End Semester Theory : **60 Marks**

Credit : **04 **Mid Semester Theory : **15 Marks**

The emphasis of the course is on applications in solving problems of interest to physicists.

Students are examined on the basis of problems, seen and unseen.

**Unit – I**

Complex Analysis: Brief Revision of Complex Numbers and their Graphical Representation

Eulers De Moivre’s theorem, Roots of complex Numbers, Functions of Complex Variables,

Analyticity and Cauchy-Riemann Conditions, Examples of analytic functions, Singular functions: poles and branch points, order of singularity, branch cuts, Integration of a function of a complex variable, Cauchy’s Inequality, Cauchy’s Integral formula, Simply and multiply connected region, Laurent and Taylors expansion, Residues and Residue Theorem, Application in solving Definite Integrals.

**Unit – II**

Integral Transforms-I: Fourier Transforms: Fourier Integral theorem, Fourier Transform,

Examples, Fourier Transform of trigonometric Gaussian finite-wave train and other functions,

Representation of Dirac delta function as Fourier Integral, Fourier transform of derivatives,

Inverse Fourier Transform.

**Unit – III**

Integral Transforms-II: Convolution theorem, Properties of Fourier Transforms (translation,

change conjugation), Three dimensional Fourier transforms with examples, Application of Fourier Transforms to differential equations: One dimensional Wave and Diffusion/Heat flow Equations.

**UNIT-IV**

Laplace Transforms: Laplace Transforms (LT) of Elementary functions.

Properties of Laplace Transforms: Change of Scale Theorem, Shifting Theorem, LTs of

Derivatives and Integrals of Functions, Derivatives and Integrals of Functions, Derivatives and

Integrals of LTs. LT of Unit Step function, Dirac Delta function. Periodic Functions, Inverse LT, Application of Laplace Transforms to Differential Equations: Damped Harmonic Oscillator, Simple Electrical Circuits.

Text Books:

- Mathematical Methods for Physicists,GB. Arfkcn H. J. Weber, F. E.Harris (2013,7th Edn.,Elsevier)
- Advanced Engineering Mathematics, ErwinKreyszig(Wiley India)

Reference Books:

- Mathematica!PhysicsandSpecialReIativitv-M.Das,P.K.JenaandB.K. Dash (SrikrishnaPrakashan)
- Mathematical Physics- H. K. Dass, Dr. Rama Verma (S. Chand Publishing) Mathematical Physics
- Harper (Prentice Hall India)
- Complex Variable: Schaum’s Outlines Series M. Spiegel (2nd Edition , Me- Graw Hill Education)
- Complex variables and applications J.W.Brown and R.V.Churchill
- Mathematical Physics, Satya Prakash (Sultan Chand)
- Mathematical Physics B.D.Gupta (4thedition,Vikas Publication)

CORE – 8 – LAB

Credit : 02 25 Marks

Scilab based simulations (XCos) experiments based on Mathematical Physics problems like.

* Solve simple differential equations like:

e x with y(x 0) 0

dx

dy + −x = z = =

-y with y(x 0) 0, y’ (x 0) 1

dx

2 dy

dx

d2y

+ = = = = =

-y with y(x 0) 0, y’ (x 0) 1

dx

e dy

dx

d y x

2

+ − = = = = =

* Direct Delta Function

Evaluate e , for 0.1, 0.01, 0.001

2

dx (x 3) 2

2

2

(x-z)

3

3 2

σ =

πσ

+ σ

− ∫ and show that it tends to 5.

Syllabus-Science 217

* Fourier Series:

Program to sum

Evaluate the Fourier coefficients of a given periodic function (square wave)

n m m,n

1

1 2n 1

d p ( )p ( ) 2 δ

+

∫ μ μ μ = −

* Frobenius method and Special functions:

Plot Pn(x), Legendre polynomical of degree n, and Jn(x), Based function of first kind.

Show recursion relation

* Calculation of error for each data point of observations recorded in experiments done in previous

semesters (choose any two).

* Calculation of least square fitting manually without giving weightage to error. Confirmation of

least square fitting of data through computer program.

* Evaluation of trigonometric functions e.g. sin θ , Given Bessels function at N points find its value

at an intermediate point.

Complex analysis: Calculate

∫ (x + 2)

dx

2

and cheek it with computer integration.

* Integral trasform: FFT of e−x2

Reference Books:

- Mathcmatical Mcthods for Physics and Engineers, K.FRiley, M.P. Hobson and S. J. Bence, 3rd

cd., 2006, Cambridge University Press.

- MatIiematics for Physicists, P. Dennery and A.Krzywicki,1967,DovcrPub-lications
- Simulation of ODE/PDE Models with MATLAB, OCTAVE and SCILAB: Scientific and Engineenng

Applications: A. VandeWouwcr, P. Saucez, C. V. Femndez. 2014 Springer ISBN: 978-331

9067896

- Scilab by example: M.Affouf, 2012. ISBN: 978-1479203444.
- Scilab(A free software to Matlab): H. Ramchandran, A.S.Nair.2011S.Chand and Company.
- Scilab Image Processing: Lambert M. Surhone. 2010 Betascript Publishing.

218 Syllabus-Science

**+3 SECOND YEAR FOURTH SEMESTER**

**Core Paper – 9**

**ELEMENTS OF MODERN PHYSICS**

Time : **3 Hrs. ** End Semester Theory : **60 Marks**

Credit **: 04 ** Mid Semester Theory : **15 Marks**

**UNIT- I**

Atomic Spectra and Models: Inadequacy of classical physics, Brief Review of Black body

Radiation, Photoelectric effect. Compton Effect, dual nature of radiation wave nature of particles, Atomic spectra, Line spectra of hydrogen atom, Ritz Rydberg combination principle, Alpha Particle Scattering, Ruther- ford Scattering Formula, Rutherford Model of atom and its limitations.

Atomic Model: Bohrs Model of Hydrogen atom, explanation of atomic spectra, correction for finite mass of the nucleus, Bohr correspondence principle, limitations of Bohr model, discrete energy exchange by atom, Frank Hertz Experiment, Sommerfeld’s modification of Bohr’s Theory.

**UNIT- II**

Wave Packet: superposition of two waves, phase velocity and group velocity, wave packets,

Gaussian Wave Packet, spatial distribution of wave packet, Localization of wave packet in time, Time development of a wave packet, Wave Particle Duality Complementarity.

Wave Particle Duality: de Broglie hypothesis, Experimental confirmation of matter wave,

Davisson Germer Experiment, velocity of de-Broglie wave, wave particle duality, Complementarity

Uncertainty Principle: Heisenberg Uncertainty Principle, Illustration of the Principle through Experiments of Gamma ray microscope and electron diffraction through a slit, Estimation of ground state energy of harmonic oscillator and hydrogen atom, non-existence of electron in the nucleus, Uncertainty, and complementarities.

**UNIT- III**

Nuclear Physics-1: Size and structure of atomic nucleus and its relation with atomic weight,

Impossibility of an electron being in the nucleus as a consequence of the uncertainty principle,

Nature of the nuclear force, NZ graph, Liquid Drop model: semi empirical mass formula and

binding energy, Nuclear Shell Model, and magic numbers.

**UNIT-IV**

Nuclear Physics- II: Radioactivity, stability of the nucleus, Law of radio-active decay, Mean and Half-life, Alpha decay, Beta decay-energy released, spectrum and Pauli’s prediction of neutrino, Gamma ray emission energy-momentum conservation: electron-positron pair creation by gamma photons in the vicinity of a nucleus, Fission and fusion, mass defect, relativity and generation of energy, Fission- nature of fragments and emission of neutrons. Nuclear reactor: slow neutron interacting with Uranium 235, Fusion and thermonuclear reactions driving stellar energy (brief qualitative discussion).

Text Books:

- Concepts of Modem Physics Arthur Beiser (McGraw Hill)
- Modern Physics Murugeshan and Sivaprasad (S. Chand)

Reference Books:

- QuantumMechanics:TheoryandApplications,A.K.GhatakandS.Lokanathan,(Macniillan)
- Introduction to Quantum Theory, David Park (Dover Publications)
- Theory and Problems of Modern Physics, Schaum’s outline, R. Gautreau and W. Savin- (Tata McGraw-Hill)
- Modern Physics-Serway (CENGAGE Learnings)
- Physics of Atoms and Molecules Bransden and Joachim (Pearsonlndia)
- Atomic and Nuclear Physics-A.B.Gupta (NcwCentral)
- Theoretical Nuclear Physics, J.M.Blatt and V.F. Wcisskopf(Springer)

**CORE – 9 – LAB**

Credit : **02 (25 Marks)**

- To show the tunnelling effect in tunnel diode using I-V characteristics.
- To determine the wavelength of laser source using diffraction of single slit.
- To determine the wavelength of laser source using diffraction of double slits.
- To determine (1) wavelength and (2) angular spread of He-Ne laser using plane diffraction

grating.

- To determine the Planck’s constant using LEDs of at least 4 different colours.
- To determine the value of e/m by (a) Magnetic focusing or (b) Bar magnet.
- To setup the Millikan oil drop apparatus and determine the charge of an electron.

Reference Books:

- Advanced Practical Physics for students, B.L. Flint and H.T. Worsnop, 1971, Asia Publishing House.
- Advanced level Physics Practical, Michael Nelson, and Jon M. Ogborn, 4th Edition, reprinted 1985, Heinemann Educational Publishers.
- A Text Books Book of Practical Physics, LPrakashand Ramakrishna, 11th Edn, 201 l, Kitab Mahal.

**+3 SECOND YEAR FOURTH SEMESTER**

**Core Paper – 10**

**DIGITAL SYSTEMS AND APPLICATIONS**

**UNIT – I**

Integrated Circuits (Qualitative treatment only): Active and Passive Components, Discrete

components, Wafer Chip, Advantages and Drawbacks of ICs, Scale of Integration: SSI, MSI,

LSI and VLSI (basic idea and definitions only). Classification of ICs, Examples of Linear and

Digital ICs.

Digital Circuits: Difference between Analog and Digital Circuits, Binary Numbers, Decimal to Binary and Binary to Decimal Conversation, BCD, Octal and Hexadecimal numbers, AND, OR and NOT. Gates (realization using Diodes and Transistor), NAND and NOR Gates as Universal Gates, XOR and XNOR Gates and application as Parity Checkers.

**UNIT-II**

Boolean algebra: De Morgans Theorems: Boolean Laws, Simplification of Logic Circuit using Boolean Algebra, Fundamental Products, Idea of Min terms and Max terms, Conversion of a Truth table in to Equivalent Logic Circuit by (1) Sum of Products Method and (2) Karnaugh Map.

Introduction to CRO: Block Diagram of CRO, Electron Gun, Deflection system and Time

Base, Deflection Sensitivity.

Applications of CRO: (I) Study of Wave Form, (2) Measurement of Voltage, Current, Frequency and Phase Difference.

**UNIT-III**

Data Processing Circuits: Basic Idea of Multiplexers, De-multiplexers, Decoders, Encoders.

Arithmetic Circuits: Binary Addition. Binary Subtraction using 2s complement. Half and Full

Adders. Half and Full Subtracters, 4 bits binary Adder/Subtractor.

Timers: 1C 555: block diagram and application as Astable multivibrator and Monostable

multivibrator.

**UNIT-IV**

Introduction to Computer Organization: Input/output Devices, Data storage (idea of RAM

and ROM), Computer memory. Memory organization and addressing, Memory Interfacing,

Memory Map.

Shift registers: Serial-in-serial-out, Serial-in-Parallel-out, Parallel-in-Serial- out and Parallel in-Parallel-out. Shift Registers (only up to 4 bits)

Counters (4 bits): Ring Counter, Asynchronous counters. Decade Counter. Synchronous

Counter.

Text Books:

- Digital Circuits and Logic design: Samuel C, Lee (Printice Hall)
- Digital Principles and Applications – A.P. Malvino, D.P. Leach and Saha (Tata McGraw)

Syllabus-Science 221

Reference Books :

- The Art of Electronics by Paul Horowitz and Wilfield Hill Cambridge University
- Electronics by Allan R. Hambley ,Prentice Hall 3. Principles of Electronics V.K. Mehta and Rohit

Mehta (S. Chand Publishing)

- Digital Logic and Computer design M. Morris Mano (Pearson)
- Concepts of Electronics D.C. Tayal (Himalaya Publishing house)

CORE – 10 – LAB

Credit : 02 25 Marks

- To measure (a) Voltage, and (b) Time period of a periodic wave form using CRO and to test a

Diode and Transistor using a Millimetres.

- To design a switch (NOT gate) using a transistor.
- To verity- and design AND, OR, NOT and XOR gates using NAND gates.
- Half Adder, Full Adder, and 4-bit binary Adder.
- Half Subtractor, Full Subtracter, Adder-Subtracter using Full Adder I.C.
- To build Flip-Flop (RS, Clocked RS, D-type and JK) circuits using NAND gates.
- To design an astable multivibrator of given specifications using 555 Timer.
- To design a monostable multivibrator of given specifications using 555 Timer.

Reference Books:

- Basic Electronics: A Text Books lab manual, RB. Zbar, A.R Malvino,
- M.A. Miller, 1994, Mc-Graw Hill.
- OP-Amps and Linear Integrated Circuit, R. A. Gayakwad, 4th edition, 2000, Prentice Hall.
- Electronic Principle, Albert Malvino, 2008, TataMc-Graw Hill. Electronic Devices and circuit Theory,

R.L.Boylestad and L.D.Nashelsky, 2009, Pearson

**+3 THIRD YEAR FIFTH SEMESTER**

**Core Paper – 11**

**QUANTUM MECHANICS**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-1**

Schrodinger equation : Time dependent Schrodinger equation, Properties of Wave Function,

Interpretation of wave function, Probability, and probability current densities in three dimensions, Conditions for Physical Acceptability of Wave Function, Normalization, Linearity and Superposition Principles. Wave function of a free particle, Wave Packet, Fourier Transform and momentum space Wavefunction, Spread of j Gaussian Wave packet, Evolution with time, Position and Momentum Uncertainty.

**UNIT-II**

Operators: Operators, Commutator Algebra, Position, Momentum, Angular Momentum and

Energy operators, Hermitian Operators, Expectation values of position and momentum, Ehrenfest Theorem, Eigenvalues and Eigenfunctions of Hermitian Operator, Energy Eigen Spectrum, Degeneracy, Orthonormality of Eigen functions, Linear Dependence, Orthogonalisation.

**UNIT-III**

Time Independent Schrodinger equation in 1 d, 2d and 3d, Hamiltonian, stationary states, and energy eigen values, expansion of an arbitrary wave function as a linear combination of energy eigen functions, General solution of the time dependent Schrodinger equation in terms of linear combinations of stationary states. General Discussion of Bound states in an arbitrary potential: Continuity of wave function, Boundary condition and emergence of discrete energy levels, Application to one dimensional problem-Square well potential, Quantum mechanics of simple Harmonic Oscillator-Energy Levels and energy eigen functions, ground state, zero point energy and uncertainty principle, One dimensional infinitely rigid box energy eigen values and eigen functions, normalization, quantum dot as example, Quantum mechanical scattering and tunnelling in one dimension across a step potential and rectangular potential barrier.

**UNIT-IV**

Atoms in Electric and Magnetic Fields: Electron angular momentum. Space quantization,

Electron Spin and Spin Angular Momentum, Larmor’s Theorem, Spin Magnetic Moment, Stern-Gerlach Experiment, Vector Atom Model, L-S and J-J coupling, Zeeman Effect, Electron Magnetic Moment and Magnetic Energy, Gyromagnetic Ratio and Bohr Magneton. Atoms in External Magnetic Fields:-Normal and Anomalous Zeeman Effect, Paschen back and Stark Effect (qualitative Discussion only)

Text Books:

- Introduction to Quantum Theory David Park (Dover Publications)
- Introduction to Quantum Theory, D. J. Griffiths(Pearson)

Reference Books :

- Quantum Mechanics, Theory and applications A. Ghatak and S. Lokanathan (Me Millan lndia)
- Quantum Mechanics- G Aruldhas (Printice Hallof India)
- Quantum Physics- S. Gasiorowicz (Wiley)
- Quantum Mechanics- G.R. Chatwal and S.K. Anand
- Quantum Mechanics – J.L. Powell and B. CrasemanfNarosa)
- Introduction to Quantum Mechanics M. Das and P.K. Jena (Shri Krishna Publication)

**CORE – 11 – LAB**

Credit : **02 (25 Marks)**

Use C/C++/Scilab for solving the following problems based on Quantum Mechanics like (Use

finite difference method, matrix method, ODE Solver method in all cases)

- Solve the s-wave Schrodinger equation for the ground state and the first excited state of the

hydrogen atom:

[V(r) E],V(r) ,

h

A(r)u(r),A(r) 2m

dr

d y

r

e

2 2

2

2 = = − =

where m is the reduced mass of the electron. Obtain the energy eigenvalues and plot the

corresponding wave functions. Remember that the ground state energy of the hydrogen atom

is ~ -13.6eV. Take e = 3.795 (eVÅ) h c = 1973 (eV oA) and m = 0.511 × 106 e V/c2.

- Solve the s-wave radial Schrodinger equation for an atom:

[V(r) E],

h

A(r)u(r),A(r) 2m

dr

d y

2 2

2

= = −

where m is the reduced mass of the system (which can

be chosen to be the mass of an electron), for the screened coulomb potential: V(r) = r / a

2

e

r

− e − .

Find the energy (in eV) of the ground state of the atom to an accuracy of three significant digits.

Also, plot the corresponding wave function. Take e = 3.795 (eVA),

o hc = 1973 (eV oA) and m

= 0.511 × 106 eV/c2, and a = 3Å, 5Å, 7Å. The ground state energy is expected to be above -12 eV

in all three cases.

- Solve the s-wave radial Schrodinger equation for a particle of mass m:

[V(r) E],

h

A(r)u(r),A(r) 2m

dr

d y

2 2

2

= = − for the anharmonic oscillator potential: V (r) =

3

br

2

kr2 3

+ .

Find the ground state energy (in MeV) of the particle to an accuracy of three significant

digits. Also, plot the corresponding wave function. Choose m = 940 Me V/c2, k = 100 Me V/fm2,

b = 0, 10, 30 MeV/fm3. In these Units, c = 197.3 Me V fm. [The gound state energy is expected

to lie between 90 and 110 M eV for all three cases.]

- Solve the s-wave radial Schrodinger equation for the vibrations of hydrogen molecule:

[V(r) E],

h

A(r)u(r),A(r) 2m

dr

d y

2 2

2

= = − where m is the reduced mass of thetwo-atom system

for the Morse potential V(r) = D(e-2ar -e-ar), where r = r – r0 Find the lowest vibrational energy (in

MeV) of the molecule to an accuracy of three significant digits. Also plot the corresponding

wave functions for the choices given below:

- a) m = 940 x 106 eV/c2, D = 0.755501eV, a = 1.44, r0 = 0.131349Å
- b) m = 940 x 106 eV/c2, D = 0.755501 eV, a = 1.44, r0 = 0.131349Å

Laboratory based experiments:

- Study of Electron spin resonance- determine magnetic field as a function of the resonance

frequency.

- Study of Zeeman effect with external magnetic field; Hyper fine splitting
- To show the tunnelling effect in tunnel diode using I-V characteristics.
- Quantum efficiency of CCDs

Reference Books:

- Schaum’s outline of Programming with C++. J. Hubbard,2000,McGraw— Hill Publication
- Numerical Recipes in C: The Art of Scientific Computing, W.H. Pressetal., 3rd Edn., 2007,

Cambridge University Press.

- An introduction to computational Physics, T. Pang, 2nd Edn.,2006, Cam- bridge Univ. Press
- Simulation of ODE/PDE Models with MATLAB, OCTAVE and SCILAB: Scientific and Engineering

Applications: A. Vande Wouwer, P. Saucez, C. V. Femndez.2014 Springer.

- Scilab (A Free Software to Matlab): H. Ramchandran, A.S. Nair. 2011S. Chand and Co.
- Scilab Image Processing L.M. Surhone.2010 Betascript Publishing ISBN:9786133459274.

**+3 THIRD YEAR FIFTH SEMESTER**

**Core Paper – 12**

**SOLID STATE PHYSICS**

Time : **3 Hrs**. End Semester Theory **: 60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Crystal Structure: Solids, Amorphous and Crystalline Materials, Lattice translation Vectors,

Lattice with a Basis. Central and Non-Central Elements. Unit Cell, Miller Indices, Types of

Lattices, Reciprocal Lattice, Brillouin zones, Diffraction of X-rays by crystals, Bragg Law, Atomic and Geometrical Factor

**UNIT-II**

Elementary Lattice Dynamics: Lattice Vibrations and Phonons: Linear, Mono-atomic and Diatomic Chains, Acoustical and Optical Phonons, Qualitative Description of the phonon spectrum in solids, Dulong and Petit’s Law, Einstein, and Debye theories of specific heat of solids, T^{3} Law

Magnetic Properties of Matter: Dia-, Para-, Ferri- and Ferromagnetic Materials, Classical Langevin’s theory of dia- and Paramagnetic Domains, Curies law, Weiss Theory of

Ferromagnetism and Ferromagnetic Domains, Discussion of B-H Curve, Hysteresis and Energy Loss.

**UNIT-III**

Dielectric Properties of Materials: Polarization Local Electrical Field at an Atom, Depolarization Field, Electric Susceptibility, Polarizability, Clausius-Moscotti Equation, Classical theory of Electronic Polarizability.

Lasers: Einstein’s A and B co-efficient, Metastable States, Spontaneous and Stimulated

emissions, Optical Pumping, and population Inversion, Three Level and Four Level Lasers,

Ruby Laser and He-Ne Laser.

**UNIT-IV**

Elementary band theory: Kronig-Penny model of band Gap, Conductor, Semiconductor (P and N-type) and insulator, Conductivity of Semiconductor, mobility, Hall Effect, Measurement of conductivity (04-probe method) and Hall Co-efficient.

Superconductivity: Experimental Results, Critical Temperature, Critical magnetic field, Meissner effect, Type I and type II Super conductors, London’s Equation and Penetration Depth, Isotope effect, Idea of BCS theory (No derivation).

Text Books:

- Introduction to Solid State Physics- Charles Kittel (Wiley lndia)
- LASERS: Fundamentals and Applications- Thyagarajan and Ghatak (Me MilIan India)

Reference Books:

- Solid State Physics- N. W. Ashcroft and N.D.Mermin (Cengage)
- Solid State Physics-R.K.Puri and V.K. Babbar (S.Chand Publication)
- Solid State Physics S. O. Pillai (New Age Publication)
- Lasers and Nonlinear Optics B.B.Laud (Wiley Eastern)
- Elements of Solid State Physics-J.P. Srivastava (Prentice Hall of lndia)
- Elementary Solid State Physics-Ali Omar (Addison Wiley)
- To study variation of magnetic field along the axis of circular coil.
- To determine H using deflection Magnetometer.

CORE – 12 – LAB

(Minimum four experiments to be done)

Credit : 02 25 Marks

- Measurement of susceptibility of paramagnetic solution (Quincks Tube- Method)
- To measure the Magnetic susceptibility of Solids.
- To measure the Dielectric Constant of a dielectric Materials with frequency
- To determine the Hall coefficient of a semiconductor sample.
- To draw the BH curve of Fe using solenoid and to determine the energy loss from Hysteresis

226 Syllabus-Science

- To measure the band gap of a given semiconductor by four-probemethod.
- To study variation of magnetic field along the axis of a circular coil carrying current.
- To determine ‘H’ using deflection Magnetometer.

Reference Books:

- Advanced Practical Physics for students, B.L. Flint and H.T. Worsnop, 1971, Asia Publishing

House.

- Advanced level Physics Practicals, Michael Nelson and Jon M. Ogborn, 4th Edition, reprinted

1985, Heinemann Educational Publishers.

- A Text Books of Practical Physics, I.Prakash and Ramakrishna, 11 Ed., 2011, Kitab Mahal
- Elements of Solid State Physics, J.P. Srivastava, 2nd Ed., 2006, Prentice- Hall of India.

**+3 THIRD YEAR SIXTH SEMESTER**

**Core Paper – 13**

**ELECTROMAGNETIC THEORY**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Maxwell Equations :Maxwells equations, Displacement Current, Vector and Scalar Potentials, Gauge Transformations: Lorentz and Coulomb Gauge, Boundary Conditions at Interface between Different Media, Wave Equations, Plane Waves in Dielectric Media, Poynting Theorem and Poynting Vector, Electro- magnetic (EM) Energy Density, Physical Concept of Electromagnetic Field Energy Density.

**UNIT-II**

EM Wave Propagation in Unbounded Media: Plane EM waves through vacuum and isotropic dielectric medium, transverse nature of plane EM waves, refractive index and dielectric constant, wave impedance, Propagation through conducting media, relaxation time, skin depth, Electrical conductivity of ionized gases, plasma frequency, refractive index, skin depth application to propagation through ionosphere.

**UNIT-III**

EM Wave in Bounded Media: Boundary conditions at a plane interface between two media,

Reflection and Refraction of plane waves at plane interface between two dielectric media,

Laws of Reflection and Refraction, Fresnel’s Formula for perpendicular and parallel polarization cases, Brewster’s law, Reflection and Transmission co-efficient, Total internal reflection, evanescent waves, Metallic reflection (normal incidence)

**UNIT IV**

Polarization of Electromagnetic Waves: Description of Linear, Circular and Elliptical

Polarization, Uniaxial and Biaxial Crystals, Light Propagation in Uniaxial Crystal, Double

Refraction, Polarization by Double Refraction, Nicol Prism, Ordinary and extraordinary refractive indices, Production, and detection of Plane, Circularly and Elliptically Polarized Light,

Phase Retardation Plates: Quarter-Wave and Half- Wave Plates. Babinet’s Compensator and

its Uses, Analysis of Polarized Light.

Rotatory Polarization: Optical Rotation, Biot’s Laws for Rotatory Polarization, Fresnel’s Theory of optical rotation, Calculation of angle of rotation, Experimental verification of Fresnel’s theory, Specific rotation, Laurents half- shade polarimeter.

Text Books:

- Introduction to Electrodynamics, D.J. Griffiths (Pearson)
- Principles of Optics- Max Bornand E.Wolf

Reference Books :

- Classical Electrodynamics by J.D.Jackson.
- Foundation of electromagnetic theory: Ritz and Milford (Pearson)
- Electricity and Magnetism : D C Tayal (Himalaya Publication)
- Optics :A.K.Ghatak
- Electricity and Magnetism: Chattopadhyaya, Rakhit (NewCentral)

**CORE – 13 – LAB**

(Minimum four experiments to be done)

Credit : **02 (25 Marks)**

- To verify the law of Malus for plane polarized light.
- To determine the specific rotation of sugar solution using Polarimeter.
- To analyze elliptically polarized Light by using a Babinets compensator.
- To determine the refractive index of liquid by total internal reflection using Wollastonsair-film.
- To determine the refractive Index of (1) glass and (2) a liquid by total internal reflection using a

Gaussian eye piece.

- To study the polarization of light by reflection and determine the polarizing angle for air-glass

interface.

- To verify the Stefan’s law of radiation and to determine Stefans constant.
- To determine the Boltzmann constant using V-I characteristics of PN junction diode.

Reference Books:

- Advanced Practical Physics for students, B.L. Flint and H.T. Worsnop, 1971, Asia Publishing

House.

- Advanced level Physics Practicals, Michael Nelson and Jon M. Ogborn, 4th Edition, reprinted

1985, Heinemann Educational Publishers

- A Text Books Book of Practical Physics, I.Prakashand Ramakrishna, 11 Ed., 2011, Kitab Mahal

Electromagnetic Field Theory for Engineers and Physicists, G Lehner, 2010,Springer

**+3 THIRD YEAR SIXTH SEMESTER**

**Core Paper – 14**

**STATISTICAL MECHANICS**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-1**

Classical Statistics-I: Microstate and Microstate, Elementary Concept of Ensemble,

Micro-canonical, Canonical and Grand Canonical ensemble, Phase Space, Entropy and

Thermodynamic Probability, Maxwell-Boltzmann Distribution Law, Partition Function.

**UNIT-II**

Classical Statistics-II: Thermodynamic Functions of an Ideal Gas, classical Entropy Expression, Gibbs Paradox, Sackur Tetrode equation, Law of equipartition of Energy (with proof)- Applications to Specific Heat and its Limitations, Thermodynamic Functions of a two energy levels system, Negative Temperature.

**UNIT-III**

Quantum Statistics: Identical particles, microstates and microstates, Fermions and Bosons,

Bose Einstein distribution function and Fermi- Dirac distribution function. Bose- Einstein

Condensation, Bose deviation from Planck’s law, Effect of temperature on Fermi-Dirac distribution function, degenerate Fermi gas, Density of States Fermi energy.

**UNIT-IV**

Radiation: Properties of Thermal Radiation, Blackbody Radiation, Pure Temperature

dependence, Kirchhoff’s law, Stefan Boltzmann law: Thermodynamic proof, Radiation Pressure, Weins Displacement law, Wiens distribution Law, Saha’s ionization Formula, Rayleigh Jeans Law, Ultra Violet catastrophe.

Planck’s Law of Black body Radiation: Experimental verification, Deduction of (1) Wiens

Distribution Law, (2) Rayleigh Jeans Law, (3) Stefan Boltzmann Law, (4) Weins Displacement

Law from Planck’s Law.

Text Books:

- Introduction to Statistical Physics by Kerson Huang (Wiley).
- Statistical Physics, Berkeley Physics Course, F. Re if (Tata Me Graw-Hill)

Reference Books:

- Statistical Mechanics, B .K.Agarwal and Melvin Eisner (New Age International)
- Thermodynamics, Kinetic Theory and Statistical Thermodynamics: Francis W.Sears and Gerhard
- Salinger (Narosa)
- Statistical Mechanics: R.K.Pathria and Paul D. Beale (Academic Press)

**CORE – 14 – LAB**

(Minimum four experiments to be done)

Credit : **02** **(25 Marks)**

Use C/C++/Scilab for solving the problems based on Statistical Mechanics like

- Plot Plancks law for Black Body radiation and compare it with Weins Law and Raleigh-Jeans

Law at high temperature (room temperature) and low temperature.

- Plot Specific Heat of Solids by comparing (a) Dulong-Petit law, (b) Einstein distribution function,

(c) Debyedistribution function for high temperature (room temperature) and low temperature

and compare them for the setwocases.

- Plot Maxwell-Boltzmann distribution function versus temperature.
- Plot Fermi-Dirac distribution function versus temperature.
- Plot Bose-Einstein distribution function versus temperature.

Reference Books:

- Elementary Numerical Analysis, K.E. Atkinson, 3rd Edn. 2007, Wiley India Edition
- Statistical Mechanics, R.K. Pathria, Butterworth Heinemann: 2nd Ed., 1996, Oxford University

Press.

- Thermodynamics, Kinetic Theory and Statistical Thermodynamics, Francis W.Sears and Gerhard

L.Salinger, 1986, Narosa.

- Modern Thermodynamics with Statistical Mechanics, Carl S. Helrich, 2009,Springer
- Simulation of ODE/PDE Models with MATLAB, OCTAVE and SCILAB: Scientific and Engineering

Applications: A. Vande Wouwer, P. Saucez, C. V. Fernndez. 2014 Springer ISBN: 978-

3319067896

- Scilab by example: M. Affouf, 2012. ISBN: 978-1479203444.
- Scilab Image Processing: L.M.Surhone. 2010, Betascript Pub., ISBN: 978-6133459274.

230 Syllabus-Science

**+3 THIRD YEAR FIFTH SEMESTER**

**DSE – 1**

**CLASSICAL DYNAMICS**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04 ** Mid Semester Theory : **15 Marks**

The emphasis of the course is on applications in solving problems of interest to physicists.

Students are to be examined on the basis of problems, seen and unseen.

**UNIT-I**

Generalised co-ordinates and Velocities, Generalised Force, Principle of virtual work Derivation of Lagranges equation of motion from D’Alembert’s Principles, Lagrangian and its Application to Simple, Compound and Double Pendulums, Single Particle in Space, Atwood’s Machine, Dumbbell, Linear harmonic oscillator.

**UNIT-II**

Hamilton’s Principle, Calculus of Variation, and derivation of Euler-Lagranges equation,

Lagrange’s Equations derived from Hamilton’s Principles, Hamiltonian, and its applications to

Shortest Distance between two points in a plane, Geodesic Problem, minimum surface of

revolution, Brachistochrone problem, The Equations of motion and first integrals, The equivalent one-dimensional problem and classification of orbits, canonical momenta,

Hamilton’s equations of motion, Motion of charged particles in external electric and magnetic fields, Applications to central force motion and coupled oscillators.

**UNIT- III**

Special theory of Relativity (Postulates of special theory of relativity),Lorentz transformations,

Minkowski space, The invariant interval, light cone and world lines, space time diagrams,

Times-dilation, length contraction and Twin paradox, Variation of mass with velocity, mass

energy relation.

**UNIT- IV**

Four Vectors: Space Like, Time-like and light-like. Four velocity and acceleration, Four

momentum and energy-momentum relation. Doppler effects from a four vector perspective,

Concept of four-force, Conservation of four momentum, Application to two body decay of an

unstable particle.

Text Books:

1 Classical Mechanics, H.Goldstein, C.P. Poole, J.L. Safko (Pearson)

- Classical Mechanics N C Rana and P S Joag.

Syllabus-Science 231

Reference Books :

- Mechanics-D.S.Mathur (Sultan Chand)
- Solved problems in Classical Mechanics, O.L. Delange and J.Pierrus (Ox-ford Press) (2010)
- Classical Mechanics-M. Das, P.K.Jena, M. Bhuyan, R.N.Mishra (Srikrishna Prakashan)
- Mathematical Physics with Classical Mechanics-Satya Prakash (Sultan Chand and Sons)
- Introduction to classical dynamics R.K.Takwale and S .Puranik (Tata McGraw Hill)
- Classical Mechanics J.C.Upadhyay (Himalayan Publisher)
- Classical Dynamics of particles and systems – S.T.Thorton and Marion (Cengage Publication)

**DSE – 1 – LAB**

Credit : **02 (25 Marks)**

- Fourier Analysis of periodic wave forms.
- Verification of Kepler’s Third Law of Planatory Motion.
- Study of power Source.
- To determine Thermal Conductivity of copper.
- To determine electrical conductivity of coper and determine Lorentz number.
- To determine thermal conductivity of a poor conductor.
- Passive Filters.

**+3 THIRD YEAR FIFTH SEMESTER**

**DSE – 2**

**NUCLEAR AND PARTICLE PHYSICS**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04 ** Mid Semester Theory : **15 Marks**

**UNIT-I**

General properties of Nuclei: Constituents of nucleus and their intrinsic properties, Quantitative facts about mass, radius, charge density (matter density), binding energy, average binding energy and its variation with mass number, main features of binding energy versus mass number curve, N/A plot, angular momentum, parity, magnetic moment electric moments, nuclear excite states.

Radioactivity decays: (a) Alpha decay: basics of alpha-decay processes, theory of alpha emission, Gamow factor, Geiger Nuttall law (b) beta-decay: energy kinematics for beta-decay,

positron emission, electron capture, neutrino hypothesis (c) Elementary idea of Gamma decay.

**UNIT-II**

Nuclear Models: Liquid drop model approach, semi empirical mass formula and significance

of its various terms, conditions of nuclear stability, two nucleon separation energies, evidence

for nuclear shell structure, nuclear magic number, basic assumption of shell models.

**UNIT-III**

Detector for nuclear radiations: Detector for nuclear radiations: Gas detectors: estimation of

Electric field, mobility of particle, For ionization chamber and GM Counter. Basic Principle of

Scintillation Detectors and Construction of photo-multiplier tube (PMT). Semiconductor Detectors (Si and Ge) for charge Particle and photon detection (Concept of charge carrier and mobility), neutron detector.

Particle Accelerators: Van-de Graff generator (Tandem Accelerator), Linear accelerator,

Cyclotron, Synchrotrons.

**UNIT-IV**

Particle Physics: Particle interactions, basic features, types of particles and its families.

Symmetries and conservation laws: Energy and momentum, angular momentum, parity,

baryon number, Lepton number, Isospin, strangeness and charm, Elementary ideas of quarks

and gluons.

Text Books:

- Introduction to Nuclear Physics By Roy and Nigam
- Atomic and Nuclear Physics-N.Subramanyam, Brij Lal and Jivan Seshan (S. Chand Publishing)

Reference Books:

- Introduction to Modern Physics-H.S.Mani and G.K.Mehta (Affilated east and west)
- Introductory nuclear Physics-Kenneth S. Krane (Wiley India Pvt. Ltd)
- Introduction to Elementary Particles-D. Griffith (John Wiley andSons)
- Concepts of Nuclear Physics – Bernard L. Cohen. (Tata Mcgraw Hill).
- Concepts of Modern Physics-Arthur Beiser (McGraw Hill)

**DSE – 2 – LAB**

Credit : **02 (25 Marks)**

- Stefan’s Law of Radiation.
- Thermal Diffusivity of brass.
- Measurement of self-inductance of a coil.
- Measurement of Capacitance.
- Study of Maxwell’s Bridge.
- Study of Max-Well-Wein Bridge.

Syllabus-Science 233

- Thermal Relaxation Time of a Serial light bulb.
- Determination of K/e using a transistor.

**+3 THIRD YEAR SIXTH SEMESTER**

**DSE – 3**

**NANO MATERIALS AND APPLICATIONS**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Nanoscale Systems: Length scales in physics, Nanostructures: 1D, 2D and 3D nanostructures

(nanodots, thin films, nanowires, nanorods), Band structure and density of states of materials

at nanoscale, size effects in nano systems, Quantum confinement, Applications of Schrodinger

equation-infinite potential well, potential step, potential box, quantum confinement of carriers in 3D, 2D, ID nanostructure and its consequences.

**UNIT-II**

Synthesis of Nanostructure Materials: Top-down and bottom-up approach, Photolithography, Ball milling. Gas phase condensation, Vacuum deposition, Physical vapour deposition (PVT): Thermal evaporation, E-beam evaporation, Pulsed Laser deposition, Chemical vapour deposition (CVD), Sol-Gel Electrodeposition, Spray pyrolysis, Hydro thermal synthesis, Preparation through colloidal methods, MBE growth of quantum dots.

**UNIT-III**

Characterization: X-Ray Diffraction, Optical Microscopy, Scanning Electron Microscopy,

Transmission Electron Microscopy, Atomic Force Microscopy, Scanning Tunnelling Microscopy

**UNIT-IV**

Applications: Applications of nanoparticles, quantum dots, nanowires, and thin films for photonic devices (LED, solar cells). Single electron devices (no derivation). CNT based transistors. Nonmaterial Devices: Quantum dots heterostructure lasers, optical switching, and optical data storage. Magnetic quantum well; magnetic dots-magnetic data storage. Micro Electromechanical Systems (MEMS), Nano Electromechanical Systems(NEMS).

Text Books:

- S.K. Kulkarni, Nanotechnology: Principles and Practices (Capital Publishing Company)
- Nano science and nano technology, K. K. Choudhury(Narosa)

234 Syllabus-Science

Reference Books:

- Nano Science and nanotechnology, Sundar Singh (Pragati Prakashan)
- C.P. Poole, Jr. Frank J. Owens, Introduction to Nanotechnology (Wiley India Pvt. Ltd.).
- Richard Booker, Earl Boysen, Nanotechnology (John Wiley and Sons).
- M. Hosokawa, K. Nogi, M. Naita, T. Yokoyama, Nanoparticle Technology Handbook

(Elsevier,2007).

- K.K. Chattopadhyay and A. N. Banerjee, Introduction to Nanoscience and Technology (PHI

Learning . Private Limited).

**DSE – 3 – LAB**

Credit : **02 (25 Marks)**

- Dielectric constant of a non-polar liquid
- Dipole moment of an organic molecule acetone
- Energy band gap of silicon.
- Study of low pass Filter.
- Study of high pass Filter.
- Study of baud pass Filter.

**+3 THIRD YEAR SIXTH SEMESTER**

**DSE – 4**

**PROJECT OR BASIC INSTRUMENTATION**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Basic of Measurement: Instruments accuracy, precision, sensitivity, resolution range etc. Errors in measurements and loading effects.

Multimeter: Principles of measurement of dc voltage and dc current, ac volt- age, ac current

and resistance. Specifications of a multimeter and their significance.

Electronic Voltmeter: Advantage over conventional multimeter for voltage measurement with respect to input impedance and sensitivity. Principles of voltage, measurement (block

Diagram only). Specifications of an electronic Voltmeter/ Multimeter and their significance.

AC millivoltmeter: Type of AC millivoltmeters: Amplifier- rectifier, and rectifier- amplifier. Block diagram ac millivoltmeter, specifications and their significance.

**UNIT-II**

Cathode Ray Oscilloscope: Block diagram of basic CRO. Construction of CRT, Electron gun,

electrostatic focusing and acceleration (Explanation only no mathematical treatment), brief

discussion on screen phosphor, visual persistence, and chemical composition. Time base

operation, synchronization, Front panel controls. Specifications of a CRO and their significance.

Use of CRO for the measurement of voltage (dc and ac frequency, time period). Special features of dual trace, introduction to digital oscilloscope, probes. Digital storage Oscilloscope: Block diagram and principle of working.

**UNIT-III**

Signal Generators and Analysis Instruments: Block diagram, explanation, and specifications of low frequency signal generators, pulse generator, and function generator, Brief idea for testing, specifications, Distortion factor meter, wave analysis.

**UNIT-V**

Digital Instruments: Principle and working of digital meters, Comparison of analog and digital instruments, Characteristics of a digital meter, Working principles of digital voltmeter.

Digital Multimeter: Block diagram and working of a digital multimeter, Working principle of

time interval, frequency and period measurement using universal counter/frequency counter,

time-base stability, accuracy, and resolution.

The test of lab skills will be of the following test items:

- Use of an oscilloscope.
- CRO as a versatile measuring device.
- Circuit tracing of Laboratory electronic equipment,
- Use of Digital multimeter/VTVM for measuring voltages
- Circuit tracing of Laboratory electronic equipment,
- Winding a coil /transformer.
- Study the layout of receiver circuit.
- Trouble shooting circuit
- Balancing of bridges

Laboratory Exercises:

- To observe the loading effect of a multimeter while measuring voltage across a low resistance and high resistance.
- To observe the limitations of a multimeter for measuring high frequency voltage and currents.
- To measure Q of a coil and its dependence on frequency, using a Q-meter.
- Measurement of voltage, frequency, time period and phase angle using CRO.
- Measurement of time period, frequency, average period using universal counter/ frequency

counter.

- Measurement of rise, fall and delay times using a CRO.
- Measurement of distortion of a RF signal generator using distortion factor meter.
- Measurement of R, L and C using a LCR bridge/universal bridge.

Open Ended Experiments:

- Using a Dual Trace Oscilloscope
- Converting the range of a given measuring instrument (voltmeter, ammeter) More emphasis

should be given on hands-on experiments.

Text Books:

- A Text Books book of electrical technology-B.L.Theraja(S.Chand Publishing)
- Digital circuits and systems Venugopal (Tata McGraw Hill)

Reference Books :

- Digital Electrordcs-Subrata Ghoshal (Cengage Leaming)
- Electronic Devices and circuits – S. Salivahanan andN. S.Kumar (TataMc-GrawHill)
- Electronic Devices-Thomas L. Floyd (Pearson)

Additional Reference Books for Practical papers :

- Advanced Practical Physics for students, B.L.Flint and H.T.Worsnop (Asia Publishing House)
- Practical Physics-B .B. Swain (KitabMahal)
- Practical Physics-B.Ghosh (Vol. I andll)
- ALaboratory Manual of Physicsfor Undergraduate Classes, D.P.Khandelwal (Vani Publication)
- B.Sc. Practical Physics- C.L.Arora (S.Chand Publishing)
- B.Sc. Practical Physics H. Singh andP.S.Hemne (S. Chand Publishing)

Syllabus-Science 237

**+3 FIRST YEAR FIRST SEMESTER**

**GE – 1/3**

**(MECHANICS AND PROPERTIES OF MATTER, OSCILLATION AND WAVES,**

**THERMAL PHYSICS, ELECTRICITY AND MAGNETISM AND ELECTRONICS)**

Time : **3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

UNIT-I

Mechanics and Properties of Matter

Moment of Inertia, Parallel axis and perpendicular axis theorem, M.I. of a Solid sphere and

Solid cylinder, Gravitational potential, and field due to a thin spherical shell and a solid sphere at external points and internal points, Relation among elastic constants, depression at free end of a light cantilever, Surface tension, pressure difference across a curved membrane, viscous flow, Poiseuille’ s formula.

**UNIT-II**

Oscillation and Waves

Simple harmonic motion, damped harmonic motion, under damped, over damped and critically

damped motion, Forced vibration, Resonance, Wave equation in a medium, Velocity of

Longitudinal waves in an elastic medium and velocity of transverse wave in a stretched string,

Composition of SHM, Lissajous figures for superposition of two orthogonal simple harmonic

vibrations (a) with same frequency, (b) frequency with 2:1.

**UNIT-III**

Thermal Physics

Entropy, change in entropy in reversible and irreversible process, Carnot engine and its efficiency.

Carnot Theorem, Second law of thermodynamics, Kelvin-Planck, Clausius formula. Thermal

conductivity, differential equation for heat flow in one dimension, Maxwell thermodynamic relation

(statement only), Clausius Clapeyron equation, Black body radiation, Planck radiation formula

(No derivation).

**UNIT-IV**

Electricity and Magnetism

Gauss law of electrostatics, use of Gauss law to compute electrostatic field due to a linear

charge distribution, Magnetic induction B, Lorentz force law, Biot Savarts law, Magnetic induction due to long straight current carrying conductor, and in the axis of a current carrying circular coil,

Amperes Circuital law, its differential form, The law of electromagnetic equations, its differential and integral form, Maxwells electro-magnetic equations and their physical significance, Growth and decay of currents in LR and RC circuits, time constant, alternating currents in RC, RL and LCR circuits, impedance, power factor, resonance.

P-type and N-type semiconductors, PN-Junction as rectifier, Half wave and Full wave rectifiers (Bridge type), efficiency, ripple factor, use of RC, LC, and filters, working of PNP and NPN transistors, transistor configurations in CE and CB circuits and relation between α and JFET, its operation and characteristics of V-I curve.

Text Books:

- Properties of Matter D.S. Mathur (S. Chand Publication).
- Heat and Thermodynamics A.B. Gupta and H.B. Ray (New Central Book Agency).
- A Text book of oscillations, waves and acoustics (5th ed.) M. Ghosh and D. Bhattacharya (S.

Chand Publication).

- Electricity and magnetism- R. Murugeshan (S. Chand Publishing)
- Fundamentals of Electronics-Raskhit and Chattopadhyay (New age International Publication)

Reference Books:

- Physics of Degree students Vol.1 M. Das, P.K. Jena etal (Sri krishna Prakashan).
- Physics of Degree students Vol.11 M. Das, P.K. Jena etal (Sri krishna Prakashan).
- Waves and Oscillations (2nd ed) N. Subramaniyam and Brij Lai (Vikas Publications)
- A Text Books book of Sound (2nd ed) – N. Subramaniyam and Brij Lai (S. Chand Publications)

**GE – 1 – LAB**

Minimum Six experiments to be done

Credit : **02 (25 Marks)**

- To determine the moment of inertia of a flywheel.
- To determine the Youngs modulus Y of a wire by Searls method.
- To determine the modulus of rigidity of a wire by Maxwells needle/Torsion Pendulum

(Dynamicmethod).

- To determine g by bar pendulum.
- To determine the value of Y of a rubber by using travelling microscope.
- To determine the Rigidity of modulus by static method.
- To determine the frequency of a tuning Fork by using Sonometer.
- Verification of Laws of Vibration of a string by using Sonometer.
- To compare capacitances using DeSautybridge.
- To determine the Law of resistance by using Carrey Foster bridge.
- Compare the specific heat of two liquids by method of Cooling.

Reference Books:

- Advanced Practical Physics for students, B.L.FlintandH.T. Worsnop, 1971, Asia Publishing House
- A Laboratory Manual of Physics for Undergraduate Classes, D.P.Khandelwal (1985), Vani

Publication

- A Text book of Practical Physics, Indu Prakash And Ramakrishna, 11th Edition (2011), Kitab

Mahal, NewDelhi.

**+3 FIRST YEAR SECOND SEMESTER**

**GE – 2**

**(OPTICS, SPECIAL THEORY OF RELATIVITY, ATOMIC PHYSICS, QUANTUM MECHANICS, AND NUCLEAR PHYSICS)**

Time **: 3 Hrs.** End Semester Theory : **60 Marks**

Credit : **04** Mid Semester Theory : **15 Marks**

**UNIT-I**

Optics-I: Elementary ideas of monochromatic aberrations and their minimization, chromatic

aberration, achromatic combination, Theory of formation of primary and secondary rainbow,

condition of interference, coherent sources, Young’s double slit experiment, biprism and

measurement of wave length of light by it, colour of thin films and Newtons rings, Fresnel and

Fraunhoffer diffraction, diffraction by single slit plane transmission grating.

Optics-II: Electromagnetic nature of light, polarized and unpolarized light, polarization by

reflection and refraction, Brewsters Law, Malus Law, Double refraction, Ordinary and extraordinary rays.

**UNIT-II**

Atomic Physics: Inadequacy of classical physics, brief outline of Rayleigh Jeans theory and

Planck’s quantum theory of radiation, particle nature of electromagnetic radiation photo electric effect, Compton effect, dual nature of radiation, wave nature of particles, de-Broglie hypothesis, matter wave, wave-particle duality, Davisson-Germer experiment.

Bohr’s theory of Hydrogen atom, explanation of Hydrogen Spectra, correction for finite mass of the nucleus, Bohr’s correspondence principle, limitations of Bohr’s theory, Discrete energy,

exchange by atom, Frank Hertz experiment.

**UNIT-III**

Quantum Mechanics: Heisenberg’s Uncertainty relation, Time dependent Schrodinger’s wave equation in one dimension and three dimensions. The physical interpretation of the wave

function, Probability density and probability current density, Equation of continuity, Normalization of the Wave function, Expectation value of an observable, Ehrenfest’s theorem. Time independent Schrodinger’s wave equation in one dimension particle in a box, energy eigen values and eigenfunctions.

**UNIT-IV**

Nuclear Physics : Properties of the nucleus Charge, Size, Spin, Magnetic Moment, Mass,

Mass defect, Binding energy, Packing fraction, Nuclear force, and its characteristics features,

Radioactive decay laws, average life, half-life, nuclear fission, nuclear fusion, Linear accelerators, and cyclotron.

Relativity: Galilean transformation, Newtonian relativity and its limitation, Michelson Morley

experiment and its consequence, postulates of special theory of relativity. Lorentz transformation, length contraction, time dilation, relativistic mass and momentum, mass energy relation.

Text Books:

- University Physics, H. D. Young, R. A. Freedman(Person)
- Fundamentals of Physics, Resnick, Halliday, Walker(Wiley)

Reference Books :

- A Text Books book of Optics N.Subrahmanyam and Brij Lai (S.Chand Publishing) *
- Introduction to Special Relativity-R. Resnick (JohnWiley)
- Concepts of Modern Physics Arthur Beiser(McGrawHill)
- Modern Physics H.S. Mani and GK.Mehta

GE – 2 – LAB

Minimum Six experiments to be done

Credit : 02 25 Marks

- Determination of E.C.E. of Copper.
- Determination of Refractiveindex of the material of a prism using Sodium light.
- To determine the wave length of light using plane diffraction grating.
- To determinethewavelengthoflightusingNewtonsring.
- Determination of refractive index of (a) glass and (b) liquid by using travelling microscope.
- To plot the I-D curve and to determine the refractive index of a prism
- Determination of radius of curvature of a convex/concave mirror using Kohlrauschs method.
- To determine the magnifying power of a given telescope.
- To Obtain the static characteristics of a P-N-P/N-P-N transistor.
- To determine the reduction factor of a tangent Galvanometer.
- To study the Variation of magnetic field along the axis of a circular coil carryingcurrent.

Reference Books:

- Advanced Practical Physics for students, B .L.FlintandH.T.Worsnop, 1971, Asia Publishing House
- A Laboratory Manual of Physics for Undergraduate Classes,D.P.Khandelwal (1985), Vani

Publication

- A Text book of Practical Physics Indu Prakash And Ramakrishna, 11 th Edition (2011), Kitab Mahal, New Delhi

- Each year 2 seminars have been held by external resource person.

- Ganapati Sahoo (Faculty of IISc., Bangalore, Now placed in German University)
- Tinku Biswal (ICS, Rank-28, Joined as IAS officer in Manipur)
- Sibasish Acharya (Faculty of IIT, Kharagpur)
- Mahatma (Scientist- E in BELL laboratory, USA)
- Seema Bahinipati (Faculty in Cincinnati University)
- Asoka Kumar Das (Vice Chancellor, Utkal University)
- Anshuman Sarangi (Faculty in MIT)
- S.R.P. Mohapatra (Sr. Scientist in Poland)
- Anita Nayak (IPS)
- Priyadarshi Nayak (IPS)
- Collin Benjamin (Faculty in NISER)
- Saroj Kumar Nayak (Faculty in IIT Bhubaneswar)