B.Sc. Physical Science Semester 3 Syllabus – Gurugram University (GU) NEP 2020

CORE

Waves and Optics Syllabus – Unit-wise Topics

Waves and Optics (CC-A3 | 240/PHYP/CC301) — Max Marks: 50 | Internal Assessment: 25 | Credit: 3 (45 Hrs) | Time: 2 hrs, plus Waves and Optics Lab: Marks (External): 20 | Marks (Internal Assessment): 05 | Credits: 1 (30 Hrs) | Time: 3 Hrs. Total: 4 Credits, 100 Marks. The examiner sets nine questions; Q1 is compulsory (five short-answer parts, 2 marks each) and the remaining eight questions are set in pairs from each unit; students attempt one from each unit along with Q1. The paper contains 20% numerical problems. Course Objective: The course on waves and optics deals with basic concepts of optics like interference, diffraction and polarisation, along with an introductory-level discussion about waves. Unit I: Waves — Oscillatory motion, simple harmonic motion, wave motion, wave equation and its solution, transverse and longitudinal waves and their examples, waves in one dimension, superposition of waves, stationary waves, waves on a stretched string with fixed ends, phase velocity and group velocity, light as a transverse wave. Important Topics: Wave Equation and Solution, Superposition of Waves, Stationary Waves, Phase and Group Velocity. Unit II: Interference — Interference by division of wave front: Young's double slit experiment, coherence, conditions of interference, Fresnel's biprism and its applications to determine the wavelength of sodium light and thickness of a mica sheet, phase change on reflection. Interference by division of amplitude: plane parallel thin film, production of colours in thin films, classification of fringes in films, interference due to transmitted and reflected light, wedge-shaped film, Newton's rings. Important Topics: Young's Double Slit Experiment, Fresnel's Biprism, Newton's Rings, Wedge-Shaped Film. Unit III: Diffraction — Fresnel's diffraction: Huygens-Fresnel's theory, Fresnel's assumptions, rectilinear propagation of light, diffraction at a straight edge, rectangular slit and diffraction at a circular aperture. Fraunhofer diffraction: single slit diffraction, double slit diffraction, plane transmission grating spectrum, dispersive power of grating, limit of resolution, Rayleigh's criterion, resolving power of telescope and a grating. Important Topics: Fraunhofer Single and Double Slit Diffraction, Plane Transmission Grating, Resolving Power, Rayleigh's Criterion. Unit IV: Polarisation — Polarisation by reflection, refraction and scattering, Malus law, phenomenon of double refraction, Huygens's wave theory of double refraction (normal and oblique incidence), analysis of polarised light, Nicol prism, quarter wave plate and half wave plate, production and detection of plane, circularly and elliptically polarised light, optical activity, Fresnel's theory of optical rotation, specific rotation, polarimeters (half shade and biquartz). Important Topics: Malus Law, Double Refraction, Nicol Prism, Quarter and Half Wave Plates, Specific Rotation, Polarimeters. Most Important Formulae:

• Young's Double Slit Fringe Width: β = λD / d
• Newton's Rings (Diameter of nth ring): Dₙ² = 4nλR
• Malus Law: I = I₀cos²θ
• Grating Equation: (a + b) sinθ = nλ

One-Night Revision Priority:

• Young's Double Slit Experiment
• Newton's Rings
• Fraunhofer Single Slit Diffraction
• Plane Transmission Grating and Resolving Power
• Malus Law and Double Refraction
• Nicol Prism and Wave Plates

Waves and Optics Lab – List of Experiments (perform at least five):

• Refractive index and dispersive power of a prism material by a spectrometer.
• Determination of the wavelength of Na light using a diffraction grating.
• Determination of wavelength of sodium light using Newton's Rings.
• Resolving power of a telescope, a prism, and a grating.
• Measurement of specific rotation / concentration of sugar solution using a polarimeter.
• Wavelength of sodium light by Fresnel's biprism.
• Diameter of a thin wire by diffraction method (using He-Ne Laser).

CORE

Ordinary and Partial Differential Equations Syllabus – Unit-wise Topics

Ordinary and Partial Differential Equations (CC-A3 | 240/MATP/CC301) — Theory: 3 Credits | Practical: 1 Credit | Total: 4 Credits, 100 Marks (Theory: 25 Internal + 50 External; Practicum: 5 Internal + 20 External) | Examination Time: 3 Hrs (Theory) + 3 Hrs (Practical). The examiner sets nine questions — two from each unit plus one compulsory question (Q1, five parts covering the entire syllabus); students attempt five questions, selecting one from each unit plus the compulsory question. Course Learning Outcomes:

• Gain foundational knowledge of ordinary differential equations and techniques to solve first-order solvable differential equations.
• Develop technical skills to solve homogeneous and non-homogeneous second-order linear ODEs with constant and variable coefficients.
• Understand the theory of total differential equations and basic concepts of partial differential equations (PDEs), and learn methods for solving first-order linear PDEs.
• Acquire knowledge of second-order PDEs, apply theory to find integral and orthogonal surfaces, and develop skills using Charpit's and Jacobi's methods.
• Attain problem-solving skills for differential equations, with hands-on experience using MAXIMA software.

Unit I: First Order and First Degree ODEs (12 Hrs) — Genesis of ordinary differential equations, solutions of differential equations of first order and first degree, exact differential equations, first order higher degree equations solvable for x, y and p, Lagrange's equations, Clairaut's form and singular solutions, orthogonal trajectories in Cartesian and polar coordinates, self orthogonal family of curves. Important Topics: Exact Differential Equations, Equations Solvable for x, y, p, Clairaut's Equation, Orthogonal Trajectories. Unit II: Linear Differential Equations (12 Hrs) — Linear differential equations with constant coefficients, linear non-homogeneous differential equations, linear differential equation of second order with variable coefficients, reduction of order, method of undetermined coefficients, method of variation of parameters, Cauchy-Euler equation. Important Topics: Method of Undetermined Coefficients, Variation of Parameters, Cauchy-Euler Equation, Reduction of Order. Unit III: Simultaneous, Total and Partial Differential Equations (11 Hrs) — Ordinary simultaneous differential equations, total differential equations. Partial Differential Equations: formation, order and degree, linear and non-linear PDEs, complete solution, singular solution and general solution of a PDE, linear PDE of first order, solution of Lagrange's linear equations. Important Topics: Total Differential Equations, Lagrange's Linear Equations, Formation and Classification of PDEs. Unit IV: Second Order PDEs (10 Hrs) — Solution of PDE passing through a given curve, surfaces orthogonal to a given system of surfaces, compatible system of first order equations, Jacobi's method, Charpit's general method of solution, special types of first order PDEs, second order partial differential equations with constant coefficients. Important Topics: Charpit's Method, Jacobi's Method, Orthogonal Surfaces, Second Order PDEs with Constant Coefficients. Practical Component (30 Hrs, two parts):

• (A) Problem Solving: Reducible-to-homogeneous and exact differential equations; linear differential equations with constant and variable coefficients; variation of parameters and undetermined coefficients; simultaneous differential equations; PDEs using Lagrange's, Charpit's and Jacobi's methods.
• (B) MAXIMA Software Practicals: Solutions of first and second order differential equations; plotting family of solutions; growth and decay, lake pollution, density-dependent growth, and predator-prey (Volterra) models; solving ODEs using plotdf, ode2, ic1/ic2, desolve and atvalue built-in functions.

CORE

Chemistry-III Syllabus – Unit-wise Topics

Chemistry-III (CC-A3 | 240/CHEP/CC301) — 4 Credits (Lecture: 3, Practical: 1) | 100 Marks (Theory External: 50 + Theory Internal: 25 + Practical External: 20 + Practical Internal: 5) | 5 Hrs/week (3 Lecture + 2 Practical). The examiner sets nine questions in total, two from each section; Q1 is compulsory (short-answer type covering all units); the paper contains 20% numerical problems. Course Objectives:

• Understand the properties and chemical behavior of non-aqueous solvents.
• Study the comparative properties, bonding, and reactivity of p-block elements.
• Explore the preparation, properties, and mechanisms of halogenated hydrocarbons, alcohols, phenols, ethers, and carbonyl compounds.
• Analyze key organic reactions, including rearrangements, additions, and oxidations/reductions.
• Develop a mathematical understanding of thermodynamics and its application to chemical equilibrium.

Unit I: Non-Aqueous Solvents and p-Block Elements (11 Hrs) — Non-aqueous solvents: physical properties and uses, self-ionization, physical properties and chemical reactions in non-liquid NH₃. p-Block elements: comparative study of properties (including diagonal relationship, excluding methods of preparation). Boron family (13th group): diborane — properties and structure, borazine — chemical properties and structure, trihalides of boron — trends in Lewis acid character, structure of aluminium (III) chloride. Carbon family (14th group): catenation, pπ–dπ bonding, silicates, silicones — preparation, properties and uses. Important Topics: Non-Aqueous Solvents, Diborane Structure and Bonding, Borazine, Boron Trihalides, Silicates and Silicones. Unit II: Halogenated Hydrocarbons (11 Hrs) — Alkyl halides: methods of preparation and properties, nucleophilic substitution reactions (SN1, SN2, SNi) with stereochemical aspects, effect of solvent and energy profile diagrams, substitution vs. elimination. Aryl halides: preparation (including from diazonium salts) and properties, nucleophilic aromatic substitution, SNAr and benzyne mechanism. Alcohols: preparation, properties and relative reactivity of 1°, 2°, 3° alcohols, hydrogen bonding, acidic nature, Bouveault-Blanc reduction, Pinacol-Pinacolone rearrangement. Important Topics: SN1, SN2 and SNi Mechanisms, SNAr and Benzyne Mechanism, Pinacol-Pinacolone Rearrangement, Bouveault-Blanc Reduction. Unit III: Phenols, Ethers, Epoxides and Carbonyl Compounds (12 Hrs) — Phenols: preparation and properties, acidity and affecting factors, ring substitution reactions, Reimer-Tiemann and Kolbe's-Schmidt reactions. Ethers and epoxides: preparation and reactions with acids, reactions of epoxides with alcohols and LiAlH₄. Carbonyl compounds: structure, reactivity, preparation and properties, nucleophilic additions and addition-elimination reactions with ammonia derivatives, mechanisms of Aldol and Benzoin condensation, Knoevenagel condensation, Claisen-Schmidt, Cannizzaro and Wittig reaction, Beckmann and Benzil-Benzilic acid rearrangements, haloform reaction and Baeyer-Villiger oxidation, Clemmensen/Wolff-Kishner/LiAlH₄ reductions, Michael addition. Important Topics: Reimer-Tiemann Reaction, Aldol and Benzoin Condensation, Cannizzaro Reaction, Wittig Reaction, Beckmann Rearrangement, Baeyer-Villiger Oxidation. Unit IV: Chemical Thermodynamics and Equilibrium (11 Hrs) — Mathematical treatment of thermodynamics, reversible and irreversible processes, first and second laws of thermodynamics, thermochemistry, thermodynamic functions (enthalpy, entropy, Gibbs free energy), relationships between thermodynamic functions, partial molar quantities, Gibbs-Duhem equation, chemical potential. Chemical equilibrium: law of mass action, equilibrium constants (Kp, Kc, Kx, Kn), effect of temperature on equilibrium, Le-Chatelier principle. Important Topics: First and Second Laws of Thermodynamics, Gibbs Free Energy, Law of Mass Action, Le-Chatelier Principle. Practical Syllabus (30 Hrs):

• Systematic qualitative analysis of organic compounds with monofunctional groups (alcohols, phenols, carbonyl, -COOH), including derivative preparation.
• Estimation of aniline by acetylation or bromate-bromide method.
• Preparation of azo dye with aniline and 2-naphthol.
• Acetylation and benzoylation of amines and phenols (Schotten-Baumann reaction).
• Determination of enthalpy change of a reaction using a calorimeter.
• Determination of the heat of neutralization of a strong acid with a strong base.
• Measurement of enthalpy of fusion of a solid.
• Inorganic preparations: tetraamminecopper(II) sulphate, cis/trans potassium dioxalatodiaquachromate(III), tetraamminecarbonatocobalt(III) ion, potassium tris(oxalate)ferrate(III).

Evaluation Scheme:

• Theory: 75 Marks (50 External + 25 Internal)
• Practical: 25 Marks (20 External + 5 Internal)
• Total: 100 Marks