Quantum Mechanics and Applications     (36Hrs) 

2.1. Experimental foundation of quantum mechanics: Elementary ideas of black body radiation, photoelectric effect and atomic spectra. Need of quantum mechanics. Concept of matter wave, de Broglie relation, uncertainty principle and its consequences. 

2.2. Postulates of Quantum Mechanics: State function or wave function postulate: Born interpretation of the wave function, well behaved functions, orthonormality of wave functions. Operator postulate: Operator algebra, linear and nonlinear operators, Laplacian operator, commuting and noncommuting operators, Hermitian operators and their properties, eigen functions and eigen values of an operator. Eigen value postulate: eigen value equation, eigen functions of commuting operators .Expectation value postulate. Postulate of time-dependent Schrödinger equation, conservative systems and time-independent Schrödinger equation.

2.3. Translational motion: Free particle in one-dimension, particle in a one dimensional box with infinite potential walls, particle in a one-dimensional box with finite potential walls-tunneling, particle in a three dimensional box ,separation of variables, degeneracy. 

2.4. Vibrational motion: One-dimensional harmonic oscillator (complete treatment), Hermite equation(solving by method of power series), Hermite polynomials, recursion relation, wave functions and energies-important features, harmonic oscillator model and molecular vibrations. 

2.5. Rotational motion: Co-ordinate systems, cartesian, cylindrical polar and spherical polar coordinates and their relationships. The wave equation in spherical polar coordinates-particle on a ring, the phi equation and its solution, wave functions in the real form. Non-planar rigid rotor (or particle on a sphere),separation of variables, the phi and the theta equations and their solutions, Legendre and associated Legendre equations, Legendre and associated Legendre polynomials. Spherical harmonics (imaginary and real forms),polar diagrams of spherical harmonics. 

2.6. Quantization of angular momentum, quantum mechanical operators corresponding to angular momenta (Lx, Ly, Lz and L2 ),commutation relations between these operators. Spherical harmonics as eigen functions of angular momentum operators Lz and L2 . Ladder operator method for angular momentum, space quantization. 

2.7. Quantum Mechanics of Hydrogen-like Atoms:Potential energy of hydrogen-like systems. The wave equation in spherical polar coordinates: separation of variables-r, theta and phi equations and their solutions, wave functions and energies of hydrogenlike atoms. Orbitals:Radial functions, radial distribution functions, angular functions and their plots. Dirac's relativistic equation for hydrogen atom (Elementary idea only).

2.8. Spin orbitals:Construction of spin orbitals from orbitals and spin functions,spin orbitals for many electron atoms, symmetric and antisymmetric wave functions. Pauli's exclusion principle,slater determinants.

Unit 2 : Approximation Methods in Quantum Mechanics (18 Hrs) 

             2.1 Many-body problem and the need of approximation methods, independent particlemodel. Variation method:Variation theorem with proof, illustration of variation theorem using the trial function x(a-x) for particle in a 1D-box and using the trial function e-αr for the hydrogen atom, variation treatment for the ground state ofhelium atom. 

            2.2 Perturbation method, time-independent perturbation method (non-degenerate case only), first order correction to energy and wave function, illustration by application to particle in a 1D-box with slanted bottom, perturbation treatment of the ground state of the helium atom. Qualitative idea of Hellmann-Feynman theorem. 

             2.3 Hartree-Fock method,multi-electron atoms. Hartree-Fock equations (no derivation). The Fock operator, core hamiltonian, coulomb operator and exchange operator.Qualitative treatment of Hartree-Fock Self-Consistent Field (HFSCF) method. Roothan's concept of basis functions, Slater type orbitals (STO) and Gaussian type orbitals (GTO), sketches of STO and GTO.

Unit 2 : Approximation Methods in Quantum Mechanics (18 Hrs) 

             2.1 Many-body problem and the need of approximation methods, independent particlemodel. Variation method:Variation theorem with proof, illustration of variation theorem using the trial function x(a-x) for particle in a 1D-box and using the trial function e-αr for the hydrogen atom, variation treatment for the ground state ofhelium atom. 

            2.2 Perturbation method, time-independent perturbation method (non-degenerate case only), first order correction to energy and wave function, illustration by application to particle in a 1D-box with slanted bottom, perturbation treatment of the ground state of the helium atom. Qualitative idea of Hellmann-Feynman theorem. 

             2.3 Hartree-Fock method,multi-electron atoms. Hartree-Fock equations (no derivation). The Fock operator, core hamiltonian, coulomb operator and exchange operator.Qualitative treatment of Hartree-Fock Self-Consistent Field (HFSCF) method. Roothan's concept of basis functions, Slater type orbitals (STO) and Gaussian type orbitals (GTO), sketches of STO and GTO.

                       AIMS AND OBJECTIVES OF THE PROGRAMME 

 AIMS:

 The Facuty of Science, Mahatma Gandhi University and Board of Studies in Chemistry (UG) recognizes that curriculum, course content and assessment of scholastic achievement play complementary roles in shaping education. The committee is of the view that assessment should support and encourage the broad instructional goals such as basic knowledge of the discipline of Chemistry including theories and techniques, concepts and general principles. This should also support the ability to ask physical questions and to obtain solutions to physical questions by use of qualitative and quantitative reasoning and by experimental investigation. The important student attributes including keen observation, curiosity, creativity and reasoned skepticism and understanding links of Chemistry to other disciplines and to societal issues should be given encouragement. With this in mind, we aim to provide a firm foundation in every aspect of Chemistry and to explain a broad spectrum of modern trends in chemistry and to develop experimental, computational and mathematics skills of students. The programme also aims to develop the following abilities: 

1. Read, understand and interpret chemical information – verbal, mathematical and graphical. 

2. Impart skills required to gather information from resources and use them. 

3. To give need based education in chemistry of the highest quality at the undergraduate level. 

4. Offer courses to the choice of the students. 

5. Perform experiments and interpret the results of observation. 

6. Provide an intellectually stimulating environment to develop skills and enthusiasms of students to the best of their potential. 7. Use Information Communication Technology to gather knowledge at will. 

8. Attract outstanding students from all backgrounds. 

 OBJECTIVES:

The syllabi are framed in such a way that it bridges the gap between the plus two and post graduate levels of Chemistry by providing a more complete and logical framework in almost all areas of basic Chemistry.

SEMESTER II CH2CRT02 – THEORETICAL AND INORGANIC CHEMISTRY Credits - 2 (36 hrs) 

 Unit 1: Atomic Structure (6 Hrs) Introduction based on historical development (Dalton's atomic theory, Thomson’s atom model Rutherford’s atom model) - failure of classical physics – black body radiation - Planck’s quantum hypothesis - photoelectric effect - generalization of quantum theory . Atomic spectra of hydrogen and hydrogen like atoms– Bohr theory of atom – Calculation of Bohr radius, velocity and energy of an electron - explanation of atomic spectra - limitations of Bohr theory - Sommerfeld modification. Louis de Broglie's matter waves – wave-particle duality - electron diffraction - Heisenberg's uncertainty principle. Schrödinger wave equation (derivation not expected), wave functions – significance of ψ and ψ 2 – atomic orbitals and concept of quantum numbers - shapes of orbitals (s, p and d) - Pauli’s Exclusion principle - Hund’s rule of maximum multiplicity - Aufbau principle – electronic configuration of atoms.

 Unit 2: Chemical Bonding – I (9 Hrs) Introduction – Octet rule and its limitations. Types of bonds: Ionic bond - factors favouring the formation of ionic bonds - lattice energy of ionic compounds - Born- Lande equation with derivation - solvation enthalpy and solubility of ionic compounds – Born-Haber cycle and its applications – properties of ionic compounds - polarisation of ions – Fajan's rule and its applications. Covalent Bond: Valence Bond Theory and its limitations. Concept of resonance - resonance structures of borate, carbonate and nitrate ions. Hybridization: Definition and characteristics – shape of molecules (BeCl2, C2H2, BF3, C2H4, CH4, NH3, H2O, NH4 + , H3O + , PCl5, SF6 and IF7). VSEPR theory: Postulates - applications - shapes of molecules CCl4, NH3, H2O, ClF3, XeF2, SF6, IF5, XeF4, IF7 and XeF6. Properties of covalent compounds - polarity of bonds – percentage of ionic character – dipole moment and molecular structure.

 Unit 3: Chemical Bonding – II (9 Hrs) Covalent Bond: Molecular Orbital Theory – LCAO - bonding and anti-bonding molecular orbitals – bond order and its significance. MO diagrams of homonuclear and heteronuclear diatomic molecules: H2, He2, Li2, Be2, B2, C2, N2, O2, F2, CO and NO – comparison of bond length, magnetic behavior and bond energy of O2, O2 + , O2 2+, O2 - and O2 2- . Metallic Bond: free electron theory, valence bond theory and band theory (qualitative treatment only) - explanation of metallic properties based on these theories. Intermolecular forces: Hydrogen bond - intra and inter molecular hydrogen bonds – effect on physical properties. Van der Waals forces, ion-dipole, dipole-dipole, ion-induced dipole, dipole-induced dipole and induced dipole-induced dipole interactions 

 Unit 4: Chemistry of s and p Block Elements (3 Hrs) Periodicity in s-and p- block elements with respect to electronic configuration, atomic and ionic size, ionization energy and electro negativity. Inert pair effect. 

Unit 5: Chemistry of d and f Block Elements (9 Hrs) Transition Metals: General characteristics: Metallic character, oxidation states, size, density, melting points, boiling points, ionization energy, colour, magnetic properties, reducing properties, catalytic properties, non-stoichiometric compounds, complex formation and alloy formation. Difference between first row and other two rows. Preparation, properties, structure and uses of KMnO4 and K2Cr2O7. Lanthanides: Electronic configuration and general characteristics – Occurrence of lanthanides Isolation of lanthanides from monazite sand - Separation by ion exchange method. Lanthanide contraction: Causes and consequences. Industrial importance of lanthanides.

 Molecular Spectroscopy-I (12 Hrs) 

Introduction: electromagnetic radiation, regions of the spectrum, interaction of electromagnetic radiation with molecules, various types of molecular spectroscopic techniques, Born-Oppenheimer approximation. 

      Rotation spectroscopy: Introduction to rotational spectroscopy, Rotational energy levels, Selection rules.

      Vibrational spectroscopy: Introduction, Selection Rules, Classical equation of vibration, calculation of force constant, concept of anharmonicity, Morse potential, dissociation energies, fundamental frequencies, overtones, hot bands. Degrees of freedom for poly atomic molecules, modes of vibration (H2O and CO2 as examples), finger print region, Fermi resonance.

     Raman spectroscopy: Introduction, Classical and quantum treatment of Raman effect, Qualitative treatment of Rotational Raman effect; Vibrational Raman spectra, Stokes and anti-Stokes lines: their intensity difference, rule of mutual exclusion. 

Molecular Spectroscopy-II (10 Hrs) 

      Electronic spectroscopy: Introduction, selection rule, Franck-Condon principle, electronic transitions, singlet and triplet states, dissociation and predissociation. Polyatomic molecules – qualitative description of σ, π and n- molecular orbitals, their energy levels and the respective transitions. Lambert-Beer’s law.

       Nuclear Magnetic Resonance (NMR) spectroscopy: Principles of NMR spectroscopy, Larmor precession, chemical shift and low resolution spectra, different scales, spin-spin coupling. 

      Electron Spin Resonance (ESR) spectroscopy: Principle, hyper fine structure, ESR of simple radical - methyl radical

SEMESTER 1- BA ECONOMICS