PAPER III -Algebra and Trigonometry |
- Mathematical Concepts and Computers:
- Logarithmic relations, Curve sketching, Regression analysis. Differentiation offunctions like fx, ex, x", Sin x, log x, maxima and minima, partial, total and exact differentials, reciprocity relations. Integration of some useful/relevant functions, permutations and combinations. Expansion oftrignometric functions. Operators, factorials and Stirling's approximation.
- Computers
- General introduction of computers. Different components of a computer, Hardware and Software, input-output devices. Binary numbers and arithmetics. Operating systems. Introduction to computer language. Basic and Fortran. Simple programming like conversion of °C to oF.
- Structure of Atom:
- Scnrodinger's equation. Concept of operators, especially energy. and angular momentum, Concept of standing waves and its, relationship with the equation. Concept of 'If function.
- Ideas of different force fields with spec' emphasis on central
- force .field and its relationship with hydrogen atom. 1
- Schrodinger equation as applied to hydrogen atom (in terms of cartesian and polar coordinates)
- Concept of good wave function for hydrogen atom (Boundary I conditions). concept offour quantum numbers.
- Concept of central force field, Repurcussion if the force field is not central type but another type. Concept of Inter elctronic repulsions between two or more electrons. Approximations for and solutions of solving schrodinger equation for multi electron system (no mathematical treatment required) Application of Schrodlnger wave equation for particle in one dimensional box.
- Nuclear Chemistry:
- Fundamental particles and their classification. Nuclear forces, Nuclear spin, magnetic moment of nuclei and magic number. Liquid drop and shell models of nucleus. Nuclear stability. Kinetics of radioactive decav Energy changes In nuclear reactions, Nuclear energy, Fission and fusion reaction. Principle of nuclear reactor. Radiolysis of water. Carbon dating and tracertechniques separation and identification of isotopes.
- 4. Chemical Bonding:
- Elementary ideas of wave mechanical concept of covalency. Molecular Orbital approach, Criteria for forming MO's from atomic orbitals, Construction of MO's by LCAO in homonuclear diatomic molecules. Physical picture of Bonding and Antibonding molecular orbital wave functions, concept of cr, cr' and 1t and 1t' molecular orbitals and their characteristics. Evaluation of bond order in simple homonuclear diatomic molecules. Valence bond approach to Hz molecule. Comparison ofV.B. and M.O. approach. Hybridisation (a qualitative quantum mechanical approach).
- Molecular Structure:
- Dipole moments: bond angles, bond moments, ionic character in bonds, and their applications in elucidation of molecular structure. Optical activity and chemical constitution. Basic principles of molecular spectroscopy: eletromagnetic radiations, regions of spectrum and concept of molecular energy levels. Lambert- Beer's law. Basic principles of UV, visible and IR spectroscopy.IR spectra of H,O and CO, molecules (only brief discussion).
- Gaseous State:
- Postulates of kinetic theory of gases, deviations from ideal behaviour, van der Waals equation of state for n-moles.
- Critical Phenomenon: PV - isotherms of real gases, continuity ofstate, the isotherms of van derWials equation, Critical constants and their experimental determination, relationship between critical constants and van derWaals constants. Law of corresponding states. Reduced equation of state. Elementary idea of other equations of state.
- Molecular Velocities: Root mean square velocity, average and most probable velocities, a qualitative discussion of Maxwell's distribution of moleculer velocities, collision number, mean free path and collision diameter, Liquefaction of gases.
- Liquid State:
- Intermolecular forces, structure of a liquid (a qualitative description). Structural differences between solids, liquids and gases. Liquid crystals: Classification, Structure, Properties and a few applications surface tension, surface energy and Parachor, viscosity and refractive index of liquids in view of molecular constitution.
- 8. Solid State:
- Crystalline state, Space lattice and Unit cell. Laws of crystallography, Symmetry elements in crystals, labelling of planes. Crystal systems and Bravais lattices. X-ray diffraction by crystals, derivation of Bragg's equation. Determination of crystal structure of NaCI and KCI crystals. Limiting radius ratio, close packing, lattice energy, Born Haver cycle and Its- importance. Defects In crystals: Point defects. Elementary ideas about semiconductors, superconductors and nanoparticle materials. Band theory of solids and solid state reactions.
- The Colloidal State and Macromolecules:
- Colloidal systems. Lyophobic and Lyophilic colloids. Preparation, kinetic optical and electrical properties. Origin of charge on colloidal particles. Coagulation of colloids, Hardy-Sehutze rule. Stability of colloids, protection and gold number. Elementary idea of electrical double layer and electrokinetic potential, Colloidal electrolytes and association colloids, Detergents Emulsions and gels. Macromolecules and their molecular weights. Determination of molecular Weights of macromolecules bJ( ultracentrifuge light scattering osmotic pressure and viscosity methods. Concept of micelles and critical micelle conecentration. Conducting and light emitting polymers.
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