Physics the great Zone

The Electron

noreply@blogger.com (Anonymous) — Sun, 14 Feb 2010 09:59:00 +0000

When first investigated in the 18th and 19th centuries, electrical and magnetic

phenomena were generally construed in terms of lethereal fluids, as were those

associated with heat and light. These fluids were thought to comprise minute mutually

repelling particles. Thus, heat was either thought to be vibrations in the fluid caloric or

an accumulation of this fluid in the interstices of materials. Light was either a flux of

particles emitted at high speed from luminous bodies or the vibrations of a ubiquitous

fluid zether. Electric fluids-electricir)*-flowed readily through metals and other

conductors but did not penetrate insulators such as paper and glass. Opinion was

divided 8s to whether there was just one electric fluid or two-a positive fluid and a

negutive fluid.

The possibility that electricity might not be a continuous fluid was first raised in

the middle of the 19th century following Faraday’s quantitative researches on

electrolysis. These showed the existence of a systematic relationship between the

amount of electricity passed through an electrolytic cell and the quantity of material

that undergoes chemical reaction (electrolysis) in the cell. Thus, the passage of a

certain amount of electricity-96,500 coulombs in modem terms-always liberates a

gramequivalent of substance from the electrolyte, whether it is the metal released at

the negative cathode or the non-metal at the positive anode. Putting aside his

misgivings about atomism, Faraday recognised that this suggested electricity might be

atomic in nature and that a natural indivisible unit of electricity exists. In 1891 Stoney’

suggested that this natural unit of electricity be called an electron.

On this view, every ion carries an integer multiple of this natural unit. For

example, a silver ion, Agf, carries a single natural unit of positive charge; a typical

copper ion, Cu++, carries two such units. Given that a gramequivalent of monovalent

ions comprises a mole, the magnitude of the natural unit of electricity, e, can be

calculated by dividing the 96,500 coulombs by Avogadro’s number, 6.02. 10²³

^{The term electron is now used to designate the elementary particle that carries the}

^{natural unit of negative charge which was first identified towards the end of the 19th}

^{century in experiments on the conduction of electricity through gases at very low}

^{pressures. At atmospheric pressure, gases do not usually conduct electricity. However,}

^{at reduced pressures of O.5mmHg to lOmmHg and with applied potentials of several}

^{thousand volts, they can be made to pass a current. These greatly reduced gas pressures}

^{were first achieved at the end of the 19th century following the advances made at that}

^{time in vacuum pump technology. The gases were contained in narrow glass tubes,}

^{called dischaee tubes, into which suitabIe electrodes had been inserted. The passage}

^{of the current is eccompanied by the appearance of striking colours in the tubes (Fig}

^1.1).

^{At still lower pressures, -0.02mmHg, the colours disappear but the glass tube itself}

^{begins to glow with a green hue. An object placed in front of the cathode (the negative}

^{electrode) casts a shadow on the opposite wall of the discharge tube (Fig 1.2). Certain}

^{minerals, when placed in front of the cathode, fluoresce with brilliant colours. It}

^{appears that something is being emitted from the cathode; this emanation was given}

^{the name cathode rays.

^{^{^{In fbrther experiments it was found that the cathode rays were deflected by a
magnetic field as would a stream of negative charge (Fig 1.3a). Furthermore, a small
paddle wheel positioned between the electrodes rotated under their impact; switching
the polarity of the electrodes reversed the direction of th}}}^{^{^{e rotation (Fig 1.3b). These
two phenomena suggested the cathode rays mig}}}^{^{^{ht be negatively charged particles.}}}
^{^{^{Nevertheless, many physicists at the time still considered them to be of an Ethereal
rather than a material nature}}}
^{^{^.}}
^{^{^{Convinced that the cathode rays were in fact charged particles of matter,
J.J.Thomson set out in 1897 to measure their velocity, v, and the ratio, q/m,between
their charge, q, and their mass, m. In one of the experiments he conducted, a narrow
collimated beam of cathode rays was aimed along the length of a very low pressure
glass discharge tube. After emerging from the hole in the anode,}}}^{^{^{the beam passed}}}
^{^{^{through a thin slit, between a pair of vertical coils and, finally, between the horizontal
parallel plates of a condenser. The green spot that appeared on the glass at the far end}}}
^{^{^{of the tube indicated where the beam impinged upon it (Fig 1.4).}}}}

^{^{^{^{^{^{^{^{^{The cathode ray beam could be deflected vertically by two different means: (i)
magnetically; (ii) electrically:

(i) Magnetically-by passing a current through the coils. This induces a uniform
horizontal magnetic field, B, in the space between them which, in turn, exerts a
force, FB, on the cathode ray particles such that
FB = Bqv (1.2)}}}}}}
^{^{^{^{^{^{where v is the velocity of the particles. This force acts at right angles to the
direction of the particle's motion and so constitutes a centripetal force. Thus, as
they pass between the pair of coils, the cathode ray particles move in a circular
path-along the arc of a circle-such that}}}}}}}}^{^{^{^{^{^{^{^{where r is the radius of the arc.}}}}}}
^{^{^{^{^{^{(ii) Electrically-by connecting the condenser plates to a potential source; this
produces a vertical electric field, E, in the space between them that exerts a
vertical force, FE, on the cathode ray particles such that
FE = Eq (1.4)

Initially, Thomson applied just the magnetic field. This had the effect of moving
the green spot down from P to Q. He then activated the electric field and adjusted the}}}}}}
^{^{^{^{^{^{potential between the condenser plates until the field was just sufficient to return the
green spot from Q to P. At this point, the two forces, FB and FE, cancelled each other
out, such that:
FE = FB
or qE = Bqv =}}}}}}^{^{^{^{^{^mv2/r}}}}}}}^{^{^{^{^{^{^{^{From which, the particles' charge to mass ratio is given by}}}}}}}}}^{^{^{Thomson knew the value of the magnetic field, B, from the dimensions of the coils
and the current flowing through them, of the arc radius, r, from the dimensions of the
apparatus and the distance PQ and of the electric field, E, from the potential applied
between the condenser plates and the distance between them. Substituting these in
equation (1.6) gave a value, in modem SI units, of -2-10 power 11 C/kg for the charge to mass
ratio of the cathode ray particles. Thornson repeated the experiment using different
metal cathodes and with different gases in the low pressure tube, but in each case he
found approximately the same value for the ratio.The value found by Thomson for the
charge to mass ratio of the cathode ray
particles was three orders of magnitude greater than the largest previously known value
of this ratio, namely, that found for the aqueous hydrogen ion, H(aq). This could be
attributed either “to the smallness of m or the largeness of q, or a combination of these
two”. Thomson opted for the “smallness of m” and assumed that the magnitude of the
charge, q, carried by the cathode ray particles was equal to the smallest charge known
to be carried by any ion, i.e., q = -1.6-10 power -19 C. On this assumption, he calculated the
mass of the cathode ray particles and obtained the result, astonishing at the time, that
their mass was only Kg36 that of the hydrogen atom, itself the smallest of all atoms.*
In an attempt to verify Thomson’s assumption, direct measurements of the
magnitude of the charges carried by gaseous ions were made. Although these
experiments suffered initially from many sources of error, their results appeared to
confirm Thomson’s supposition. The issue was finally and unequivocally settled in
1906 when, in a series of accurate and careful experiments, Millikan8 measured the
magnitude of the electrical charges carried by both positively and negatively charged
oil droplets. In none of the hundreds of measurements he made, did he detect a droplet
that carried a charge whose magnitude was less than 1.6.1O power-l9 C , nor one that carried
a charge whose magnitude was a fractional multiple of this amount. In every case, the
magnitude of the charges was an integer multiple of e = 1.6.10power-19 C . The clear
inference was that electrical charge-positive or negative-always appears as an
integer multiple of the natural unit e.
The cathode ray particles Thomson had discovered are the elementary particles we
now call electrons; the electron was the first elementary particle to be discovered.
Electrons carry the natural unit, -e, of negative charge. They are the smallest of the
three constituent particles--protons, neutrons and electrons--of ordinary matter.
Though electrons have no discernible internal structure or dimensions, they
nevertheless possess an intrinsic angular momentum (spin) and an associated magnetic
moment.
Cathode rays were not the only emanations observed in discharge tubes. If the
cathode in the discharge tube was pierced, rays were seen to emerge from the hole in
the direction away from the anode (the positive electrode), i.e., in the opposite
direction to the cathode rays (Fig 1.5). These emanations were called canal rays; they
were found to be positively charged.
Having identified the cathode rays, Thomson proceeded to investigate the nature of
the canal rays. These too proved to be particles of matter. By measuring the ratio
between their charge and their mass he identified them as positive ions of the gas
present in the discharge tube. He construed that these positive ions were produced in
the space between the cathode and the anode from the bombardment of the gaseous
atoms by the cathode rays (electrons). Since they carried a positive charge, they were
attracted to and accelerated towards the negative cathode, passing through the hole that
had been pierced in it and emerging from the other side. In one notable experiment, in
which the gas in the discharge tube was a pure sample of the noble gas neon, Thomson
discovered two different species of positive ions in the canal rays whose masses
differed by about 10%. The ions could only be neon ions, the purity of the sample
ensured this. This discovery of different species of neon ions first demonstrated the
existence of atoms that share the same chemical identity but have different masses;
what we now refer to as isotopes.
In 1932, a particle was discovered that is identical to the electron in all its
properties except that it is positively and not negatively charged; it was designated the
unti-electron or positron. When a positron and electron collide, the pair of particles
self-destruct, releasing a burst of high frequency electromagnetic radiation- Y rays.}}}

APTITUDE TEST B.ARCH./B.PLANNIN

noreply@blogger.com (Anonymous) — Sun, 14 Feb 2010 08:45:00 +0000

Part I

Awareness of persons, places, Buildings, Materials.) Objects, Texture related to Architecture and build~environment. Visualising three dimensional objects from two dimensional drawings. Visualising. different sides of three dimensional objects. Analytical Reasoning Mental Ability (Visual, Numerical and Verbal).

Part II

Three dimensional - perception: Understanding and appreciation of scale and proportion of objects, building forms and elements, colour texture, harmony and contrast. Design and drawing of geometrical or abstract shapes and patterns in pencil. Transformation of forms both 2 D and 3 D union, substraction, rotation, development of surfaces and volumes, Generation of Plan, elevations and 3 D views of objects. Creating two dimensional and three dimensional compositions using given shapes and forms. Sketching of scenes and activities from memory of urbanscape (public space, market, festivals, street scenes, monuments, recreational spaces etc.), landscape (river fronts, jungles. gardens, tre es, plants etc.) and rural life.

CHEMISTRY

noreply@blogger.com (Anonymous) — Sun, 14 Feb 2010 08:06:00 +0000

Section A
PHYSICAL CHEMISTRY

Unit 1: SOME BASIC CONCEPTS IN CHEMISTRY

Matter and its nature, Dalton’s atomic theory; Concept of atom, molecule, element and compound; Physical quantities and their measurements in Chemistry, precision and accuracy, significant figures, S.I. Units, dimensional analysis; Laws of chemical combination; Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae; Chemical equations and stoichiometry.

Unit 2: STATES OF MATTER

Classification of matter into solid, liquid and gaseous states.
Gaseous State:
Measurable properties of gases; Gas laws - Boyle’s law, Charle’s law, Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial pressure; Concept of Absolute scale of temperature; Ideal gas equation, Kinetic theory of gases (only postulates); Concept of average, root mean square and most probable velocities; Real gases, deviation from Ideal behaviour, compressibility factor, van der Waals equation, liquefaction of gases, critical constants.
Liquid State:
Properties of liquids - vapour pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only).
Solid State:
Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea); Bragg’s Law and its applications; Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, imperfection in solids; Electrical, magnetic and dielectric properties.

Unit 3: ATOMIC STRUCTURE

Discovery of sub-atomic particles (electron, proton and neutron); Thomson and Rutherford atomic models and their limitations; Nature of electromagnetic radiation, photoelectric effect; Spectrum of hydrogen atom, Bohr model of hydrogen atom - its postulates, derivation of the relations for energy of the electron and radii of the different orbits, limitations of Bohr’s model; Dual nature of matter, de-Broglie’s relationship, Heisenberg uncertainty principle. Elementary ideas of quantum mechanics, quantum mechanical model of atom, its important features, * and *2, concept of atomic orbitals as one electron wave functions; Variation of * and * 2 with r for 1s and 2s orbitals; various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significance; shapes of s, p and d - orbitals, electron spin and spin quantum number; Rules for filling electrons in orbitals – aufbau principle, Pauli’s exclusion principle and Hund’s rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals.

Unit 4: CHEMICAL BONDING AND MOLECULAR STRUCTURE

Kossel - Lewis approach to chemical bond formation, concept of ionic and covalent bonds.
Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy.
Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment; Valence Shell Electron Pair Repulsion (VSEPR) theory and shapes of simple molecules.
Quantum mechanical approach to covalent bonding: Valence bond theory - Its important features, concept of hybridization involving s, p and d orbitals; Resonance.
Molecular Orbital Theory - Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, concept of bond order, bond length and bond energy.
Elementary idea of metallic bonding. Hydrogen bonding and its applications.

Unit 5: CHEMICAL THERMODYNAMICS

Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, types of processes.
First law of thermodynamics - Concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity; Hess’s law of constant heat summation; Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution.
Second law of thermodynamics- Spontaneity of processes; DS of the universe and DG of the system as criteria for spontaneity, DGo (Standard Gibbs energy change) and equilibrium constant.

Unit 6: SOLUTIONS

Different methods for expressing concentration of solution - molality, molarity, mole fraction, percentage (by volume and mass both), vapour pressure of solutions and Raoult’s Law - Ideal and non-ideal solutions, vapour pressure - composition, plots for ideal and non-ideal solutions; Colligative properties of dilute solutions - relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure; Determination of molecular mass using colligative properties; Abnormal value of molar mass, van’t Hoff factor and its significance.

Unit 7: EQUILIBRIUM

Meaning of equilibrium, concept of dynamic equilibrium.
Equilibria involving physical processes: Solid -liquid, liquid - gas and solid - gas equilibria, Henry’s law, general characterics of equilibrium involving physical processes.
Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of DG and DGo in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, effect of catalyst; Le Chatelier’s principle.
Ionic equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius, Br?nsted - Lowry and Lewis) and their ionization, acid - base equilibria (including multistage ionization) and ionization constants, ionization of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions.

Unit 8: REDOX REACTIONS AND ELECTROCHEMISTRY

Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions.
Eectrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration: Kohlrausch’s law and its applications.
Electrochemical cells - Electrolytic and Galvanic cells, different types of electrodes, electrode potentials including standard electrode potential, half - cell and cell reactions, emf of a Galvanic cell and its measurement; Nernst equation and its applications; Relationship between cell potential and Gibbs’ energy change; Dry cell and lead accumulator; Fuel cells; Corrosion and its prevention.

Unit 9: CHEMICAL KINETICS

Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressure and catalyst; elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its units, differential and integral forms of zero and first order reactions, their characteristics and half - lives, effect of temperature on rate of reactions - Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).

Unit 10: SURFACE CHEMISTRY

Adsorption- Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids - Freundlich and Langmuir adsorption isotherms, adsorption from solutions.
Catalysis - Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism.
Colloidal state - distinction among true solutions, colloids and suspensions, classification of colloids - lyophilic, lyophobic; multi molecular, macromolecular and associated colloids (micelles), preparation and properties of colloids - Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation and flocculation; Emulsions and their characteristics.

Section B

Inorganic Chemistry

Unit 11: CLASSIFICATON OF ELEMENTS AND PERIODICITY IN PROPERTIES

Modem periodic law and present form of the periodic table, s, p, d and f block elements, periodic trends in properties of elements atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence, oxidation states and chemical reactivity.

Unit 12: GENERAL PRINCIPLES AND PROCESSES OF ISOLATION OF METALS

Modes of occurrence of elements in nature, minerals, ores; steps involved in the extraction of metals - concentration, reduction (chemical. and electrolytic methods) and refining with special reference to the extraction of Al, Cu, Zn and Fe; Thermodynamic and electrochemical principles involved in the extraction of metals.

Unit 13: HYDROGEN

Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen; Physical and chemical properties of water and heavy water; Structure, preparation, reactions and uses of hydrogen peroxide; Classification of hydrides - ionic, covalent and interstitial; Hydrogen as a fuel.

Unit 14: S - BLOCK ELEMENTS (ALKALI AND ALKALINE EARTH METALS)

Group - 1 and 2 Elements
General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships.
Preparation and properties of some important compounds - sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate; Industrial uses of lime, limestone, Plaster of Paris and cement; Biological significance of Na, K, Mg and Ca.

Unit 15: P - BLOCK ELEMENTS

Group - 13 to Group 18 Elements
General Introduction: Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups; unique behaviour of the first element in each group.
Groupwise study of the p – block elements Group - 13
Preparation, properties and uses of boron and aluminium; Structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium chloride and alums.
Group - 14
Tendency for catenation; Structure, properties and uses of allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites and silicones.
Group - 15
Properties and uses of nitrogen and phosphorus; Allotrophic forms of phosphorus; Preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides, (PCl3, PCl5); Structures of oxides and oxoacids of nitrogen and phosphorus.
Group - 16
Preparation, properties, structures and uses of dioxygen and ozone; Allotropic forms of sulphur; Preparation, properties, structures and uses of sulphur dioxide, sulphuric acid (including its industrial preparation); Structures of oxoacids of sulphur.
Group - 17
Preparation, properties and uses of chlorine and hydrochloric acid; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxoacids of halogens.
Group -18
Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon.

Unit 16: d – and f – BLOCK ELEMENTS
Transition Elements
General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first row transition elements - physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation; Preparation, properties and uses of K₂Cr₂O₇ and KMnO₄.
Inner Transition Elements
Lanthanoids - Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction.
Actinoids - Electronic configuration and oxidation states.

Unit 17: CO-ORDINATION COMPOUNDS
Introduction to co-ordination compounds, Werner’s theory; ligands, co-ordination number, denticity, chelation; IUPAC nomenclature of mononuclear co-ordination compounds, isomerism; Bonding-Valence bond approach and basic ideas of Crystal field theory, colour and magnetic properties; Importance of co-ordination compounds (in qualitative analysis, extraction of metals and in biological systems).

Unit 18: ENVIRONMENTAL CHEMISTRY
Environmental pollution - Atmospheric, water and soil.
Atmospheric pollution - Tropospheric and stratospheric
Tropospheric pollutants - Gaseous pollutants: Oxides of carbon, nitrogen and sulphur, hydrocarbons; their sources, harmful effects and prevention; Green house effect and Global warming; Acid rain;
Particulate pollutants: Smoke, dust, smog, fumes, mist; their sources, harmful effects and prevention.
Stratospheric pollution- Formation and breakdown of ozone, depletion of ozone layer - its mechanism and effects.
Water Pollution - Major pollutants such as, pathogens, organic wastes and chemical pollutants; their harmful effects and prevention.
Soil pollution - Major pollutants such as: Pesticides (insecticides,. herbicides and fungicides), their harmful effects and prevention.
Strategies to control environmental pollution.

Section C

Organic Chemistry

Unit 19: PURIFICATION AND CHARACTERISATION OF ORGANIC COMPOUNDS
Purification - Crystallization, sublimation, distillation, differential extraction and chromatography - principles and their applications.
Qualitative analysis - Detection of nitrogen, sulphur, phosphorus and halogens.
Quantitative analysis (basic principles only) - Estimation of carbon, hydrogen, nitrogen, halogens, sulphur, phosphorus.
Calculations of empirical formulae and molecular formulae; Numerical problems in organic quantitative analysis.

Unit 20: SOME BASIC PRINCIPLES OF ORGANIC CHEMISTRY
Tetravalency of carbon; Shapes of simple molecules - hybridization (s and p); Classification of organic compounds based on functional groups: - C = C - , - C ? C - and those containing halogens, oxygen, nitrogen and sulphur; Homologous series; Isomerism - structural and stereoisomerism.
Nomenclature (Trivial and IUPAC)
Covalent bond fission - Homolytic and heterolytic: free radicals, carbocations and carbanions; stability of carbocations and free radicals, electrophiles and nucleophiles.
Electronic displacement in a covalent bond - Inductive effect, electromeric effect, resonance and hyperconjugation.
Common types of organic reactions - Substitution, addition, elimination and rearrangement

Unit 21: HYDROCARBONS
Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.
Alkanes - Conformations: Sawhorse and Newman projections (of ethane); Mechanism of halogenation of alkanes.
Alkenes - Geometrical isomerism; Mechanism of electrophilic addition: addition of hydrogen, halogens, water, hydrogen halides (Markownikoff’s and peroxide effect); Ozonolysis, oxidation, and polymerization.
Alkynes - Acidic character; Addition of hydrogen, halogens, water and hydrogen halides; Polymerization.
Aromatic hydrocarbons - Nomenclature, benzene - structure and aromaticity; Mechanism of electrophilic substitution: halogenation, nitration, Friedel – Craft’s alkylation and acylation, directive influence of functional group in mono-substituted benzene.

Unit 22: ORGANIC COMPOUNDS CONTAINING HALOGENS
General methods of preparation, properties and reactions; Nature of C-X bond; Mechanisms of substitution reactions.
Uses; Environmental effects of chloroform, iodoform, freons and DDT.

Unit 23: ORGANIC COMPOUNDS CONTAINING OXYGEN
General methods of preparation, properties, reactions and uses.
ALCOHOLS, PHENOLS AND ETHERS
Alcohols: Identification of primary, secondary and tertiary alcohols; mechanism of dehydration.
Phenols: Acidic nature, electrophilic substitution reactions: halogenation, nitration and sulphonation, Reimer - Tiemann reaction.
Ethers: Structure.
Aldehyde and Ketones: Nature of carbonyl group;
Nucleophilic addition to >C=O group, relative reactivities of aldehydes and ketones; Important reactions such as - Nucleophilic addition reactions (addition of HCN, NH3 and its derivatives), Grignard reagent; oxidation; reduction (Wolff Kishner and Clemmensen); acidity of ? - hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction; Chemical tests to distinguish between aldehydes and Ketones.
CARBOXYLIC ACIDS
Acidic strength and factors affecting it.

Unit 24: ORGANIC COMPOUNDS CONTAINING NITROGEN
General methods of preparation, properties, reactions and uses.
Amines: Nomenclature, classification, structure, basic character and identification of primary, secondary and tertiary amines and their basic character.
Diazonium Salts: Importance in synthetic organic chemistry.

Unit 25:POLYMERS
General introduction and classification of polymers, general methods of polymerization - addition and condensation, copolymerization; Natural and synthetic rubber and vulcanization; some important polymers with emphasis on their monomers and uses - polythene, nylon, polyester and bakelite.

Unit 26: BIO MOLECULES
General introduction and importance of biomolecules.
CARBOHYDRATES - Classification: aldoses and ketoses; monosaccharides (glucose and fructose), constituent monosaccharides of oligosacchorides (sucrose, lactose, maltose) and polysaccharides (starch, cellulose, glycogen).
PROTEINS - Elementary Idea of ? - amino acids, peptide bond, polypeptides; Proteins: primary, secondary, tertiary and quaternary structure (qualitative idea only), denaturation of proteins, enzymes.
VITAMINS - Classification and functions.
NUCLEIC ACIDS - Chemical constitution of DNA and RNA.
Biological functions of nucleic acids.

Unit 27: CHEMISTRY IN EVERYDAY LIFE
Chemicals in medicines - Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamins - their meaning and common examples.
Chemicals in food - Preservatives, artificial sweetening agents - common examples.
Cleansing agents - Soaps and detergents, cleansing action.

Unit 28: PRINCIPLES RELATED TO PRACTICAL CHEMISTRY
• Detection of extra elements (N,S, halogens) in organic compounds; Detection of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl and amino groups in organic compounds.
• Chemistry involved in the preparation of the following:
Inorganic compounds: Mohr’s salt, potash alum.
Organic compounds: Acetanilide, p-nitroacetanilide, aniline yellow, iodoform.
• Chemistry involved in the titrimetric excercises - Acids bases and the use of indicators, oxalic-acid vs KMnO₄, Mohr’s salt vs KMnO₄.
• Chemical principles involved in the qualitative salt analysis:
Cations - Pb²⁺ , Cu²⁺, AI³⁺, Fe³⁺, Zn²⁺, Ni²⁺, Ca²⁺, Ba²⁺, Mg²⁺, NH⁴⁺.
Anions- CO₃^2-, S^2-, SO₄^2-, NO^2-, NO^3-, CI^-, Br, I. (Insoluble salts excluded).
• Chemical principles involved in the following experiments:
1. Enthalpy of solution of CuSO₄
2. Enthalpy of neutralization of strong acid and strong base. .
3. Preparation of lyophilic and lyophobic sols.
4. Kinetic study of reaction of iodide ion with hydrogen peroxide at room temperature.

PHYSICS

noreply@blogger.com (Anonymous) — Sun, 14 Feb 2010 07:32:00 +0000

The syllabus contains two Sections - A and B. Section - A pertains to the Theory Part having 80% weightage, while Section - B contains Practical Component (Experimental Skills) having 20% weightage.

SECTION A

Unit 1: PHYSICS AND MEASUREMENT
Physics, technology and society, S I units, Fundamental and derived units. Least count, accuracy and precision of measuring instruments, Errors in measurement, Significant figures. Dimensions of Physical quantities, dimensional analysis and its applications

Unit 2: KINEMATICS

Frame of reference. Motion in a straight line: Position-time graph, speed and velocity. Uniform and non-uniform motion, average speed and instantaneous velocity Uniformly accelerated motion, velocity-time, position- time graphs, relations for uniformly accelerated motion. Scalars and Vectors, Vector addition and Subtraction, Zero Vector, Scalar and Vector products, Unit Vector, Resolution of a Vector. Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion.

Unit 3: LAWS OF MOTION

Force and Inertia, Newton’s First Law of motion; Momentum, Newton’s Second Law of motion; Impulse; Newton’s Third Law of motion. Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces.
Static and Kinetic friction, laws of friction, rolling friction.
Dynamics of uniform circular motion: Centripetal force and its applications.

Unit 4: WORK, ENERGY AND POWER

Work done by a constant force and a variable force; kinetic and potential energies, workenergy theorem, power. Potential energy of a spring, conservation of mechanical energy, conservative and nonconservative forces; Elastic and inelastic collisions in one and two dimensions

Unit 5: ROTATIONAL MOTION

Centre of mass of a two-particle system, Centre of mass of a rigid body; Basic concepts of rotational motion; moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Rigid body rotation, equations of rotational motion.

Unit 6: GRAVITATION

The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Kepler’s laws of planetary motion. Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity of a satellite. Geo-stationary satellites.

Unit7: PROPERTIES OF SOLIDS AND LIQUIDS

Elastic behaviour, Stress-strain relationship, Hooke’s Law, Young’s modulus, bulk modulus, modulus of rigidity. Pressure due to a fluid column; Pascal’s law and its applications. Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, Reynolds number. Bernoulli’s principle and its applications. Surface energy and surface tension, angle of contact, application of surface tension - drops, bubbles and capillary rise. Heat, temperature, thermal expansion; specific heat capacity, calorimetry; change of state, latent heat. Heat transfer- conduction, convection and radiation, Newton’s law of cooling.

Unit 8: THERMODYNAMICS

Thermal equilibrium, zeroth law of thermodynamics, concept of temperature. Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics: reversible and irreversible processes. Carnot engine and its efficiency.

Unit 9: KINETIC THEORY OF GASES

Equation of state of a perfect gas, work doneon compressing a gas.Kinetic theory of gases - assumptions, concept of pressure. Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy,applications to specific heat capacities of gases; Mean free path, Avogadro’s number.

Unit 10: OSCILLATIONS AND WAVES

Periodic motion - period, frequency, displacement as a function of time. Periodic functions. Simple harmonic motion (S.H.M.) and its equation; phase; oscillations of a spring -restoring force and force constant; energy in S.H.M. - kinetic and potential energies; Simple pendulum - derivation of expression for its time period; Free, forced and damped oscillations, resonance.

Wave motion. Longitudinal and transverse waves, speed of a wave. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect in sound

Unit 11: ELECTROSTATICS

Electric charges: Conservation of charge, Coulomb’s law-forces between two point charges, forces between multiple charges; superposition principle and continuous charge distribution.
Electric field: Electric field due to a point charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque on a dipole in a uniform electric field.

Electric flux, Gauss’s law and its applications to find field due to infinitely long uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field.

Conductors and insulators, Dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor.

Unit 12: CURRENT ELECTRICITY

Electric current, Drift velocity, Ohm’s law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and nonohmic conductors, Electrical energy and power, Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance.

Electric Cell and its Internal resistance, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchhoff’s laws and their applications. Wheatstone bridge, Metre bridge. Potentiometer - principle and its applications.

Unit 13: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM

Biot - Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields. Cyclotron.

Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter.

Current loop as a magnetic dipole and its magnetic dipole moment. Bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements. Para-, dia- and ferro- magnetic substances.

Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.

Unit 14: ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual inductance. Alternating currents, peak and rms value of alternating current/ voltage; reactance and impedance; LCR series circuit, resonance; Quality factor, power in AC circuits, wattless current. AC generator and transformer.

Unit 15: ELECTROMAGNETIC WAVES

Electromagnetic waves and their characteristics. Transverse nature of electromagnetic waves.

Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, Xrays, gamma rays). Applications of e.m. waves.

Unit 16: OPTICS

Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications, Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens, Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifyingpowers.

Wave optics: wavefront and Huygens’ principle, Laws of reflection and refraction using Huygen’s principle. Interference, Young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes, Polarisation, plane polarized light; Brewster’s law, uses of plane polarized light and Polaroids.

Unit 17: DUAL NATURE OF MATTER AND RADIATION

Dual nature of radiation. Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation; particle nature of light. Matter waves-wave nature of particle, de Broglie relation. Davisson-Germer experiment.

Unit 18: ATOMS AND NUCLEI

Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity-alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion.

Unit 19: ELECTRONIC DEVICES

Semiconductors; semiconductor diode: I-V characteristics in forward and reverse bias; diode as a rectifier; I-V characteristics of LED, photodiode, solar cell and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch.

Unit 20: COMMUNICATION SYSTEMS

Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude and Frequency Modulation, Bandwidth of signals, Bandwidth of Transmission medium, Basic Elements of a Communication System (Block Diagram only)

SECTION-B

Unit 21: EXPERIMENTAL SKILLS

Familiarity with the basic approach and observations of the experiments and activities:
1. Vernier callipers-its use to measure internal and external diameter and depth of a vessel.
2. Screw gauge-its use to determine thickness/diameter of thin sheet/wire.
3. Simple Pendulum-dissipation of energy by plotting a graph between square of amplitude and time.
4. Metre Scale - mass of a given object by principle of moments.
5. Young’s modulus of elasticity of the material of a metallic wire.
6. Surface tension of water by capillary rise and effect of detergents.
7. Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
8. Plotting a cooling curve for the relationship between the temperature of a hot body and time.
9. Speed of sound in air at room temperature using a resonance tube. 10. Specific heat capacity of a given
(i) solid and
(ii) liquid by method of mixtures.
11. Resistivity of the material of a given wire using metre bridge.
12. Resistance of a given wire using Ohm’s law.
13. Potentiometer –
(i) Comparison of emf of two primary cells.
(ii) Determination of internal resistance of a cell.
14. Resistance and figure of merit of a galvanometer by half deflection method.
15. Focal length of:
(i) Convex mirror
(ii) Concave mirror, and
(iii) Convex lens using parallax method.
16. Plot of angle of deviation vs angle of incidence for a triangular prism.
17. Refractive index of a glass slab using a travelling microscope.
18. Characteristic curves of a p-n junction diode in forward and reverse bias.
19. Characteristic curves of a Zener diode and finding reverse break down voltage.
20. Characteristic curves of a transistor and finding current gain and voltage gain.
21. Identification of Diode, LED, Transistor, IC, Resistor, Capacitor from mixed collection of such items.
22. Using multimeter to:
(i) Identify base of a transistor
(ii) Distinguish between npn and pnp type transistor
(iii) See the unidirectional flow of current in case of a diode and an LED.
(iv) Check the correctness or otherwise of a given electronic component (diode, transistor or IC).

AIEEE Examination

noreply@blogger.com (Anonymous) — Sun, 14 Feb 2010 06:46:00 +0000

All India Engineering/Architecture Entrance Examination 2010

Scheme of Examination
Entrance examination would consist of two papers i.e. 1st paper consisting of three parts of Physics, Chemistry and Mathematics of equal weightage with objective type questions for BE/B.Tech courses and 2nd paper – consisting of Mathematics,Aptitude Test and Drawing for B. Architecture and B. Planning. The Aptitude Test is designed to evaluate candidate’s perception, imagination, observation, creativity and architectural awareness.

Scoring and Negative Marking
There will be objective type questions with four options having single correct answer. For each incorrect response one fourth (1/4) of the total marks allotted to the question would be deducted. No deduction from the total score will, however, be made if no response is indicated for an item in the answer sheet. The candidates are advised not to attempt such item in the answer sheet if they are not sure of the correct response. More than one answer indicated against a question will be deemed as incorrect response and will be negatively marked. All objective type questions are required to be answered on specially designed machine gradable answer sheets. Answers are to be marked using ball point pen (black/blue) only. For the purpose of evaluation, Test Booklet Code as printed in the Answer Sheet on Side-2 will be accepted as final. Subject combination for each paper & type of questions in each paper are given in the table below :

Requirement of papers for different courses is given in the table below:

Schedule of Examination
AIEEE will be conducted on the following dates as per schedule given below:

For those unable to appear in AIEEE on scheduled date of examination for any reason, including loss of application form/admit card in transit, no re-examination shall be held under any circumstances. The schedule will remain unaltered even if the date is declared as a public holiday.
Students may move to the venue of examination for refreshment etc. if they have applied for BE/B.Tech and B. Arch/B. Planning together.

Syllabus
The question papers for the Examination shall be based on a common minimum syllabus drawn from syllabi taught in different State Boards.

Syllabus Of Mathematics

Syllabus Of Physics

Syllabus Of Chemistry

SYLLABUS FOR APTITUDE TEST B.ARCH./B.PLANNING

Language of the Question Papers
Candidates can opt for question papers either in English or in Hindi. The option has to be exercised while filling Application Form. It cannot be changed later.

Eligibility Criteria : Candidates are, however, required to appear in the papers as per Scheme of Examination for AIEEE specified in para 2.4 of this Bulletin.

The minimum academic qualification for admission through AIEEE 2010 is a pass in the final examination of 10+2 (Class XII) or its equivalent referred to as the qualifying examination

LIST OF QUALIFYING EXAMINATIONS

Those appearing in 10+2 (Class XII) final or equivalent examination may also appear in AIEEE 2010 for consideration of provisional admission. Those appearing in 10+2 (Class 12) in 2011 are not eligible to appear in AIEEE-2010.

Subject combinations required in the qualifying examination for admission to B.E./B.Tech. and B. Arch./B. Planning Courses shall be as under:

*This is as per decision of the All India Council for Technical Education (AICTE).

**Provisionally as per the orders of the Hon'ble High Court of Delhi and directive recieved from the Ministry of Human Resource Development, Govt. of India.

The number of attempts which a candidate can avail at All India Engineering/Architecture Entrance Examination shall be limited to 03(three) uniformly for all the candidates in consecutive years. The candidates passed +2 to exam in 2008, 2009 or appearing in +2 in 2010 are only eligible to appear in AIEEE-2010. Candidates passed +2 in 2007 or before or appearing in 2011 are not eligible to appear in AIEEE-2010.

Date of Birth

Only those candidates whose date of birth falls on or after October 01, 1985 are eligible. However, in the case of Scheduled Caste (SC), Scheduled Tribe (ST) and Physically Handicapped (PH) candidates, upper age limit is relaxed by 5 years, i.e. SC, ST and PH candidates who were born on or after October 01, 1980 are eligible. Date of birth as recorded in the Secondary Education Board/University certificate only will be taken as authentic.

Examination Centres Cities

List of cities where the examination will be conducted is given in Appendix VI. Candidates are required to give four options convenient to them. While every effort will be made to allot a Centre in one of the places opted by the candidate, the Board reserves its discretion to allot a Centre other than that of candidate’s choice any where in India. Under no circumstances, the Centre once allotted shall be changed by the Board.

Admit Card

The Admit Card will be sent by post "Under Certificate of Posting (UPC)" to the candidates (including those who made application online) about four weeks before the conduct of the examination, however, the Board will not be responsible for any consequences that may arise due to loss of admit card in transit. It will be the responsiblity of the candidate to contact/write to the Board in case he/she is not in receipt of the Admit Cards by 6th April 2010. Such requests be sent to Assistant Secretary (AIEEE), Central Board of Secondary Education, PS 1-2 Institutional Area, IP Extension, Patparganj, Delhi-110 092 with 2 photographs (as pasted on the Application Form), one should be attested by Principal of the institution where candidate is studying/passed XII or by the gazetted officer. Photocopy of the Application Form, proof regarding remittance of fee (photocopy of the Demand Draft/Challan) in respect of those candidates who have made application online, and the original postal receipt issued by the Post Office for having dispatched the Application Form by Registered/Speed Post in order to get a duplicate Admit Card. Such request for issue of duplicate admit card should accompany with a Demand Draft in favour of Secretary,CBSE payable at Delhi/New Delhi amounting Rs.50/- as fee and additional Rs.30/- as postal charges for outstation candidates.Request for the issue of admit card after the examination will not be entertained.
In no case the duplicate Admit Card would be issued at the Examination Centres.

Procedure for Conduct of Examination and Use of Answer Sheet

Procedure for conduct of examination and instructions for use of the Test Booklet and Answer Sheet are given in Appendix VII. Candidates are advised to go through carefully before going for the Examination.

Evaluation and Declaration of Results

On the basis of performance in AIEEE, separate rank lists will be prepared for B.E./B.Tech. and B.Arch/B.Planning. Score Card indicating All India Rank and State Rank with total marks and marks in each subject shall be sent to all candidates appearing in AIEEE.

Candidates scoring above a certain cut off percentage of marks (being different for General, OBC, SC/ST/PH category candidates) to be called for counselling shall be determined at the time of declaration of AIEEE results.All India/State Rank and marks shall also be released on AIEEE website. The results of AIEEE-2010 is likely to be declared on or before 7th June, 2010.The All India/State Rank to be called for Central counselling will be decided by Central Counselling Board which will be constituted by the Ministry of Human Resource Development, Govt. of India and decision of seat matrix etc. will be taken by Central Counselling Board. The required information will be displayed at apropriate time on website www.ccb.nic.in .
The score cards will be dispatched to the candidates from 12.06.2010 to 27.06.2010 under Certificate of Posting (UPC). The Board will not be responsible for any consequences that may arise due to loss of score card in transit.In case of non-receipt of the score card within the stipulated period candidate may apply for duplicate score card on payment of Rs. 50/- (plus postal charges of Rs. 30/- for outstation candidates) in the form of Demand Draft in favour of Secretary, CBSE, payable at Delhi/New Delhi between 09.07.2010 to 31.08.2010. No request for issue of duplicate score card will be entertained thereafter.

As per the notified cut off score and the candidates declared eligible up to the notified Rank shall be called to appear for counselling.

In case of two or more candidates obtaining equal marks, inter-se merit of such candidates shall be determined as follows:

B.E/B.Tech - By marks obtained in Mathematics and then in Physics in the AIEEE and then by age (preference to older candidates).

B.Arch/B.Planning - By marks obtained in Aptitude Test and then in Mathematics in the AIEEE and then by age (preference to older candidates).

Rules For Rechecking/Re-Evaluation of Answer Sheets

Since the AIEEE answer sheets are machine graded with extreme care and repeatedly scrutinized, there is no provision for rechecking/re-evaluation of answer sheets. No correspondence in this regard will be entertained.

Counselling, Seat Allocation, Document Verification and Admissions

Final list of institutions admitting students (with intake in each discipline and category as per reservation) through AIEEE-2010, including counselling procedure, counselling schedule and counselling centres would be displayed on the CCB website in May/June 2010. The decision for the above will be taken by the CCB.

The Central Counselling Board shall send by post the Information Brochure for Counselling only to the candidates eligible for counselling. The counselling will be made on line Offcampus and Depending upon the requirement and facilities.

Verification of documents would be done at the time of counselling/admission. The purpose would be to verify different records regarding identification, age, qualifying examination, state of eligibility and category of the candidate. On failing to establish of any of the documents, the candidates will not be considered for admission.

SC, ST, OBC and PH candidates will be required to produce original certificate issued by the competent authority at the time of counselling, failing which they will not be considered for admission.

All correspondence regarding counselling and refund of the amount paid to the Central Counselling Board (CCB) or any of the participating institution should be made with the concerned authorities. No correspondence in this regard be made to CBSE. Legal Jurisdiction

All disputes pertaining to the conduct of AIEEE shall fall within the jurisdiction of Delhi only. The Secretary of the Board shall be the legal person in whose name the Board may sue or may be sued. If any person or officer dealing with the conduct of AIEEE engages himself/herself in act(s) that would result in the leakage of the question paper(s) or attempt to use or help in the use of unfair means in this examination, he/she shall be liable to prosecution under the Indian Penal Code.

Rules Of Reservation

Reservation for SC/ST/OBC and Physically Handicapped candidates will be applicable as per Govt. of India/State concerned existing rules or amended from time to time.

MATHEMATICS

noreply@blogger.com (Anonymous) — Sun, 14 Feb 2010 06:30:00 +0000

Unit 1: SETS, RELATIONS AND FUNCTIONS:

Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.

Unit 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS:

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.

Unit 3: MATRICES AND DETERMINANTS:

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

Unit 4 : PERMUTATIONS AND COMBINATIONS:

Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.

Unit 5: MATHEMATICAL INDUCTION:

Principle of Mathematical Induction and its simple applications.

Unit 6: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications.

Unit 7: SEQUENCES AND SERIES:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: Sn, Sn², Sn³. Arithmetico - Geometric progression.

Unit 8: LIMIT, CONTINUITY AND DIFFERENTIABILITY:

Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.

Unit 9: INTEGRAL CALCULUS:

Integral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.
Evaluation of simple integrals of the type

Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

Unit 10: DIFFERENTIAL EQUATIONS:

Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type:
dy
-- + p (x) y = q (x)
dx

Unit 11: CO-ORDINATE GEOMETRY:

Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
Straight lines
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.
Circles, conic sections
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

Unit 12: THREE DIMENSIONAL GEOMETRY:

Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.

Unit 13: VECTOR ALGEBRA:

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.

Unit 14: STATISTICS AND PROBABILITY:

Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

Unit 15: TRIGONOMETRY:

Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.

Unit 16: MATHEMATICAL REASONING:

Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive.

Concept of the Hole in ELECTRICAL CONDUCTION IN SOLIDS

noreply@blogger.com (Anonymous) — Fri, 11 Sep 2009 16:00:00 +0000

In considering the two-dimensional representation of the covalent bonding shown in
Figure 3.13a, a positively charged "empty state" was created when a valence electron
was elevated into the conduction band. For T > 0 K, all valence electrons may gain
thermal energy; if a valence electron gains a small amount of thermal energy, it may hop
into the empty state. The movement of a valence electron into the empty state is equivalent
to the movement of the positively charged empty state itself. Figure 3.17 shows the
movement of valence electrons in the crystal alternately filling one empty state and creating a new empty state, a motion equivalent to a positive charge moving in the valence
band. The crystal now has a second equally important charge carrier that can give rise to
a current. This charge carrier is called a hole and, as we will see, can also be thought of
as a classical particle whose motion can be modeled using Newtonian mechanics.
The drift current density due to electrons in the valence band, such as shown in
Figure 3.14b, can be written as
where the summation extends over all filled states. This summation is inconvenient
since it extends over a nearly full valence band and takes into account a very large
number of states. We may rewrite Equation (3.49) in the form
If we consider a band that is totally full, all available states are occupied by electrons.
The individual electrons can be thought of as moving with a velocity as given
by Equation (3.39):

The band is symmetric ink and each state is occupied so that, for every electron with
a velocity v l , there is a corresponding electron with a velocity -|v|. Since the band is
full, the distribution of electrons with respect to k cannot he changed with an
externally applied force. The net drift current density generated from a completely full
band, then, is zero, or

We can now write the drift current density from Equation (3.50) for an almost
full band as

where the u, in the summation is the

associated with the empty state. Equation (3.52) is entirely equivalent to placing a
positively charged particle in the empty states and assuming all other states in the hand
are empty, or neutrally charged. This concept is shown in Figure 3.18. Figure 3.18a
shows the valence band with the conventional electron-filled states and empty states,
while Figure 3.18b shows the new concept of positive charges occupying the original
empty states. This concept is consistent with the discussion of the positively charged
"empty state" in the valence band as shown in Figure 3.17.
The vi in the summation of Equation (3.52) is related to how well this positively
charged particle moves in the semiconductor. Now consider an electron near the top of
the allowed energy band shown in Figure 3.16b. The energy near the top of the allowed
energy hand may again he approximated by a parabola so that we may write

The energy E,, is the energy at the top of the energy hand. Since E i E,, for electrons
in this band, then the parameter C? must be a positive quantity.
Taking the second derivative of E with respect to k from Equation (3.53). we
obtain
We may rearrange this equation so that

Comparing Equation (3.55) with Equation (3.41), we may write

where m* is again an effective mass. We have argued that C2 is a positive quantity,
which now implies that m *is a negative quantity. An electron moving near the topo
an allowed energy hand behaves as if it has a negative mass.
We must keep in mind that the effective mass parameter is used to relate quantum
mechanics and classical mechanics. The attempt to relate these two theories
leads to this strange result of a negative effective mass. However, we must recall that
solutions to Schrodinger's wave equation also led to results that contradicted classical
mechanics. The negative effective mass is another such example.
In discussing the concept of effective mass in the last section, we used an analogy
of marbles moving through two liquids. Now consider placing an ice cube in the center
of a container filled with water: the ice cube will move upward toward the surface
in a direction opposite to the gravitational force. The ice cube appears to have a negative
effective mass since its acceleration is opposite to the external force. The effective
mass parameter takes into account all internal forces acting on the particle.
If we again consider an electron near the top of an allowed energy band and use
Newton's force equation for an applied electric field, we will have

However, m* is now a negative quantity, so we may write

An electron moving near the top of an allowed energy band moves in the same direction
as the applied electric field.
The net motion of electrons in a nearly full hand can he described by considering
just the empty states, provided that a positive electronic charge is associated with
each state and that the negative of m* from Equation (3.56) is associated with each
state. We now can model this band as having particles with a positive electronic
charge and a positive effective mass. The density of these particles in the valence
band is the same as the density of empty electronic energy states. This new particle
is the hole. The hole, then, has a positive effective mass denoted by mg and a positive
electronic charge, so it will move in the same direction as an applied field.

Drift Current in ELECTRICAL CONDUCTION IN SOLIDS

noreply@blogger.com (Anonymous) — Fri, 11 Sep 2009 15:43:00 +0000

Current is due to the net flow of charge. If we had a collection of positively charged ions with a volume density N (cm^-3) and an average drift velocity Vd(cm/s), then the drift current density would be If, instead of considering the average drift velocity, we considered the individual ion velocities, then we could write the drift current density as
where vi is the velocity of the ith ion. The summation in Equation (3.33) is taken over
a unit volume so that the current density J is still in units of A/cm² .
Since electrons are charged particles, a net drift of electrons in the conduction
band will give rise to a current. The electron distribution in the conduction band, as
shown in Figure 3.14b. is an even function of k when no external force is applied. Recall
that k for a free electron is related to momentum so that, since there are as many
electrons with a +|k| value as there are with a -|k| value, the net drift current density due to these electrons is zero. This result is certainly expected since there is no
externally applied force.
If a force is applied to a particle and the particle moves, it must gain energy. This
effect is expressed as
where F is the applied force, dx is the differential distance the particle moves, v is the I
velocity, and dE is the increase in energy. If an external force is applied to the electrons
in the conduction band, there are empty energy states into which the electrons
can move: therefore, because of the external force, electrons can gain energy and a net
momentum. The electron distribution in the conduction band may look like that
shown in Figure 3.15, which implies that the electrons have gained a net momentum.
We may write the drift current density due to the motion of electrons as
where e is the magnitude of the electronic charge and n is the number of electrons
per unit volume in the conduction hand. Again, the summation is taken over a unit

volume so the current density is A/cm² . We may note from Equation (3.35) that the
current is directly related to the electron velocity; that is, the current is related to how
well the electron can move in the crystal.

Electrical conductivity in solids

noreply@blogger.com (Anonymous) — Mon, 31 Aug 2009 14:25:00 +0000

Again, we are eventually interested in determining the current-voltage characteristics
of semiconductor devices. We will need to consider electrical conduction in
solids as it relates to the band theory we have just developed. Let us begin by considering
the motion of electrons in the various allowed energy hands

The Energy Band and the Bond Model

we discussed the covalent bonding of silicon. Figure 3.12 shows a twodimensional
representation of the covalent bonding in a single-crystal silicon lattice.
This figure represents silicon at T = 0 Kin which each silicon atom is surrounded by
eight valence electrons that are in their lowest energy state and are directly involved
in the covalent bonding. Figure 3.4b represented the splitting of the discrete silicon
energy states into bands of allowed energies as the silicon crystal is formed. At
T = 0 K, the 4N states in the lower band, the valence band, are tilled with the valence
electrons. All of the valence electrons schen~aticallys hown in Figure 3.12 are
in the valence band. The upper energy band, the conduction band, is completely
empty at T = 0 K.

As the temperature increases above 0 K, a few valence band electrons may gain
enough thermal energy to break the covalent bond and jump into the conduction
band. Figure 3.13a shows a two-dimensional representation of this bond-breaking
effect and Figure 3.13b. a simple line representation of the energy-band model,
shows the same effect.
The semiconductor is neutrally charged. This means that, as the negatively
charged electron breaks away from its covalent bonding position, a positively
charged "empty state" is created in the original covalent bonding position in the valence
band. As the temperature further increases, more covalent bonds are broken,
more electrons jump to the conduction hand, and more positive "empty states" are
created in the valence band.
We can also relate this hond breaking to the E versus k energy bands.
Figure 3.14a shows the E versus k diagram of the conduction and valence bands at

T = 0 K. The energy states in the valence band are completely full and the states in
the conduction band are empty. Figure 3.14b shows these same bands for T > 0 K,
in which some electrons have gained enough energy to jump to the conduction band
and have left empty states in the valence hand. We are assuming at this point that no
external forces are applied so the electron and "empty state" distributions are symmetrical
with k

Applications-of-schrodingers-wave

noreply@blogger.com (Anonymous) — Mon, 31 Aug 2009 14:07:00 +0000

The solution to this differential equation can be written in the form

Recall that the time-dependent portion of the solution is

This wave function solution is a traveling wave, which means that a particle moving
in free space is represented by a traveling wave. The first term, with the coefficient A.
is a wave traveling in the +I direction, while the second term, with the coefficient B.
is a wave traveling in the x direction. The value of these coefficients will he determined
from boundary conditions. We will again see the traveling-wave solution for
an electron in a crystal or semiconductor material.
Assume, for a moment, that we have a particle traveling in the +x direction.
which will be described by the +x traveling wave. The coefficient B = 0. We can
write the traveling-wave solution in the form

A free particle with a well-defined energy will also have a well-defined wavelength
and momentum.
The probability density function is Y(x, t)Y*(x, t) = AA*, which is a constant
independent of position. A free particle with a well-defined momentum can be found
anywhere with equal probability. This result is in agreement with the Heisenberg uncertainty
principle in that a precise momentum implies an undefined position.
A localized free particle is defined by a wave packet, formed by a superposition
of wave functions with different momentum or k values. We will not consider the
wave packet here.

The Infinite Potential Well

The problem of a particle in the infinite potential well is a classic example of a bound
particle. The potential V(x) as a function of position for this problem is shown in

Figure 2.5. The particle is assumed to exist in region II so the particle is contained
within a finite region of space. The time-independent Schrodinger's wave equation is
again given by Equation (2.13) as

where E is the total energy of the particle. If E is finite, the wave function must be
zero, or=0, in both regions I and III. A particle cannot penetrate these infinite
potential barriers, so the probability of finding the particle in regions I and
III is zero.
The time-independent Schrodinger's wave equation in region II, where V = 0.
becomes

Click on image to enlarge

The total energy can then be written as

where the constant K must have discrete values, implying that the total energy of the
particle can only have discrete values. This result means that the energy of the particle
is quantized. That is, the energy of the particle can only have particular discrete
values. The quantization of the particle energy is contrary to results from classical
physics, which would allow the particle to have continuous energy values. The discrete
energies lead to quantum states that will be considered in more detail in this
and later chapters. The quantization of the energy of a bound particle is an extremely
important result.

Introduction to the Quantum Theory of Solids

noreply@blogger.com (Anonymous) — Mon, 31 Aug 2009 13:34:00 +0000

In the last chapter, use applied quantum mechanics and Schrodinger's wave equation
to determine the behavior of electrons in the presence of various potential
functions. We found that one important characteristic of an electron bound to an
atom or bound within a finite space is that the electron can take on only discrete values
of energy; that is, the energies are quantized. We also discussed the Pauli exclusion
principle, which stated that only one electron is allowed to occupy any given
quantum state. In this chapter, we will generalize these concepts to the electron in a
crystal lattice.
One of our goals is to determine the electrical properties of a semiconductor material,
which we will then use to develop the current-voltage characteristics of semiconductor
devices. Toward this end, we have two tasks in this chapter: to determine
the properties of electrons in a crystal lattice, and to determine the statistical characteristics
of the very large number of electrons in a crystal.
To start, we will expand the concept of discrete allowed electron energies that
occur in a single atom to a band of allowed electron energies in a single-crystal solid.
First we will qualitatively discuss the feasibility of the allowed energy bands in a
crystal and then we will develop a more rigorous mathematical derivation of this theory
using Schrodinger's wave equation. This energy band theory is a basic principle
of semiconductor material physics and can also be used to explain differences in
electrical characteristics between metals, insulators, and semiconductors.
Since current in a solid is due to the net flow of charge, it is important to determine
the response of an electron in the crystal to an applied external force, such as an
electric field. The movement of an electron in a lattice is different than that of an electron
in free space. We will develop a concept allowing us to relate the quantum mechanical
behavior of electrons in a crystal to classical Newtonian mechanics. This analysis leads to a parameter called the electron effective mass. As part of this development,
we will find that we can define a new particle in a semiconductor called a
hole. he motion of both electrons and holes gives rise to currents in a semiconductor.
Because the number of electrons in a semiconductor is very large, it is impossible
lo follow the motion of each individual particle. We will develop the statistical
behavior of electrons in a crystal, noting that the Pauli exclusion principle is an important
factor in determining the statistical law the electrons must follow. The resulting
probability function will determine the distribution of electrons among the available
energy states. when we develop the theory of the semiconductor in
equilibrium

Allowed and Forbidden energy bands

noreply@blogger.com (Anonymous) — Mon, 31 Aug 2009 13:10:00 +0000

we treated the one-electron, or hydrogen, atom. That analysis showed that the energy of the bound electron is quantized: Only discrete values of electron energy are allowed. The radial probability density for the electron was also determined. This function gives the probability of finding the electron at a particular distance from the nucleus and shows that the electron is not localized at a given radius. We can extrapolate these single-atom results to a crystal and qualitatively derive the concepts of allowed and forbidden energy bands. We can then apply quantum mechanics and Schrodinger's wave equation to the problem of an electron in a single crystal. We find that the electronic energy states occur in hands of allowed Elates that are separated by forbidden energy bands.

Formation of Energy Bands
Figure 3.la shows the radial probability density function for the lowest electron
energy state of the single, non interacting hydrogen atom, and Figure 3.lb shows the
same probability curves for two atoms that are in close proximity to each other. The
wave functions of the two atom electrons overlap, which means that the two electrons

will interact. This interaction or perturbation results in the discrete quantized energy
level splitting into two discrete energy levels, schematically shown in Figure 3.1~.
The splitting of the discrete state into two states is consistent with the Pauli exclusion
principle.
A simple analogy of the splitting of energy levels by interacting particles is the
following. Two identical race cars and drivers are far apart on a race track. There is
no interaction between the cars, so they both must provide the same power to
achieve a given speed. However, if one car pulls up close behind the other car, there
is an interaction called draft. The second car will be pulled to an extent by the lead
car. The lead car will therefore require more power to achieve the same speed, since
it is pulling the second car and the second car will require less power since it is
being pulled by the lead car. So there is a "splitting" of power (energy) of the two
interacting race cars. (Keep in mind not to take analogies too literally.)
Now, if we somehow start with a regular periodic arrangement of hydrogen type
atoms that are initially very far apart, and begin pushing the atoms together, the
initial quantized energy level will split into a band of discrete energy levels. This effect
is shown schematically in Figure 3.2, where the parameter ro represents the
equilibrium inter atomic distance in the crystal. At the equilibrium inter atomic distance,
there is a band of allowed energies, but within the allowed band, the energies
are at discrete levels. The Pauli exclusion principle states that the joining of atoms
to form a system (crystal) does not alter the total number of quantum states regardless
of size. However, since no two electrons can have the same quantum number.
the discrete energy must split into a band of energies in order that each electron can
occupy a distinct quantum state.
We have seen previously that, at any energy level, the number of allowed quantum
states is relatively small. In order to accommodate all of the electrons in a crystal,
then, we must have many energy levels within the allowed band. As an example,
suppose that we have a system with 10¹⁹ one-electron atoms and also suppose that,
at the equilibrium inter atomic distance, the width of the allowed energy band is I eV.
For simplicity, we assume that each electron in the system occupies a different energy
level and, if the discrete energy states are equidistant, then the energy levels ate
separated by 10^-19 eV. This energy difference is extremely small, so that for all practical
purposes, we have a quasi-continuous energy distribution through the allowed

energy band. The fact that 10^-19 eV is a very small difference between two energy
states can be seen from the following example.

To calculate the change in kinetic energy of an electron when the velocity changes by a small value
Consider an electron traveling at a velocity of 10⁷ cm/s. Assume the velocity increases by
a value of 1 cm/s. The increase in kinetic energy is given by

The Kronig-Penney Model

noreply@blogger.com (Anonymous) — Sun, 30 Aug 2009 09:31:00 +0000

In the previous section, we discussed qualitatively the spitting of allowed electron
energies as atoms are brought together to form a crystal. The concept of allowed and
forbidden energy bands can be developed more rigorously by considering quantum
mechanics and Schrodinger's wave equation. It may be easy for the reader to "get
lost" in the following derivation, but the result forms the basis for the energy-band
theory of semiconductors.
The potential function of a single, noninteracting, one-electron atom is shown in
Figure 3.5a. Also indicated on the figure are the discrete energy levels allowed for
the electron. Figure 3.5b shows the same type of potential function for the case when
several atoms are in close proximity arranged in a one-dimensional array. The potential
functions of adjacent atoms overlap, and the net potential function for this
case is shown in Figure 3 . 5 c I.t is this potential function we would need to use in
Schrodinger's wave equation to model a one-dimensional single-crystal material.
The solution to Schrodinger's wave equation, for this one-dimensional single crystal
lattice, is made more tractable by considering a simpler potential function.
Figure 3.6 is the one-dimensional Kronig-Penney model of the periodic potential
function, which is used to represent a one-dimensional single-crystal lattice. We need
to solve Schrodinger's wave equation in each region. As with previous quantum mechanical
problems, the more interesting solution occurs for the case when E <>o,
which corresponds to a particle being bound within the crystal. The electrons are
contained in the potential wells, but we have the possibility of tunneling between
wells. The Kronig-Penney model is an idealized periodic potential representing a
one-dimensional single crystal. but the results will illustrate many of the important
features of the quantum behavior of electrons in a periodic lattice.
To obtain the solution to Schrodinger's wave equation, we make use of a mathematical
theorem by Bloch. The theorem states that all one-electron wave functions,

Figure 3.5 (a) Potential function of a single isolated
atom. (b) Overlapping potential functions of adjacent
atoms. (c) Net potential function of a one-dimensional
single crystal.

APPLICATIONS OF SCHRODINGER'S WAVE EQUATION

noreply@blogger.com (Anonymous) — Wed, 19 Aug 2009 13:53:00 +0000

We will now apply Schrodinger's wave equation in several examples using various
potential functions. These examples will demonstrate the techniques used in the solution
of Schrodinger's differential equation and the results of these examples will
provide an indication of the electron behavior under these various potentials. We will
utilize the resulting concepts later in the discussion of semiconductor properties

Electron in Free Space
As a first example of applying the Schrodinger's wave equation, consider the motion
of an electron in free space. If there is no force acting on the particle, then the potential
function V(x) will be constant and we must have E > V(x). Assume, for simplicity,
that the potential function V(x) = 0 for all x. Then, the time-independent
wave equation can he written from Equation (2.13) as

The solution to this differential equation can be written in the form

Recall that the time-dependent portion of the solution is

This wave function solution is a traveling wave, which means that a particle moving
in free space is represented by a traveling wave. The first term, with the coefficient A.
is a wave traveling in the +I direction, while the second term, with the coefficient B.
is a wave traveling in the x direction. The value of these coefficients will he determined
from boundary conditions. We will again see the traveling-wave solution for
an electron in a crystal or semiconductor material.
Assume, for a moment, that we have a particle traveling in the +x direction.
which will be described by the +x traveling wave. The coefficient B = 0. We can
write the traveling-wave solution in the form
A free particle with a well-defined energy will also have a well-defined wavelength
and momentum.
The probability density function is Y(x, t)Y*(x, t) = AA*, which is a constant
independent of position. A free particle with a well-defined momentum can be found
anywhere with equal probability. This result is in agreement with the Heisenberg uncertainty
principle in that a precise momentum implies an undefined position.
A localized free particle is defined by a wave packet, formed by a superposition
of wave functions with different momentum or k values. We will not consider the
wave packet here.

The Infinite Potential Well

The problem of a particle in the infinite potential well is a classic example of a bound
particle. The potential V(x) as a function of position for this problem is shown in

Figure 2.5. The particle is assumed to exist in region II so the particle is contained
within a finite region of space. The time-independent Schrodinger's wave equation is
again given by Equation (2.13) as

where E is the total energy of the particle. If E is finite, the wave function must be
zero, or = 0, in both regions I and III. A particle cannot penetrate these infinite
potential barriers, so the probability of finding the particle in regions I and
III is zero.
The time-independent Schrodinger's wave equation in region II, where V = 0.
becomes

Click on image to enlarge

The total energy can then be written as

where the constant K must have discrete values, implying that the total energy of the
particle can only have discrete values. This result means that the energy of the particle
is quantized. That is, the energy of the particle can only have particular discrete
values. The quantization of the particle energy is contrary to results from classical
physics, which would allow the particle to have continuous energy values. The discrete
energies lead to quantum states that will be considered in more detail in this
and later chapters. The quantization of the energy of a bound particle is an extremely
important result.

Boundary Conditions for Schrodinger's Wave equation

noreply@blogger.com (Anonymous) — Wed, 19 Aug 2009 13:25:00 +0000

Since the function| |² represents the probability density function, then for a
single particle. we must have that

The probability of finding the particle somewhere is certain. Equation (2.18) allows
us to normalize the wave function and is one boundary condition that is used to determine
some wave function coefficients.
The remaining boundary conditions imposed on the wave function and its derivative
are postulates. However. we may state the boundary conditions and present arguments
that justify why they must be imposed. The wave function and its first derivative
must have the following properties if the total energy E and the potential V(x) are finite
everywhere.

Since| |² is a probability density, then must be finite and single-valued.
If the probability density were to become infinite at some point in space, then the
probability of finding the particle at this position would be certain and the uncertainty
principle would be violated. If the total energy E and the potential V(x) are
finite everywhere, then from Equation (2.13), the second derivative must be finite,
which implies that the first derivative muht be continuous. The first derivative is
related to the particle momentum, which must be finite and single-valued. Finally, a
finite first derivative implies that the funclion itself must he continuous. In some of
the specific examples that we will consider, the potential function will become infinite
in particular regions of space. For these cases. the first derivative will not necessarily
be continuous, but the remaining boundary conditions will still hold.

Physical Meaning of the Schrodinger's Wave Function

noreply@blogger.com (Anonymous) — Sun, 16 Aug 2009 07:32:00 +0000

We are ultimately trying to use the wave function to describe the behavior of
an electron in a crystal. The function a wave function. so it is reasonable to
ask what the relation is between the function and the electron. The total wave function
is the product of the position-dependent, or time-independent, function and the
time-dependent function. We have from Equation (2.7) that
Since the total wave function is a complex function. it cannot by itself represent a real physical quantity. Max Born postulated in 1926 that the function| |²dx is the probability of finding the particle between .x and x + dx at a given time, or that| |² is a probability density function. We have that

is the probability density function and is independent of time. One major difference
between classical and quantum mechanics is that in classical mechanics, the position
of a particle or body can be determined precisely, whereas in quantum mechanics,
the position of a partical is found in terms of a probability. We will determine the
probability density function for several examples, and, since this property is independent
of time. we will, in general, only be concerned with the time-independent
wave function.

Schrodinger's Wave equation

noreply@blogger.com (Anonymous) — Sun, 16 Aug 2009 07:05:00 +0000

The various experimental results involving electromagnetic waves and particles.
which could not be explained by classical laws of physics, showed that a revised formulation
of mechanics was required. Schrodinger, in 1926. provided a formulation
called wave mechanics, which incorporated the principles of quanta introduced by
Planck, and the wave-particle duality principle introduced by de Broglie. Based on the
wave-particle duality principle. we will describe the motion of electrons in a crystal
by wave theory. This wave theory is described by Schrodinger's wave equation.

The Wave Equation
The one-dimensional, nonrelativistic Schrodinger's wave equation is given by

where the wave function, V(x) is the potential function assumed to he independent
of time, fn is the mass of the particle, and, is the imaginary constant iota
There are theoretical arguments that justify the form of Schrodinger's wave equation.
hut the equation is a basic postulate of quantum mechanics. The wave function
will be used to describe the behavior of the system and, mathematically,
can be a complex quantity.
We may determine the time-dependent portion of the wave function and the
position-dependent, or time-independent, portion of the wave function by using the
technique of separation of variables. Assume that the wave function can he written in
the form

Since the left side of Equation (2.9) is a function of position x only and the right side
of the equation is a function of time r only, each side of this equation must he equal
to a constant. We will denote this separation of variables constant by
The time-dependent portion of Equation (2.9) is then written as

where again m is the mass of the particle, V(x) is the potential experienced by the particle,
and E is the total energy of the particle. This time-independent Schrodinger's
wave equation can also be justitied on the basis of the classical wave equation as
shown in Appendix E. The pseudo-derivation in the appendix is a simple approach
but shows the plausibility of the time-independent Schrodinger's equation

The Uncertainty Principle

noreply@blogger.com (Anonymous) — Sun, 16 Aug 2009 05:57:00 +0000

The Heisenberg uncertainty principle, given in 1927, also applies primarily to very
small particles, and states that we cannot describe with absolute accuracy the hchavior
of these subatomic particles. The uncertainty principle describe a fundamental
relationship between conjugate variables, including position and momentum and also
energy and time.
The first statement of the uncertainty principle is that it is impossible to simultaneously
describe with absolute accuracy the position and momentum of a particle. If
the uncertainty in the momentum is delta p and the uncertainty in the postion is Ax, then
the uncertainty principle is stated as

The second statement of the uncertainty principle is that it is impossible to simultaneously
describe with absolute accuracy the energy of a particle and the instant
of time the particle has this energy. Again. if the uncertainty in the energy is given by
AE and the uncertainty in the time is given by Ar, then the uncertainty principle is
stated as

One way to visualize the uncertainty principle is to consider the simultaneous
measurement of position and momentum, and the simultaneous measurement of energy
and time. The uncertainty principle implies that these simultaneous measurements
are in error to a certain extent. However, the modified Planck's constant ti is very
small; the uncertainty principle is only significant for subatomic particles. We must
keep in mind nevertheless that the uncertainty principle is a fundamental statement and
does not deal only with measurements.
One consequence of the uncertainty principle is that we cannot. for example. determine
the exact position of an electron. We will, instead, determine the probability
of finding an electron at a particular position. In later chapters, we will develop a
probability density function that will allow us to determine the probability that an
electron has a particular energy. So in describing electron behavior, we will he dealing
with probability functions.

Wave-Particle Duality

noreply@blogger.com (Anonymous) — Sat, 15 Aug 2009 12:13:00 +0000

We have seen in the last section that light waves, in the photoelectric effect, behave
as if they are particles. The particle-like behavior of electromagnetic waves was also
instrumental in the explanation of the Compton effect. In this experiment. an x-ray
beam was incident on a solid. A portion of the x-ray beam was deflected and the frequency
of the deflected wave had shifted compared to the incident wave. The observed
change in frequency and the deflected angle corresponded exactly to the expected
results of a "billiard ball" collision between an x-ray quanta, or photon, and
an electron in which both energy and momentum are conserved.
In 1924. de Broglie postulated the existence of matter waves. He suggested that
since waves exhibit particle-like behavior, then particles should be expected to
show wave-like properties. The hypothesis of de Broglie was the existence of a
wave-particle duality principle. The momentum of a photon is given by

Energy Quanta

noreply@blogger.com (Anonymous) — Sat, 15 Aug 2009 11:35:00 +0000

One experiment that demonstrates an inconsistency between experimental results and the classical theory of light is called the photoelectric effect. If monochromatic light is incident on a clean surface of a material, then under certain conditions, electrons (photo electrons) are emitted from the surface. According to classical physics. if the intensity of the light is large enough, the work function of the material will be overcome and an electron will be emitted from the surface independent of the incident frequency. This result is not observed. The observed effect is that, at a constant incident intensity, the maximum kinetic energy of the photo electron varies linearly with frequency with a limiting frequency v = Vo. below which no photo electron is produced. This result is shown in Figure 2.1. If the incident intensity varies at a constant frequency, the rate of photo electron emission changes, but the maximum kinetic energy remains the same. Planck postulated in I900 that thermal radiation is emitted from a heated surface in discrete packets of energy called qunnta. The energy of these quanta is given by E = hv, where v is the frequency of the radiation and h is a constant now known as Planck's constant (h=6.63x10^-34J-s)
Then in 1905. Einstein interpreted
the photoelectric results by suggesting that the energy in a light wave is also
contained in discrete packets or bundles. The particle-like packet of energy is
called aphoton, whose energy is also given by E = hv. A photon with sufficient
energy, then, can knock an electron from the sul-face of the material. The minimum
energy required to remove an electron is called the work function of the material
and any excess photon energy goes into the kinetic energy of the photoelectron.
This result was confirmed experimentally as demonsttated in Figure 2.1. The photoelectric
effect shows the discrete nature of the photon and demonstrates the
particle-like behavior of the photon.
The maximum kinetic energy of the photoelectron can be written as

Introduction to Quantum mechanics and PRINCIPLES

noreply@blogger.com (Anonymous) — Sat, 15 Aug 2009 11:32:00 +0000

The goal of this text is to help readers understand the operation and characteristics
of semiconductor devices. Ideally, we would like to begin discussing
these devices immediately. However, in order to understand the currentvoltage
characteristics, we need some knowledge of the electron behavior in a crystal
when the electron is subjected to various potential functions.
The motion of large objects, such as planets and satellites, can be predicted to a
high degree of accuracy using classical theoretical physics based on Newton's laws
of motion. But certain experimental results, involving electrons and high-frequency
electromagnetic waves, appear to he inconsistent with classical physics. However,
these experimental results can be predicted by the principles of quantum mechanics.
The quantum mechanical wave theory is the basis for the theory of semiconductor
physics.
We are ultimately interested in semiconductor materials whose electrical properties
arc directly related to the behavior of electrons in the crystal lattice. The behavior
and characteristics of these electrons can be described by the formulation of
quantum mechanics called wave mechanics. The essential elements of this wave mechanics,
using Schrodinger's wavc equation, are presented in this chapter.
The goal of this chapter is to provide a brief introduction to quantum mechanics
so that readers gain an understanding of and become comfortable with the analysis
techniques. This introductory material forms the basis of semiconductor physics..

PRINCIPLES OF QUANTUM MECHANICS

there are three principles
we need to consider: the principle of energy quanta, the wave-puticle duality principle,
and the uncertainty principle.

Epitaxial Growth

noreply@blogger.com (Anonymous) — Fri, 14 Aug 2009 15:32:00 +0000

A common and versatile growth technique that is used extensively in device and integrated
circuit fabrication is epitaxial growth. Epitaxial growth is a process whereby
a thin, single-crystal layer of material is grown on the surface of a single-crystal substrate.
In the epitaxial process, the single-crystal substrate acts as the seed, although
the process takes place far below the melting temperature. When an epitaxial layer is
grown on a substrate of the same material, the process is termed homoepitaxy. Growing
silicon on a silicon substrate is one example of a homoepitaxy process. At present,
a great deal of work is being done with heteroepitaxy. In a heteroepitaxy
process, although the substrate and epitaxial materials are not the same, the two crystal
structures should be very similar if single-crystal growth is to he obtained and if
a large number of defects are to be avoided at the epitaxial-substrate interface.
Growing epitaxial layers of the ternary alloy AlGaAs on a GaAs substrate is one example
of a heteroepitaxy process.
One epitaxial growth technique that has been used extensively is called chemical
vapor-phase deposition (CVD). Silicon epitaxial layers, for example, are grown
on silicon substrates by the controlled deposition of silicon atoms onto the surface
from a chemical vapor containing silicon. In one method, silicon tetrachloride reacts
with hydrogen at the surface of a heated substrate. The silicon atoms are released in
the reaction and can he deposited onto the substrate, while the other chemical reactant,
HCI, is in gaseous form and is swept out of the reactor. A sharp demarcation between
the impurity doping in the substrate and in the epitaxial layer can be achieved
using the CVD process. This technique allows great flexibility in the fabrication of
semiconductor devices.
Liquid-phase epitaxy is another epitaxial growth technique. A compound of the
semiconductor with another element may have a melting temperature lower than that
of the semiconductor itself. The semiconductor substrate is held in the liquid compound
and, since the temperature of the melt is lower than the melting temperature of
the substrate, the substrate does not melt. As the solution is slowly cooled, a single-crystal
semiconductor layer grows on the seed crystal. This technique, which occurs
at a lower temperature than the Czochralski method, is useful in growing group Ill-V
compound semiconductors.
A versatile technique for growing epitaxial layers is the molecular bean1 epitaxy
(MBE) process. A substrate is held in vacuum at a temperature normally in the range
of 400 to 800"C, a relatively low temperature compared with many semiconductor processing
steps. Semiconductor and dopant atoms are then evaporated onto the surface
of the substrate. In this technique, the doping can he precisely controlled resulting
in vety complex doping profiles. Complex ternary compounds, such as AIGaAs,
can be grown on substrates, such as GaAs, where abrupt changes in the crystal composition
are desired. Many layers of various types of epitaxial compositions can be
grown on a substrate in this manner. These structures are extremely beneficial in optical
devices such as laser diodes.

GROWTH OF SEMICONDUCTOR MATERIALS

noreply@blogger.com (Anonymous) — Fri, 14 Aug 2009 15:23:00 +0000

The success in fabricating very large scale integrated ( VL SI) circuits is a result, to a
large extent, of the development of and improvement in the formation or growth of
pure single-crystal semiconductor materials. Semiconductors are some of the purest
materials. Silicon, for example, has concentrations of most impurities of less than
1 part in 10 billion. The high purity requirement means that extreme care is necessary
in the growth and the treatment of the material at each step of the fabrication process.
The mechanics and kinetics of crystal growth are extremely complex and will be described
in only very general term in this text. However, a general knowledge of the
growth techniques and terminology is valuable.

Growth from a Melt
A common technique for growing single-crystal materials is called the Czochralski
method. In this technique, a small piece of single-crystal material, known as a seed,
is brought into contact with the surface of the same material in liquid phase, and then
slowly pulled from the melt. As the seed is slowly pulled, solidification occurs along
the plane between the solid-liquid interface. Usually the crystal is also rotated slowly
as it is being pulled, to provide a slight stirring action to the melt, resulting in a more
uniform temperature. Controlled amounts of specific impurity atoms, such as boron
or phosphorus, may be added to the melt so that the grown semiconductor crystal is
intentionally doped with the impurity atom. Figure 1.20 shows a schematic of the
Czochralski growth process and a silicon ingot or boule grown by this process.

Some impurities may be present in the ingot that are undesirable. Zone refining
is a common technique for purifying material. A high-temperature coil. or r-f induction
coil, is slowly passed along the length of the boule. The temperature induced by
the coil is high enough so that a thin layer of liquid is formed. At the solid-liquid interface,
there is a distribution of impurities between the two phases. The parameter
that describes this distribution is called the segregation coefficient: the ratio of the
concentration of impurities in the solid to the concentration in the liquid. If the segregation
coefficient is 0.1, for example, the concentration of impurities in the liquid
is a factor of 10 greater than that in the solid. As the liquid zone moves through the
material. the impurities are driven along with the liquid. After several passes of the
r-f coil, most impurities are at the end of the bar, which can then be cut off. The moving
molten zone, or the zone-refining technique, can result in considerable purification.
After the semiconductor is grown, the boule is mechanically trimmed to the
proper diameter and a Rat is ground over the entire length of the boule to denote the
crystal orientation. The Rat is perpendicular to the [ 1101 direction or indicates the (I 10)
plane. (See Figure 1.20b.) This then allows the individual chips to be fabricated along
given crystal planes so that the chips can he sawed apan more easily. The boule is then
sliced into wafers. The wafer must he thick enough to mechanically support itself. A
mechanical two-sided lapping operation produces a Rat wafer of uniform thickness.
Since the lapping procedure can leave a surface damaged and contaminated by the mechanical
operation, the surface must be removed by chemical etching. The final step is
polishing. This provides a smooth surface on which devices may be fabricated or further
growth processes may be carried out. This final semiconductor wafer is called the
substrate material.

Impurities in Solids

noreply@blogger.com (Anonymous) — Fri, 14 Aug 2009 15:18:00 +0000

Foreign atoms, or impurity atoms, may be present in a crystal lattice. Impurity atoms
may be located at normal lattice sites, in which case they are called . substitutional impurities.
Impurity atoms may also be located between normal sites, in which case
they are called interstitial impurities. Both these impurities are lattice defects and are
schematically shown in Figure 1.19. Some impurities, such as oxygen in silicon, tend
to he essentially inert; however, other impurities, such as gold or phosphorus in silicon,
can drastically alter the electrical properties of the material.
In Chapter 4 we will see that, by adding controlled amounts of particular impurity
atoms, the electrical characteristics of a semiconductor material can be favorably
altered. The technique of adding impurity atoms to a semiconductor material in order
to change its conductivity is called doping. There are two general methods of doping:
impurity diffusion and ion implantation.
The actual diffusion process depends to some extent on the material but, in general,
impurity diffusion occurs when a semiconductor crystal is placed in a high temperature
(= 1000°C) gaseous atmosphere containing the desired impurity atom.
At this high temperature, many of the crystal atoms can randomly move in and out of
their single-crystal lattice sites. Vacancies may be created by this random motion so
that impurity atoms can move through the lattice by hopping from one vacancy to another.
Impurity diffusion is the process by which impurity particles move from a region
of high concentration near the surface, to a region of lower concentration within
the crystal. When the temperature decreases, the impurity atoms become permanently
frozen into the substitutional lattice sites. Diffusion of various impurities into selected
regions of a semiconductor allows us to fabricate complex electronic circuits in a
single semiconductor crystal.
Ion implantation generally takes place at a lower temperature than diffusion. A
beam of impurity ions is accelerated to kinetic energies in the range of 50 keV or
greater and then directed to the surface of the semiconductor. The high-energy impurity
ions enter the crystal and come to rest at some average depth from the surface.
One advantage of ion implantation is that controlled numbers of impurity atoms can
be introduced into specific regions of the crystal. A disadvantage of this technique is
that the incident impurity atoms collide with the crystal atoms. causing lattice displacement
damage. However, most of the lattice damage can he removed by thermal
annealing, in which the temperature of the crystal is raised for a short time. Thermal
annealing is a required step after implantation.

Imperfections in Solids

noreply@blogger.com (Anonymous) — Fri, 14 Aug 2009 15:08:00 +0000

One type of imperfection that all crystals have in common is atomic thermal vibration.
Aperfect single crystal contains atoms at particular lattice sites, the atoms separated
from each other by a distance we have assumed to be constant. The atoms in a
crystal, however, have a certain thermal energy, which is a function of temperature.
The thermal energy, causes the atoms to vibrate in a random manner about an eauilibrium
lattice point. This random thermal motion causes the distance between atoms
to randomly fluctuate, slightly disrupting the perfect geometric arrangement of atoms.
This imperfection, called lattice vibrations, affects some electrical parameters, as we
will see later in our discussion of semiconductor material characteristics.
Another type of defect is called a point defect. There are several of this type that
we need to consider. Again, in an ideal single-crystal lattice, the atoms are arranged
in a perfect periodic arrangement. However, in a real crystal, an atom may be missing
from a particular lattice site. This defect is referred to as a vacancy; it is schematically
shown in Figure 1.17a. In another situation, an atom may be located between lattice
sites. This defect is referred to as an interstitial and is schematically shown in Figure
1.17b. In the case of vacancy and interstitial defects, not only is the perfect geometric
arrangement of atoms broken, but also the ideal chemical bonding between
atoms is disrupted, which tends to change the electrical properties of the material. A
vacancy and interstitial may be in close enough proximity lo exhibit an interaction
between the two point defects. This vacancy-interstitial defect, also known as a
Frenkel defect, produces different effects than the simple vacancy or interstitial.
The point defects involve single atoms or single-atom locations. In forming
single-crystal materials, more complex defects may occur. A line defect. for example,
occurs when an entire row of atoms is missing from its normal lattice site. This defect
is referred to as a line dislocation and is shown in Figure 1.18. As with a point
defect, a line dislocation disrupts both the normal geometric periodicity of the lattice
and the ideal atomic bonds in the crystal. This dislocation can also alter the electrical
properties of the material, usually in a more unpredictable manner than the simple
point defects.
Other complex dislocations can also occur in it crystal lattice. However. this introductory
discussion is intended only to present a few of the basic types of defect,
and to show that a red crystal is not necessarily a perfect lattice structure. The effect
of these imperfections on the electrical properties of a semiconductor will be considered as imperfection in solids