Crysals

1 SOLIDS Classification v Solids are classified into two v Amorphous and Crystalline Amorphous and Crystalline Solids & Classification of Crystalline Solids Amorphous and Crystalline Solids • Based on the nature of the order of arrangement of the constituent particles, solids are classified as amorphous and crystalline. • Differences between amorphous and crystalline solids are listed in the given table. Amorphous solids Crystalline solids 1 Have irregular shape 1 Have definite characteristic geometrical shape 2 Have only short-range order in the arrangement of constituent particles 2 Have long-range order in the arrangement of constituent particles 3 Gradually soften over a range of temperature 3 Have sharp and characteristic melting point 4 When cut with a shape-edged tool, they cut into two pieces with irregular shapes 4 When cut with a shape-edged tool, they split into two pieces with plain and smooth newly generated surfaces. 5 Do not have definite heat of fusion 5 Have definite and characteristic heat of fusion 6 Isotropic in nature 6 Anisotropic in nature 7 Pseudo solids or super-cooled 7 True solids 2 liquids Classification of Crystalline Solids • Based on the nature of intermolecular forces, crystalline solids are classified into categories − o Molecular solids o Ionic solids o Metallic solids o Covalent solids • Molecular solids o Constituent particles are molecules four 3 • Ionic solids o Constituent particles are ions o Hard but brittle o Insulators of electricity in solid state, but conductors in molten state and in aqueous solution o High melting point o Attractive forces are Coulombic or electrostatic o Example − NaCl, MgO, ZnS • Metallic solids o In metallic solids, positive ions are surrounded and are held together in a sea of delocalized electrons. o Hard but malleable and ductile o Conductors of electricity in solid state as well as molten state o Fairly high melting point o Particles are held by metallic bonding o Example − Fe, Cu, Mg • Covalent or network solids 4 o Constituent particles are atoms o Hard (except graphite, which is soft) o Insulators of electricity (except graphite, which is a conductor of electricity) o Very high melting point o Particles are held by covalent bonding o Example − SiO2 (quartz), SiC, diamond, graphite Crystal Lattices and Unit Cells Crystal Lattice • Regular three-dimensional arrangement of points in space • There are 14 possible three • Characteristics of a crystal lattice: o Each point in a lattice is called lattice point or lattice site. o Each lattice point represents one constituent particle (atom, molecule or ion). o Lattice points are joined by straight lines to bring out the geometry of the lattice. Unit Cell • Smallest portion of a crystal lattice which, when repeated in different directi entire lattice o Characterised by − three-dimensional lattices, known as Bravais lattices. directions, generates the ons, 5 (i) Its dimensions along the three edges (ii) Angles between the edges o There are seven types of primitive unit cells, as given in the following table. Seven Crystal Systems The given table lists seven primitive unit cells and their possible variations as centered unit cells. a, b and c α, β and γ 6 Crystal Class Axial Distances Axial Angles Possible Types of Unit Cells Examples 1. Cubic a = b = c α = β = γ = 90° Primitive, bodycentred, face-centred KCl, NaCl 2. Tetragonal a = b ≠ c α = β = γ = 90° Primitive, bodycentred SnO2, TiO2 3. Orthorhombic a ≠ b ≠ c α = β = γ = 90° Primitive, bodycentred, facecentred, end-centred KNO3, BaSO4 4. Hexagonal a = b ≠ c α = β = 90°; γ = 120° Primitive Mg, ZnO 5. Trigonal or Rhombohedral a = b = c α = β = γ ≠ 90° Primitive (CaCO3) Calcite, HgS (Cinnabar) 6. Monoclinic a ≠ b ≠ c α = γ = 90°; β ≠ 90° Primitive and endcentred Monoclinic sulphur, Na2SO4.10H2O 7. Triclinic a ≠ b ≠ c α ≠ β ≠γ≠ 90° Primitive K2Cr2O7, H3BO3 • Unit cells of 14 types Bravais lattices: o Cubic lattices: All sides are of the same length, and the angles between the faces are 90° each 7 o Tetragonal lattices: One side is different in length from the other two, between the faces are 90° each o Orthorhombic lattices: Unequal sides; angles between the faces are 90° each • Monoclinic lattices: Unequal sides; two faces have angles not equal to 90° and the angles 8 • Hexagonal lattice: One side is different in length on two faces are 60° • Rhombohedral lattice: All sides are of equal length, and the marked angles on two faces are less than 90° • Triclinic lattice: Unequal sides; unequal angles, with none equal to 90° Number of Atoms in a Unit Cell Primitive Cubic Unit Cell Open structure for a primitive cubic unit cell is shown in the given figure. Actual portions belonging to one unit cell are shown in the given figure. from the other two, and the marked angles 9 Total number of atoms in one unit cell Body-Centred Cubic Unit Cell Open structure for a body-centred cubic unit cell is shown in the given figure. Actual portions belonging to one unit cell are shown in the given figure. 10 Total number of atoms in one unit cell = 8 corners per corner atom + 1 Face-Centred Cubic Unit Cell Open structure for a face-centred cubic unit cell is shown in given figure. Actual portions of atoms belonging to one unit cell are shown in the given figure. Total number of atoms in one unit cell = 8 corner atoms atom per unit cell + 6 face body-centre atom face-centred atoms atom per unit cell 11 Closed-Packed Structures Coordination number − The number of nearest neighbours of a particle Close-Packing in One dimension • Only one way of arrangement, i.e., the particles are o Coordination number = 2 Close-Packing in Two Dimensions • Square close-packing in two dimensions o AAA type arrangement o The particles in the second row are exactly above those in the first row. o Coordination number • Hexagonal close-packing in two dimensions o ABAB type arrangement arranged in a row, touching each other = 4 12 o The particles in the second row are fitted in the depressions of the first row. The particles in the third row are aligned with those in the first row. o More efficient packing than square close o Coordination number = 6 Close-Packing in Three Dimensions Three-dimensional close-packing is obtained by stacking two or hexagonal close-packed) one above the other • By stacking two-dimensional square close o The particles in the second layer are exactly above those in the first layer. o AAA type pattern o The lattice generated is simple cubic lattice, and its unit cell is primitive cubic unit cell. o Coordination number = 6 • By stacking two-dimensional hexagonal close o Placing the second layer over the first layer § The two layers are differently aligned. § Tetrahedral void is formed when a particle in the second layer is above a void of the first § Octahedral void is formed when a void of the second layer is above the void of the first layer. close-packing two-dimensional layers (square close other. close-packed layers ation close-packed layers layer. close-packed 13 Number of octahedral voids = Number of close Number of octahedral voids = 2 × Numbe o Placing the third layer over the second layer: There are two ways § Covering tetrahedral voids: ABAB … pattern. The particles in the third layer are exactly aligned with those in the first layer. It results in a hexagonal close packed (hcp § Covering octahedral voids: ABCABC … octahedral voids. The particles in the third layer are not aligned either with those in the first layer or with those in the second laye first layer. This arrangement is called ‘C’ type. It results in cubic close (ccp) or face Here, T = Tetrahedral void, O = Octahedral void close-packed particles Number of close-packed particles − hcp) structure. Example: Arrangement of atoms in metals like Mg and Zn layer, but with those in the fourth layer aligned with those in the ) face-centred cubic (fcc) structure. Example: Arrangement of atoms in metals like Cu and Ag| close-) r, close-packed ) 14 § Coordination number in both § Both hcp and § § = 74%) Formula of a Compound and Number of Voids Filled • Number of octahedral voids = Number of close Number of tetrahedral voids = 2 × Number of close • In ionic solids, the bigger ions (usually anions) form the close smaller ions (usually cations) occupy the voids. o If the latter ion is small enough, then it occupie then it occupies the octahedral void. • Not all the voids are occupied. Only a fraction of the octahedral or tetrahedral voids are occupied. • The fraction of the octahedral or tetrahedral voids that are occupied depends formula of the compound. A compound is formed by two elements X and Y. The atoms of element X form ination hcp ad ccp structures is 12. ccp structures are highly efficient in packing (packing efficiency close-packed particles close-packed particles close-packed structure and the occupies the tetrahedral void, and if bigger, Example s on the chemical hcp lattice and 15 those of element Y occupy formed? Solution: It is known that the number of tetrahedral voids formed is equal to twice the number of atoms of element X. It is given that only of the tetrahedral voids are occupied by the atoms of element Y. Therefore, ratio of the number of atoms of X and Y = = 2: 1 Hence, the formula of the compound formed is X Locating Tetrahedral Voids • A unit cell of ccp or fcc lattice is divided into eight small cubes. Then, each small cube has 4 atoms at alternate corners. When these are joined to each other, a regular tetrahedron is formed. • This implies that one tetrahedral void is present in each small cube. Therefore, a t tetrahedral voids are present in one unit cell. • Since each unit cell of ccp structure has 4 atoms, the number of tetrahedral voids is twice the number of atoms. th of the tetrahedral voids. What is the formula of the compound nown X2Y. total of eight 16 Locating Octahedral Voids • When the six atoms of the face centres that the unit cell has one octahedral void at the body centre. • Besides the body centre, there is one octahedral void at the centre of each of the 12 edges. But only of each of these voids belongs to • Now, the total number of octahedral voids in a cubic loose This means that in ccp structure, the number of octahedral voids is equal to the number of atoms in each unit cell. are joined, an octahedron is generated. This implies the unit cell. loose-packed structure 17 in Solids Defects • Irregularities or deviations from the ideal arrangement of constituent particles • Two types: o Point defects − Irregularities in the arrangement of constituent particles around a point or an atom in a crystalline substance. o Line defects − Irregularities in the arrangement of constituent particles in entire rows of lattice points. • These irregularities are called crystal defects. Types of Point Defects • Three types: o Stoichiometric defects o Impurity defect o Non-stoichiometric defects Stoichiometric Defects • Do not disturb stoichiometry of the solid • Also called intrinsic or thermodynamic defects • Two types − (i) Vacancy defect (ii) Interstitial defect • Vacancy defect o When some of the lattice sites are vacan o Shown by non-ionic solids o Created when a substance is heated o Results in the decrease in density of the substance 18 • Interstitial defect o Shown by non-ionic solids o Created when some constituent particles (atoms or molecules) occupy an interstitial • Ionic solids show these two defects as Frenkel defect and S • Frenkel defect o Shown by ionic solids containing large differences in the sizes of ions o Created when the smaller ion (usually cation) is dislocated from its normal site to an interstitial site o Creates a vacancy defect as well as an o Also known as dislocation defect o Ionic solids such as AgCl, AgBr, AgI and ZnS show this type of defect. site of the crystal. Schottky defect. interstitial defect 19 • Schottky defect o Basically a vacancy defect shown by ionic solids o An equal number of cations o Results in the decrease in the density of the substance o Significant number of Schottky defect is present in ionic solids. For example, in NaCl, there are approximately 10 o Shown by ionic substances containing similar Impurity Defect • Point defect due to the presence of foreign atoms • For example, if molten NaCl containing a little amount of Sr of Na+ ions are occupied by Sr of one ion, leaving the other site vacant. The cationic vacancies thus produced are equal in number to those of Sr2+ ions. and anions are missing to maintain electrical neutrality 106 Schottky pairs per cm3, at room temperature. similar-sized cations and anions; for example, NaCl, KCl CsCl, AgBr SrCl2 is crystallised, some of the sites Sr2+ ions. Each Sr2+ ion replaces two Na+ ions, occupying the site 20 o Solid solution of CdCl Non-Stoichiometric Defects • Result in non-stoichiometric ratio of the constituent elements • Two types − o Metal excess defect o Metal deficiency defect • Metal excess defect o Metal excess defect due to § Alkali metals like NaCl and KCl show this type of defect. § When crystals of NaCl are heated in an atmosphere of sodium vapour, the sodium atoms are deposited on the surface of the crystal. The Cl from the crystal to its surf During this process, the Na atoms on the surface of the crystal lose electrons. These released electrons diffuse into the crystal and occupy the vacant anionic sites, creating F § When the ionic sites of CdCl2 and AgCl also shows this defect anionic vacancies: surface and combine with Na atoms, forming NaCl. F-centres. a crystal are occupied by unpaired electrons, the ionic sites are called F-centres. Cl− ions diffuse ace 21 § Metal excess defect due to the presence of extra cations at interstitial sites: § When white zinc oxide is heated, it loses oxygen and turns yellow. Then, zinc becomes . The excess Zn • Metal deficiency defect o Arises when a solid contains lesser number of cation proportion. o For example, FeO is mostly found with a composition of some Fe2+ ions are missing, and the loss of positive charge is made up by the presence of the required number of Fe Imperfections in Solids Defects excess in the crystal, leading the formula of the oxide to Zn2+ ions move to the interstitial sites, and the electrons move to the neighbouring interstitial sites. cations compared to the stoichiometric . In crystals of FeO, Fe3+ ions. s 22 • Irregularities or deviations from the ideal arrangement of constituent particles • Two types: o Point defects − Irregularities in the arrangement of constituent particles around a point or an atom in a crystalline substance. o Line defects − Irregularities in the arrangement of constituent particles in entire rows of lattice points. • These irregularities are called crystal defects. Types of Point Defects • Three types: o Stoichiometric defects o Impurity defect o Non-stoichiometric defec Stoichiometric Defects • Do not disturb stoichiometry of the solid • Also called intrinsic or thermodynamic defects • Two types − (i) Vacancy defect (ii) Interstitial defect • Vacancy defect o When some of the lattice sites are vacan o Shown by non-ionic solids o Created when a substance is heated o Results in the decrease in density of the substance defects 23 • Interstitial defect o Shown by non-ionic solids o Created when some constituent particles (atoms or molecules) occupy an interstitial • Ionic solids show these two defects as Frenkel defect and Schottky defect. • Frenkel defect o Shown by ionic solids containing large differences in the sizes of ions o Created when the smaller ion (usually cation) is dislocated from its normal site to an interstitial site o Creates a vacancy defect as well as an interstitial defect o Also known as dislocation defect o Ionic solids such as AgCl, AgBr, AgI and ZnS show this type of defect. • Schottky defect o Basically a vacancy defect shown by ionic solids o An equal number of o Results in the decrease in the density of the substance site of the crystal. lids cations and anions are missing to maintain electrical neutrality 24 o Significant number of Schottky defect is present in ionic solids. For example, in NaCl, there are approximately 10 o Shown by ionic substances containing similar Impurity Defect • Point defect due to the presence of foreign atoms • For example, if molten NaCl containing a little amoun of Na+ ions are occupied by Sr of one ion, leaving the other site vacant. The cationic vacancies thus produced are equal in number to those of Sr2+ ions. o Solid solution of CdCl Non-Stoichiometric Defects • Result in non-stoichiometric ratio of the constituent elements • Two types − o Metal excess defect 106 Schottky pairs per cm3, at room temperature. similar-sized cations and anions; for example, NaCl, KCl CsCl, AgBr amount of SrCl2 is crystallised, some of the sites Sr2+ ions. Each Sr2+ ion replaces two Na+ ions, occupying the site CdCl2 and AgCl also shows this defect , 25 o Metal deficiency defect • Metal excess defect o Metal excess defect due § Alkali metals like NaCl and KCl show this type of defect. § When crystals of NaCl are heated in an atmosphere of sodium vapour, the sodium atoms are deposited on the surface of the crystal. The Cl from the crystal to its During this process, the Na atoms on the surface of the crystal lose electrons. These released electrons diffuse into the crystal and occupy the vacant anionic sites, creating F § When the ionic sites sites are called F § Metal excess defect due to the presence of extra cations at interstitial sites: § When white zinc oxide is heated, it loses oxygen and turns yellow. Then, zinc beco . The excess Zn to anionic vacancies: surface and combine with Na atoms, forming NaCl. F-centres. of a crystal are occupied by unpaired electrons, the ionic F-centres. becomes excess in the crystal, leading the formula of the oxide to Zn2+ ions move to the interstitial sites, and the electrons move to the neighbouring interstitial sites. Cl− ions diffuse mes 26 • Metal deficiency defect o Arises when a solid contains lesser number of proportion. o For example, FeO is mostly found with a composition of some Fe2+ ions are missing, and the loss of positive charge is made up by the presence of the required number of Fe Imperfections in Solids Defects • Irregularities or deviations from the ideal arrangement of constituent particles • Two types: o Point defects − Irregularities in the arrangement of constituent particles around a point or an atom in a crystalline substance. o Line defects − Irregularities in the arrangement of constituent particles in entire rows of lattice points. • These irregularities are called crystal defects. Types of Point Defects • Three types: o Stoichiometric defects o Impurity defect o Non-stoichiometric defects Stoichiometric Defects cations compared to the stoichiometric . In crystals of FeO, Fe3+ ions. erfections 27 • Do not disturb stoichiometry of the solid • Also called intrinsic or thermodynamic defects • Two types − (i) Vacancy defect (ii) Interstitial defect • Vacancy defect o When some of the lattice sites are vacan o Shown by non-ionic solids o Created when a substance is heated o Results in the decrease in density of the substance • Interstitial defect o Shown by non-ionic solids o Created when some constituent particles (atoms or molecules) occupy an interstitial • Ionic solids show these two defects as Frenkel defect and Schottky defect. • Frenkel defect o Shown by ionic solids containing large differences in the sizes of ions eated site of the crystal. 28 o Created when the smaller ion (usually cation) is dislocated from its normal site to an interstitial site o Creates a vacancy defect as well as an interstitial defect o Also known as dislocation defect o Ionic solids such as AgCl, AgBr, AgI and ZnS show this type of defect. • Schottky defect o Basically a vacancy defect shown by ionic solids o An equal number of cations and anions are missing to maintain electrical neutrality o Results in the decrease in the density of the substance o Significant number of Schottky defect is present in ionic solids. For example, in NaCl, there are approximately 10 o Shown by ionic substances containing similar Impurity Defect • Point defect due to the presence of foreign atoms 106 Schottky pairs per cm3, at room temperature. similar-sized cations and anions; for example, NaCl, KCl CsCl, AgBr , 29 • For example, if molten NaCl containing a l of Na+ ions are occupied by Sr of one ion, leaving the other site vacant. The cationic vacancies thus produced are equal in number to those of Sr2+ ions. Electrical Properties Conduction of Electricity in Metals • Metals conduct electricity in solid as well as molten state. • The conductivity of metals depends upon the number of valence electrons. • In metals, the valence bond is partially conduction band so that electrons can flow easily under an applied electric field. • In the case of insulators, the gap between filled valence shell and the next higher unoccupied band is large so that electrons cannot jump from the valence band to the conduction band. Conduction of Electricity in Semiconductors • The gap between the valence band and conduction band is so small that some electrons may jump to the conduction band. ` little amount of SrCl2 is crystallised, some of the sites Sr2+ ions. Each Sr2+ ion replaces two Na+ ions, occupying the site filled, or it overlaps with a higher energy unoccupied lectrons 30 • Electrical conductivity of semiconductors increases with increase in temperature. • Substances like Si, Ge show this type of behaviour, and are called intrinsic semiconductors. • Doping − Process of adding an appropriate amount of suitable impurity to increase conductivity o Doping is done with either electron the intrinsic semiconductor Si or Ge. • There are two types of semiconductors: i. n − type semiconductor ii. p − type semiconductor • n − type semiconductor o Conductivity increases due to neg o Generated due to the doping of the crystal of a group 14 element such as Si or Ge, with a group 15 element such as P or As • p − type semiconductor o Conductivity increases as a result of electron hole o Generated due to the doping of the crystal of a group 14 element such as Si or Ge, with a group 13 element such as B, Al or Ga electron-rich or electron-deficient impurity as compared to negatively charged electrons 31 • Applications of n − type and o In making a diode, which is used as a rectifier o In making transistors, whi o In making a solar cell, which is a photo diode used for converting light energy into electrical energy • A large number of compounds (solid) have been prepared by the combination of groups 13 and 15 or 12 and 16 to stimulate average valence of four as in Si or Ge. o Examples of compounds of groups 13 o Examples of compounds of groups 12 • Some transition metal oxides like TiO, CrO o For example, ReO3 o Some oxides like VO, VO on temperature. • p − type semiconductors which are used for detecting or amplifying radio or audio signals − 15 are InSb, AlP, GaAs − 16 are ZnS, CdS, CdSe, HgTe CrO2, ReO3 behave like metals. resembles metallic copper in its conductivity and appearance VO2, VO3, TiO3 show metallic or insulating properties depending ch 32 o Solid solution of CdCl Non-Stoichiometric Defects • Result in non-stoichiometric ratio of the constituent elements • Two types − o Metal excess defect o Metal deficiency defect • Metal excess defect o Metal excess defect due to anionic vacancies: § Alkali metals like § When crystals of NaCl are heated in an atmosphere of sodium vapour, the sodium atoms are deposited on the surface of the crystal. The Cl from the crystal to its surface and combine with Na atoms, forming During this process, the Na atoms on the surface of the crystal lose electrons. These released electrons diffuse into the crystal and occupy the vacant anionic sites, creating F § When the ionic sites of a crystal are occupied by unpaired ele sites are called F CdCl2 and AgCl also shows this defect NaCl and KCl show this type of defect. F-centres. F-centres. Cl− ions diffuse NaCl. ctrons, the ionic 33 § Metal excess defect due to the presence of extra cations at interstitial sites: § When white zinc oxide is heated, it loses oxygen and turns yellow. Then, zinc becomes excess in the crystal, leading the for . The excess Zn • Metal deficiency defect o Arises when a solid contains lesser number of cations compared to the stoichiometric proportion. o For example, FeO is mostly found with a composition of some Fe2+ ions are missing, and the loss of positive charge is made up by the presence of the required number of Fe Magnetic Properties • Each electron in an atom behaves like a tiny magnet. • The magnetic moment of an electron originates from its two types of motion. o Orbital motion around the nucleus o Spin around its own axis • Thus, an electron has a permanent spin and an orbital magnetic moment associated with it. o An orbiting electron formula of the oxide to Zn2+ ions move to the interstitial sites, and the electrons move to the neighbouring interstitial sites. . In crystals of FeO, Fe3+ ions. mula 34 o A spinning electron • Based on magnetic properties, substances are classified into five categories o Paramagnetic o Diamagnetic o Ferromagnetic o Ferrimagnetic o Anti-ferromagnetic Paramagnetism • The substances that are attracted by a magnetic o Some examples of paramagnetic substances are O • Paramagnetic substances get magnetised in a magnetic field in the same direction, but lose magnetism when the magnetic field is removed. • To undergo paramagnetism, a substance must have one or more unpaired electrons. This is because the unpaired electrons are attracted by a magnetic field, thereby causing paramagnetism. Diamagnetism • The substances which are weakly repelled by magnetic field o Example − H2O, NaCl, C • Diamagnetic substances are weakly magnetised in a magnetic field in opposite direction. • In diamagnetic substances, all the electrons are paired. • Magnetic characters of these substances are lost due pairing of electrons. Ferromagnetism − field are called paramagnetic substances. O2, Cu2+, Fe3+ and Cr are said to have diamagnetism. O, C6H6 to the cancellation of moments by the Cr3+. 35 • The substances that are strongly attracted by a magnetic field are called ferromagnetic substances. • Ferromagnetic substances can be permanently magnetised even in the absence of a m field. • Some examples of ferromagnetic substances are iron, cobalt, nickel, gadolinium and CrO2. • In solid state, the metal ions of ferromagnetic substances are grouped together into small regions called domains, and each domain acts as a tiny a ferromagnetic substance, the domains are randomly oriented, so their magnetic moments get cancelled. However, when the substance is placed in a magnetic field, all the domains get oriented in the direction of the magn produced. This ordering of domains persists even after the removal of the magnetic field. Thus, the ferromagnetic substance becomes a permanent magnet. • Schematic alignment of magnetic moments in ferromag Ferrimagnetism • The substances in which the magnetic moments of the domains are aligned in parallel and anti-parallel directions, in unequal numbers, are said to have ferrimagnetism. • Examples include Fe3O4 (magnetite), ferr • Ferrimagnetic substances are weakly attracted by a magnetic field as compared to ferromagnetic substances. • On heating, these substances become paramagnetic. • Schematic alignment of magnetic moments in ferrimagnetic substanc Anti-ferromagnetism • Antiferromagnetic substanceshave domain structures similar to ferromagnetic substances, but are oppositely oriented. • The oppositely oriented domains cancel out each other’s magnetic moments. • Schematic alignment of ma magnet. In an un-magnetised piece of magnetic field. As a result, a strong magnetic effect is ferromagnetic substances is as follows: ferrites such as MgFe2O4 and ZnFe2O4. substances is as follows: magnetic moments in anti-ferromagnetic substances is as follows: magnetic etic netic es 36 37 CBSE Class VI CBSE Class VII CBSE Class VIII CBSE Class IX CBSE Class X CBSE Class XI CBSE Class XII VI Ncert Solutions VII Ncert Solutions VIII Ncert Solutions IX Ncert Solutions X Ncert Solutions XI Ncert Solutions XII Ncert Solutions VI Intelligent Sys VII Intelligent Sys VIII Intelligent Sys IX Intelligent Sys X Intelligent Sys XI Intelligent Sys XII Intelligent Sys VI Study Materials VII Study Materials VIII Study Materials IX Study Materials X Study Materials XI Study Materials XII Study Materials VI Test Papers VII Test Papers VIII Test Papers IX Test Papers X Test Papers XI Test Papers XII Test Papers VI Revision Notes VII Revision Notes VIII Revision Notes IX Revision Notes X Revision Notes XI Revision Notes XII Revision Notes VI Puzzles VII Puzzles VIII Puzzles IX Puzzles X Puzzles XI Puzzles XII Puzzles 38 ICSE Class VI ICSE Class VII ICSE Class VIII ICSE Class IX ICSE Class X Ask Answer General Links VI Study Materials VII Study Materials VIII Study Materials IX Study Materials X Study Materials Curriculum About us VI Test Papers VII Test Papers VIII Test Papers IX Test Papers X Test Papers Board Exams Privacy Policy VI Revision Notes VII Revision Notes VII Revision Notes IX Revision Notes X Revision Notes Engineering Entrance Website Terms & Use VI Puzzles VII Puzzles VIII Puzzles IX Puzzles X Puzzles General Information Cancellation & Refund Medical Entrance FAQ NTSE, Olympiad Contact Us Parent Zone Sitemap School Talk More Features Teacher Zone Personality Tests Website Features Aptitude Tests Question List Skill Builder