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SOLID STATE, Total Sessions – 07, SESSION –, , 1, , AIM, ✓ To introduce solid as a state of matter, ✓ To introduce classification of solids, ✓ To discuss terms involved in solid state, INTRODUCTION, Matter exists mainly in three states, viz. solids, liquids and gases. The existence of matter, in any of these three forms depends upon two factors, 1. Intermolecular forces of attraction (keeps particle closer), 2. Thermal energy (keeps particles apart), Some of the common properties of solids, which distinguish them from other two, states of matter, are:, • Solids are rigid and have definite shapes., • Solids have definite volume irrespective of the size or shape of the container in which, they are placed., • Solids are almost incompressible., • Solids diffuse very slowly as compared to liquids and gases. Constituent particles are, very closely packed in solids permitting very little space for their movement., • Solids have a much higher density (mass to volume ratio) than that of gases and liquids., • Most solids become liquids when heated. Some undergo sublimation on heating. The, temperature at which a solid changes into liquid is called the melting point and the, process is called as melting. Due to the varying natures of solids their melting, temperatures vary considerably., CLASSIFICATION OF SOLIDS, Solids are divided into two classes, namely crystalline and amorphous solids. A solid is said, to be crystalline if the constituents arrange themselves in regular manner throughout the, three-dimensional network. The ordered arrangement of building constituents extends over, a large distance (long range order). On the other hand, in amorphous solids, the, arrangement of building constituents is not regular (short range order)., i) Crystalline solids: A crystalline solid is a homogeneous solid in which the constituent particles, (atoms, ions or molecule) are arranged in a definite repeating pattern., Example: Diamond, Quartz, NaCl, K2SO4 etc.

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Active site edutech-9844532971, , General characteristics of Crystalline solids:, i), A crystalline solid is a homogeneous solid in which the constituent particles (i.e. atoms,, ions or molecules) are arranged in a definite repeating pattern in all dimensions., ii) The total intermolecular force of attraction in crystalline solid is maximum thus, imparting maximum stability, the forces responsible for the stability involves ionic bonds,, covalent bonds, hydrogen bonds and Van der Waal’s forces., iii) A crystalline solid usually consist of a large number of small tiny crystals called unit, cell, each having a definite characteristic geometrical shape., iv) Crystalline solid has regular arrangement of particles which repeats periodically over, entire crystal, thus exhibiting short and long range order., v) Crystalline solids have sharp melting point, thus have definite heat of fusion., vi) Crystalline solids are true solids., vii) Crystalline solid on cutting gives a clean cleavage., viii) Crystalline solid shows different physical properties in different direction, this type of, behavior is called anisotropy and the substances exhibiting this type of behavior are, called anisotropic. The properties like electrical conductivity, refractive index, thermal, expansion etc. have different value in different direction., ix) Two or more crystalline substances having same crystal structure are said to be, isomorphous. Isomorphous substance contains constituent atom of same atomic ratio., Example: a) NaF and MgO (Ratio is 1:1), b) NaNO3 and CaCO3 (Ratio is 1:1:3), c) K2SO4 and K2SeO4 (Ratio is 2:1:4), d) Cr2O3 and Fe2O3 (Ratio is 2 : 3), Exceptional: NaCl and KCl have all properties identical [same atomic ratio, similar molecular, formula or similar chemical properties] but are not isomorphous., x) A single substance that crystallises in two or more forms under different conditions is, called polymorphous. (allotropic forms), ., Example: a) Carbon has two allotropes graphite and diamond., b) Sulphur has two polymorphic forms monoclinic and rhombic., c) CaCO3 and SiO2 have two allotropic forms., , https://wa.me/919844532971

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Active site edutech-9844532971, , ii) Amorphous solids: Substances that appear like solids but do not have perfectly ordered, crystalline structure and no regular arrangement of constituent particles in structure is, called amorphous solids., Example: Tar, glass, plastic, rubber, butter etc., General characteristics of Amorphous solids:, i) Amorphous substances appear like solids but they do not have perfectly ordered, crystalline structure, hence they are not real solids., ii) An amorphous solid does not have regular arrangement of constituent particles., iii) The arrangement of constituent particles like atoms or molecules has only short range, order hence periodically repeating regular pattern is only over a short distance., iv) Regular patterns are scattered and hence the arrangement is disordered., v) Amorphous solids are called supercooled liquids of very high viscosity or pseudo solids., vi) Physical properties do not change with change in directions hence amorphous solids are, isotropic in nature., vii) Amorphous solids behave like fluids and very slowly float under gravity., viii) Amorphous solids do not have sharp melting points., ix) When cut, they split into pieces with irregular and rough surfaces., Uses of amorphous solids:, i) The most widely used amorphous solid are the inorganic glasses viz. construction, houseware, laboratory ware, etc., ii) Used as rubber in making tyres, shoe soles, etc., iii) Used in plastics., iv) Amorphous silica used for converting sunlight into electricity (in photovoltaic cell)., B, , Anisotropy: The ability of crystalline solids to change their, physical properties when measured in different directions, is called anisotropy., Explanation: This property is due to different arrangement, of constituents in different directions., Different types of particles fall on the way of measurements, in different directions. Hence, the composition of, crystalline solids changes with directions changing their, physical properties., https://wa.me/919844532971, , A, , B, , A, , B, , A, , B, , B, , A, , B, , A, , B, , A, , A, , B, , A, , B, , A, , B, , B, , A, , B, , A, , A, , B, , A, , B, , B, A, C, , D, , A, B, , A

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Active site edutech-9844532971, , Isotropy: The ability of amorphous solids to have same physical properties when measured in, different directions is called isotropy., Explanation: This property is due to no regular arrangement of particles in any direction., Hence the properties like electrical conductivity, thermal expansion are identical in all the, direction., , Difference between Crystalline and Amorphous Solid:, Crystalline solids, 1) They have definite and regular geometry, due to definite and orderly arrangement of, atoms, ions or molecules in threedimensional space., 2) They have sharp melting points and, change abruptly into liquids, 3) Crystalline solids are anisotropic. Some of, their physical properties are different in, different directions, 4) These are considered as true solids, , Amorphous solids, They do not have any pattern of arrangement, of atoms, ions or molecules and, thus do not, have any definite geometrical shape., Amorphous solids do not have sharp melting, points and do not change abruptly into liquids., Amorphous solids are isotropic. Their physical, properties are same in all direction, , These are considered pseudo solids or, super cooled liquid., 5) Crystalline solids are rigid and their shape Amorphous solids are not very rigid. These, is not distorted by mild distorting forces can be distorted by bending or compressing, force, 6) Crystals are bound by plane faces. The Amorphous solids not have well defined planes., angle between any two faces is called When an amorphous solid is broken, the surfaces, interfacial angle. For a given crystalline of the broken pieces are generally and not flat, solid, it is a definite angle and remains and intersect at random angles. (Amorphous, always constant no matter how the faces solids do not have any symmetry), develop. When a crystalline solid is, hammered, it breaks up into smaller crystals, of the same geometrical shape., 7) Ex.: NaCl, KCl, Sugar, Quartz etc., Ex.: Plastic, Glass, Rubber etc., , Types of crystalline solids: Crystalline solids are classified into four main types as follows:, Molecular solids: They are further classified into three types:, a. Polar molecular solids., b. Non-polar molecular solids., c. Hydrogen bonded molecular solids., ii) Ionic solids., iii) Metallic solids., iv) Covalent solids., i), , https://wa.me/919844532971

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Active site edutech-9844532971, , Molecular solids:, In the crystalline molecular solids, the constituent particles are molecules of same, compound., ii) Depending upon the type of molecules involved in crystal formation and the nature of, intermolecular force of attraction between the neighboring molecules, they are further, sub-divided as :, a) Non-polar molecular solids:, 1. These are those crystalline solid in which the constituent particles are either atoms, [Noble gases] or non-polar molecules [H2, Cl2, I2, CH4, etc.] or weakly polar molecules, like CO or other hydrocarbons., 2. They are formed at relatively lower temperature and are in usually gaseous state at, normal temperature., 3. In these atoms or non-polar molecules are held by weak dispersion forces or London, forces., 4. These solids are generally soft, having low melting and boiling point and are nonconductor of electricity., 5. As polar molecules exist in gaseous state, polar molecular solids is obtained by, subjecting the gas high pressure and low temperature., b) Polar-molecular solids:, 1. These are the crystalline solid in which the constituent particles are polar molecules, [HCl, SO2, etc.], 2. In polar molecule there is separation of charges, in which the opposite charges of, neighboring molecules are brought closer., 3. The forces holding these molecules are dipole-dipole forces of attraction, this force of, attraction is stronger than London forces., 4. These solids show following characteristic:, i) They are soft., ii) Their melting point and boiling point are comparatively higher than non-polar, molecular solids but lower than ionic and metallic., iii) They also exist as liquid or gases at room temperature., iv) They are non-conductor of electricity., i), , https://wa.me/919844532971

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Active site edutech-9844532971, , v) They possess permanent dipole moment., c) Hydrogen bonded molecular solids:, 1. In these solids, the constituent particles are such molecules which contain hydrogen atom, l inked to a highly electronegative atom [O, N or F]. Example: solid ice, NH3, etc., 2. In these, molecules are held by hydrogen bond in which the H atom of one molecule is, bonded to electronegative atom of another molecule., 3. This intermolecular force of attraction existing among the molecules is strong hydrogen, bonds., 4. Characteristic of hydrogen bonded molecular solid :, i) They exist as volatile liquid or soft solids at room temperature., ii) They are non-conductors of electricity., iii) Their melting point and boiling are usually higher than non-polar molecular solids, and polar molecular solids., 5. They solidify on cooling., Ionic solids:, i), In these crystalline solids, the constituent particles are positive and negative ions i.e., cations and anions. e.g. Na+ and Cl– ions in case of NaCl., ii) These ions in the solid are held in their lattice points by strong electrostatic force of, attraction resulting into well ordered three dimensional arrangement of ions., iii) All salts are crystalline in nature and are called Ionic solids., iv) In Ionic solids, the charges on the ions and the arrangement of ions are in such a, manner that they balance each other and hence the molecule is electrically neutral., v) The arrangement of ions in the solid depends upon :, a) Size of cation and anion, b) charges on the ion, c) ease with which anion is polarized (i.e. polarizability of anions)., vi) Ionic solids are hard and brittle and have high melting point and boiling point., vii) They are electrical insulators in solid state because their ions are not free to move., viii) In aqueous solution or in molten state as the ions become free they are good conductor, of electricity., https://wa.me/919844532971

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Active site edutech-9844532971, , ix), x), , They are soluble in polar solvent but insoluble in non-polar solvent., On application of shearing force, ionic crystals undergo distortion and fracture in, crystal structure., , Metallic solids:, i) In metallic solids the constituent particles are positively charged metal ion and free, electron., ii) Due to low ionization energy of metal atom the metal atom loses their valence electron, and becomes positively charged ions., iii) Thus electrons lost are delocalized over the crystal space and flows throughout the, crystal like water in sea, hence also called sea of free electrons., iv) The force of attraction between positively charged metallic ion and negatively charged, sea of delocalized electron is called metallic bond., v) If energy is supplied, the valence electron from sea of electrons move from one place to, another, this presence of mobile electrons makes all the metal good conductor of heat, and electricity., vi) On application of shearing force, the layers slide on one another and hence the structure, is not fractured imparting the properties of malleability and ductility., vii) They have high melting point, boiling point and density., viii) The mixtures of metals can be fused together to form alloys, which exhibit all, properties of metals., ix) They possess lusture and colour. [Gold metal exhibit yellow lusture and copper has reddish, lusture]., x) Metallic bonds are stronger than ionic and covalent bond., , Covalent solids or Network solids:, , https://wa.me/919844532971

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Active site edutech-9844532971, , These are crystalline solids in which the constituent particles are non-metal atoms linked, to the adjacent atoms by covalent bonds throughout the crystal forming a giant threedimensional structure., ii) Hence covalent solids are called giant solids and the constituting molecules are called, giant molecules., iii) Since covalent bonds are strong and directional, atoms are held strongly at their lattice, positions., iv) They are hard or brittle depending on the event of bonding., v) They have high melting points., vi) They act as good conductors of electricity or insulators depending upon the availability, of free electrons., The examples of covalent solids are diamond, graphite, Silicon carbide (carborundum),, fullerene, boron nitride, etc., i), , Comparison of different types of crystalline solids:, Type of solid, Ionic solids, , Constituent, particles, Cations and anions, , Binding forces, , Hard soft, , Hard but, malleable, and ductile, , Conductors in solid and, molten state, , Fairly high, , H2, I2, CO2, Ar, , Soft, , Insulator, , Very low, , Soft, , Insulator, , Low, , Hard, , Insulator, , Low, , Metallic solids, , Kernels and free, mobile, electrons, , Metallic bond, , Atoms of noble gas, or non-polar, molecules, , London or, dispersion, forces, , Molecules, , Very high, , HCl, SO2, Dipole-dipole, interaction, , Molecules, containing H, bonded to F, N, or O, , Melting, point, High, , Diamond,, graphite,, Quartz, Zinc, copper, , Covalent, bonding, , iii. Hydrogen, bonded, , Electrical, conductivity, Insulator in solids but, conductors, in, molten state or, solution, state, (aqueous), Insulators and, conductors, , NaCl, MgO, , Non-metallic atoms, , ii. Polar, , Physical, nature, Hard and brittle, , Electrostatic, forces, , Covalent, solids, , Molecular, solids, i. Non-polar, , Examples, , Hydrogen, bonding, , TERMS AND CONCEPTS, https://wa.me/919844532971, , Ice

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Active site edutech-9844532971, , Space lattice or crystal lattice:, It may be defined as a regular three-dimensional arrangement of constituent particles of, a solid substance in space., The positions which are occupied by atoms, ions or molecules in the crystal lattice are, called lattice points or lattice sites., Y, , Lattice Points, , c, b, , O, a, Z, , X, , Space lattice and a Unit cell, , Characteristics of Crystal lattice:, 1. Lattice points or lattice sites: The crystal lattice of a substance is represented by, showing the position of the particle in space. These positions are represented by points, and are referred to as Lattice points., 2. Each point in a crystal lattice represents one constituent particle which may be an, atom, a molecule (group of atoms) or an ion., 3. Lattice points are joined by straight lines to bring out the geometry of the molecule., , Unit Cell: It is the smallest portion of a crystal lattice which, when repeated in three, dimensions produces crystal lattice., Characteristics of Unit cell: A unit cell is characterized by following parameters,, 1. Edges or edge length: The intersection of two faces of crystal lattice is called as, edge. The three edges denoted by a, b and c represent the dimensions (lengths) of the, unit cell along three axes. These edges may or may not be mutually perpendicular., 2. Angles between the edges (or planes): There are three angles between the edges of, the unit cell represented as α , β and γ . The crystal is defined with the help of these, parameters of its unit cell., c, a) The angle α is between edges b and c., , b) The angle β is between edges a and c., , b, a, , c) The angle γ is between edges a and b., https://wa.me/919844532971

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Active site edutech-9844532971, Edge, , Corner, , 2. face, , 1., , dia, gon, , 5. Edge, centre, , al, , diag, o, , ody, , 7. F, ace, , 8. B, , nal, , 3. Corner, , e, Edg, , 4. body, centre, , 6. Face, centre, , 1), 2), 3), 4), 5), 6), , A space lattice can be sub-divided into a number of small cells known as unit cells. It can, be defined as the smallest block from which entire crystal can be built up by its, translational repetition in three dimensions, Total number of edges in a cube = 12, Total number of faces in a cube = 6, Total number of corners in a cube = 8, Total number of body centre in a cube = 1, Total number of face diagonals in a cube = 6 × 2 = 12, Total number of body diagonals in a cube = 4, , TYPES OF LATTICES AND TYPES OF UNIT CELL, Unit Cells are of two types: Primitive & Non- primitive., (i) Primitive or simple Unit Cells: In a primitive unit cell, the same type of particles is present, at all the corners of the unit cell., •, , •, , •, , •, •, , •, , •, •, simple cubic, , (ii) Non-primitive or centered unit cells:, There are three types of non-primitive unit cells as follows:, (a) Face Centered: When atoms are present in all 8-corners and six face centers in a cubic, unit cell then this arrangement is known as FCC., •, , •, , •, •, , •, •, , •, •, , •, , •, •, , •, , •, •, face centred cubic (fcc), https://wa.me/919844532971

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Active site edutech-9844532971, , AIM, ✓ To analyse cubic crystal system. i.e., Calculation of no. of points in unit cell, ✓ Calculation of nearest neighbors, CALCULATION OF NUMBER OF PARTICLES IN A UNIT CELL (Z), In a crystal, atom located at the corner and face center of a unit cell are shared by, other cells and only a portion of such an atom actually lies within a given unit cell., (i) A face-centered point is shared by two unit cells and only one half of it is present in, given unit cell, hence the contribution of the particle per unit cell is 1/2., 2, , 3, , 1, , 4, , •6, , 5, 8, , 7, , (ii) A point along an edge is shared by four-unit cells and only one-fourth of it lies within, one cell, hence the contribution of the particle per unit cell is 1/4., 1, , 2, , •, 4, , 3, , (iii) A point that lies at the corner of a unit cell is shared among eight-unit cells and, therefore, only one eighth of each such point lies within the given unit cell, hence the, contribution of the particle per unit cell is 1/8., 6, , 8, , 5, 2, , 7, , •, , 1, , 4, 3, , (iv) A body-centered point lies entirely within the unit cell and contributes one complete, point to the cell., 2, •, 1•, , •3, , •, , •4, •6, , 5•, 8•, , https://wa.me/919844532971, , •, 7

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Active site edutech-9844532971, , i., , , Type of Lattice point, Contribution to one unit cell, 1/2, Face-center, Edge, 1/4, Corner, 1/8, Body Center, 1, Calculation of number of particles per unit cell in a primitive cubic unit cell: In this, type of unit cell, there are eight particles at the corners of the unit cell., Number of particles per unit cell = No. of particles in unit cell x share of particles per, unit cell, = 8x 1, 8, , = 1 particle., ii., , Calculation of number of particles per unit cell in a Bodycentred cubic unit cell:, , This type of unit cell has 8 particles at the corners and 1, particle at the centre of the unit cell., 1,  Number of particles per unit cell = 8 x +1x 1, 8, = 2 particles., iii., , Calculation of number of particles per unit cell in a Face- centred cubic unit cell:, , This type of unit cell has 8 particles at the corners and 6 particles at centre of 6 faces, of the unit cell., 1, 1,  Number of particles unit cell =8 x + 6 x, 8, 2, =1 + 3, = 4 particles., , https://wa.me/919844532971

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Active site edutech-9844532971, , Calculation of number of particles in a unit cell, Type of unit, cell, , SC, , Lattice points, at corners, 8, , Lattice points at, face-centered, 0, , Lattice points at, body centered, 0, , BCC, , 8, , 0, , 1, , FCC, , 8, , 6, , 0, , Z = no. of lattice points, per unit cell, 1, 8 × = 1, 8, 1, 8 × + 1 × 1 = 2, 8, 1, 1, 8× + 6 × = 4, 8, 2, , CALCULATION OF NEAREST NEIGHBOURS, Note: In a simple cube, the atoms at the corners touch each other. But, the atoms at the, corners of face centered cube and body centered cube do not touch each other. In fcc,, each sphere at the corner touches the three spheres at the face centres of three adjuring, faces similarly, in bcc, all the atoms at the corners touch the central sphere., The relationship between the nearest neighbor distance (d) and the radius of atom ®, (for crystals of pure elements) and the edge of unit cell (a) are given below:, 1] Simple Cube:, d = AB = a, r = a/2, 2] Face Centered Cube:, AC, , d=, in right angled Δ ABC AC2 = AB2 + BC2, 2, AC2 = a2 + a2 = 2a2, AC = √2. a, AC √2. a, a, d=, =, =, 2, 2, √2, , ∵r=, , d, a, =, 2 2√2, , 3] Body Centered Cube: d = AD, 2, In right angled ΔABC, AC2 = AB2 + BC2 = 2a2, AC = √2. a, , In right angled ΔADC, AD2 = AC2 + DC2 = (√2.a) 2 + a2, AD2 = 3a2  AD = √3. a  d =, , √3. a, 2, , r=, , d √3, =, a, 2, 4, , SESSION – 3, AIM, ✓ To study close packing in crystals, ✓ To introduce interstitial voids, (i) Close packing in two dimensions:, https://wa.me/919844532971

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Active site edutech-9844532971, , Initially the spheres arrange themselves in a row to form an edge of the crystal., There are two ways to build a crystal plane, (a) Sphere are packed in a such a way that the rows have a horizontal as well as vertical, alignment. In this arrangement, the spheres are found to form square. This type of packing, is also called square close packing., The number of spheres which are touching a given sphere is called co-ordination number., Thus, the coordination number of each sphere in square close packing is four., (b) The sphere is packed in such a way that the spheres in the second row are placed in, the depressions between the spheres of the first row and so on. This gives rise to hexagonal, close packing of spheres and the coordination number of each sphere is six., , (ii) Close packing in three dimensions:, It is clear from the figure (X) that there are two types of voids or hollows in the first, layer. These are marked as b and c. All the hollows are equivalent but the sphere of, second layer may be placed either on hollows which are marked b or on the other set of, hollows marked c. The second layer is indicated as dotted circles in figure (Y)., a, , a, c, , a, c, , b, a, , b, a, , c, b, a, , a, c, , b, , (X), , a, c, , a, , a, b, a, , a, , b, , b, , c, , a, c, , b, a, , a, c, , a, , b, a, , a, c, , a, c, , b, a, , a, c, , b, , c, b, , a, , a, , b, a, , c, , a, , a, c, , b, a, , a, , (Y), , When a third layer is to be added, again there two types of hollows available. One type, of hollows marked ‘c’ are unoccupied hollows of the first layer. The other type of hollows, are hollows in the second layer (marked a). Thus, there are two alternatives to build the, third layer., (i) When the third layer is placed over the second layer so as to cover the tetrahedral or, ‘a’ voids, a three-dimensional closest packing is obtained where the spheres in every third, layer are vertically aligned to the first layer. This arrangement is called ABAB.,…, pattern or hexagonal (HCP) close packing (calling first layer as A and second layer B)., https://wa.me/919844532971

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Active site edutech-9844532971, , Hexagonal close packing (hcp), (a) For HCP geometry Coordination number = 12, (b) For HCP geometry no. of atoms per unit cell, = 12 (corners) ×, , 1, 1, + 2(face centres) × + 3 (inside the body) × 1 = 6, 6, 2, , (c) For HCP geometry packing efficiency = 74 %, (ii) When the third layer is placed over the second layer such that the spheres cover the, octahedral or ‘a’ voids, a layer different from A and B is formed. This pattern is called, ABCABC……pattern or cubic close packing (CCP)., The ABC ABC....... packing has cubic symmetry and is known as cubic close packing (ccp)., The cubic close packing has face centered cubic (fcc) unit cell., , •, , •, , •, •, , •, •, •, , Cubic close packing (ccp), (i) For CCP geometry coordination number = 12, (ii) For CCP geometry no. of atoms per unit cell = 4(as calculated before), (iii) For CCP geometry packing efficiency = 74 %, , VOIDS, https://wa.me/919844532971, , •, •, , •, •, , •, , •, , •

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Active site edutech-9844532971, , In the close packing of spheres, certain hollows are left vacant. These holes or voids in the, crystals are called interstitial sites or interstitial voids., (i) Triangular, (ii) tetrahedral, (iii) Octahedral, (iv) cubical void, (i) Triangular: The vacant space (void) formed by touching three spheres., , rvoid, rsphere, , = 0.155, , (ii) Tetrahedral: The vacant space among four spheres having tetrahedral arrangement is, r, called tetrahedral site or tetrahedral hole. For tetrahedral void void = 0.225., rsphere, , •, , •, , •, , •, , T, , T, , •, , T, , T, , •, , •, T, , T, , •, , T, , T, , •, , •, , •, , •, , Tetrahedral void, , (iii) Octahedral: This type of site is formed at the centre of six sphere. The void formed by, two equilateral triangles with apices in opposite direction is called octahedral site or, octahedral hole. For octahedral void, rvoid, = 0.414, rsphere, •, , •, , •, , O, , •, , O, , •, , O, , •, •, , •, , O, , •, , •, , O, , •, , O, , O, , O, , •, , O, , O, , •, , O, , O, , Octahedral void, , •, , O, , iv) Cubical void: The vacant space (void) formed by touching eight spheres, rvoid, , rsphere, , = 0.732, , https://wa.me/919844532971

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Active site edutech-9844532971, , Note: If a close packing (array) is made up of n number of atoms or ions then it has n no., of octahedral voids and 2n no. of tetrahedral voids., , SESSION – 4, , https://wa.me/919844532971

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Active site edutech-9844532971, , AIM, ✓ To introduce calculations involving unit cell dimensions, ✓ To calculate packing efficiency of crystal lattice, DENSITY OF UNIT CELL, • The length of edge of the cell = a cm, • Volume of unit cell = a3 cm3, Density =, , Mass of unit cell, Volume of unit cell, , • Mass of unit cell = number of atoms in a unit cell, • Density =, ,  mass of each atom, Number of atom in unit cell×mass of one atom, , • Mass of one atom (m) =, •, , Density =, , Z×M, , = Z.m, , Volume of unit cell, Gram Atomic Weight, Avogadro′ snumber, , =, , M, NA, , Z → Number of atoms per unit cell., , a3 ×NA, , PACKING EFFICIENCY, Packing efficiency is the % of total space occupied by particles. Both types of close, packing (hcp and ccp) are equally efficient and occupy 74% of available value. In bcc,, the efficiency is 68% while is simple cubic structure, it is 52.4%, Packing efficiency =, , Vol. occupied by all atoms in unit cell v, =, Total vol. of unit cell, V, , Let a be the cube edge length and r the radius of atom., 4, V = volume of unit cell = a3; Volume of sphere, v = πr 3, 3, a. Packing efficiency in CCP or FCC arrangement:, Both type of close packing (hcp and ccp) are equally efficient. Let us calculate the, efficiency of packing in ccp structure., In ccp, the unit cell is face centred. In face centred cubic unit cell,, there are four spheres per unit cell. Let ‘r’ is the radius of sphere and, ‘a’ be the edge length of the cube., Volume of the sphere = 4 πr 3, 3, , Since there are four spheres per unit cell of fcc, volume of it = 4 x, https://wa.me/919844532971, , 4 3, πr, 3

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Active site edutech-9844532971, , In a face centred cubic unit cell, the spheres at corners are in contact with the sphere, at the centre of the face and the particles at the corners are not in touch with each, other., Therefore we can find the radius of the sphere as follows:, From Δle ABC,, AC2 = AB2 + BC2,  b2 = a2 + a2,  b2 = 2a2,  b = 2a 2, Since b = 4r, we have,  4r, , , , =, , , , r=, , , , r=, , a=, , , a, , C, , B, , b, A, , 2a 2, 2a 2, 4, 2a, 4, , or a =, , 2x2xr, 2 or, , 4r, 2, , a=, , 2x 2 x 2 xr, 2, , AC = face diagonal = b = 4r, Edge length of the cube = a, , a=2 2 r, , Packing Efficiency =, 4x, , (, , =, =, , Volume of space occuped by atoms in one unit cell, 100, Volume of one cubic unit cell, , 4, x π x r3, 3, x 100, 3, 2 2r, , ), , 4 x 4 x π x r3, x 100, 3 x 8 x 2 x 2 r3, π, x 100, 3 2, , =, Packing Efficiency = 74.04%, , https://wa.me/919844532971, , ; 74%

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Active site edutech-9844532971, , b) HCP arrangement:, Volume of unit cell = base area height = 6√342 × 4r √2/3 = 24√2r 3, , 1, 1, 4, no. of atoms in hcp = 12 × + 2 × + 3 × 1 = 6 v = 6 × 4πr 3 = 8πr 3, 6, 2, 3, Packing efficiency =, , 8πr 3, 24√2r 3, , c) BCC arrangement:, , × 100 =, , π, 3√2, , × 100 = 74%, a, , A, , B, , b, C, , c=, , 4r, , D, , In Body centred cubic unit cell, atoms are located at the, corners of the cube and 1 particle at the centre of the, AC = face diagonal = b, cube., CD = body diagonal = c = 4r, Number of particles per unit cell of BCC structure = 2, 8, 4, Edge length of the cube = a,  Volume occupied by spheres = 2× πr 3 = πr 3, 3, 3, Where r → radius of the spheres., Edge length of cube = a, In a body centred cubic unit cell, the spheres at the corners are not touching each other, but are in contact with the sphere at the centre of the cube., From the above figure, we can find, Face-diagonal as, from Δle ABC,, AC2 = AB 2 + BC2 = a2 + a2, b2 = 2a2, To find body diagonal consider the Δle ACD,, Body diagonal CD can be calculated as, CD2 = AC2 + AD2, c2 = b2 + a2 = 2a2 + a2, https://wa.me/919844532971

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Active site edutech-9844532971, , =c=, = 4r, , 3a 2, ,  CD, , CD =,  4r =, , , , r, , =, , Volume, , 3a, , =, , 3a, , 3a, , 3, 4, , a or a =, , 4, √3, , r, 4, , of unit cell = a3 = [√3 𝑟], , 3, ,  a3 = 64 𝑟 3, 3√3, , Packing Efficiency =, Packing Efficiency =, , Volume of space occuped by atoms in one unit cell, Volume of one cubic unit cell, 8 3, πr, 3, 64 3, 𝑟, 3√3, , x 100 =, , 8πr 3 3√3, 64 x 3 r 3, , × 100, , x 100, , Packing efficiency = 67.98 % ≃ 68 %, d) Simple cubic arrangement: In simple cubic unit cell, atoms are located, , only at the corners of the cube. The particles touch one another, along the edge., If edge length of the cube= a, and radius of each particle is r; then a is, related to r as a = 2r, The volume of the cubic unit cell = a3, = 2r3 = 8r3, Since a simple cubic unit cell contains only 1 atom, The volume of the occupied space = 4 πr 3, Packing, , 3, Volume of space occuped by atom, Efficiency=, × 100%, Volume of cubic unit cell, 4/3πr 3, =, ×100, 8r 3, 4πr 3, =, ×100, 3×8r 3, 𝜋, =, ×100, 6, , =, , AIM, https://wa.me/919844532971, , 52.36%, SESSION – 5, , a, , 2r

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Active site edutech-9844532971, , ✓ To introduce radius ratio rules, ✓ To explain structure of simple ionic compounds, RADIUS RATIO RULES, In ionic crystals, the coordination numbers as well as the geometrical shapes of the crystals, depend mainly on the relative sizes of the ions. The ration of the radii of the positive, and negative ions is called radius ratio., Radius of postive ion (cation) rc+, Radius ratio =, =, Radius of negative ion (anion) ra−, Common coordination numbers are 3, 4, 6 and 8., 𝐫𝐜, , Co-ord. No., , Shape, , Example, , 2, , Linear, , BeF2, , ii) 0.155 – 0.225, , 3, , Trigonal planar, , B2O3, , iii) 0.225 – 0.414, iv) 0.414 − 0.732, v) 0.732 − 0.999, , 4, 6, 8, , Tetrahedral, octahedral, B.C.C., , ZnS, NaCl, CsCl, , Limiting, i), , 𝐫𝐚, , radius ratio, , < 0.155, , STRUCTURE OF IONIC COMPOUNDS, (A) Ionic Compounds of AB type:, These compounds can have following three type of structures., 1] Rock salt structure (NaCl):, (a) Cl¯ is forming a FCC unit cell in which Na+ is in the, octahedral voids. The co-ordination number of Na+ is 6 and, that of Cl¯ would also be 6., (b) Ratio of ionic radii = (, , rNa+, = 0.525), rCl−, , Na+, Cl—, , Sodium chloride structure, , 1, (c) No. of sodium ions = 12 (At edge centre) × + 1 (At body centre) × 1 = 4, 4, 1, 1, No. of Cl− ions = 8 (At corners) × + 6 (At face centres) × = 4, 8, 2, , (Thus formula is Na4Cl4 i.e. NaCl), (d) Most of the halides of alkali metals and oxides of alkaline-earth metal have this, type of structure. e.g. NaI, KCl, RbI and RbF. FeO also has rock-salt structure in which, oxide ions are arranged in ccp and Fe2+ ions occupy octahedral voids., 2] Caesium chloride structure (CsCl):, , https://wa.me/919844532971

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Active site edutech-9844532971, , (a) CsCl has body-centered cubic (bcc) arrangement. This structure has 8: 8 co-ordinations,, i.e., each Cs+ ion is touching eight Cl– ions and each Cl– ions in touching eight Cs+ ions., (bcc)., (b), , rCs+, = 0.933, rCl−, , •, , •, , •, , •, , •, •, , •, •, , •, , •, , •, , •, , •, •, (a), , •, , •, , •, •, , •, , •, •, , •, , •, , •, , •, , (c)No. of Cl− ions = 8 (At corners) ×, , Cs+, , •, , •, , • Cl—, , •, , •, , •, , •, , •, , •, , •, , •, , (b), One unit cell, , 1, = 1, 8, , No. of Cs+ ions = 1 (At the body centre) × 1 = 1, No. of CsCl unit per unit cell = 1, (d) Compounds having this type of structure are CsBr, CsI, TlCl, and TlBr., 3] Zinc blende structure or Sphalerite structure (ZnS):, (a) Sulphide ions are face centered and zinc is present in alternate tetrahedral voids., r 2+, (b) Zn = 0.40, rS2−, , (c) No. of S2– ions = 8 at corners × + 6 at face centres ×, 1, , 1, , 8, , 2, , = 4, , No. of Zn2+ ions = 4 (within the body) × 1 = 4, No. of ZnS units per unit cell = 4, (Formula is Zn4S4, i.e. ZnS), (d) Ionic solids having zinc blende structure are CuCl, CuBr, CuI & AgI, (B) Ionic Compounds of AB2 type:, Fluorite structure (CaF2):, (a) The cations are arranged in cubic close packing (ccp) while the anion occupy all the, tetrahedral voids. Calcium fluoride has 8: 4 co-ordination. (ccp), (b) In unit cell no. of calcium ions, 1, 1, = 8 at corners × + 6 at face centres × = 4, 8, , https://wa.me/919844532971, , 2

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Active site edutech-9844532971, , ✓ To introduce defects in solid, IMPERFECTIONS OR DEFECTS IN SOLIDS, At absolute zero, crystals tend to have a perfectly ordered arrangement. This, arrangement corresponds to state of lowest energy. As the temperature increases, the, crystals start deviating from the perfectly ordered arrangement. Any deviation from the, perfectly ordered arrangement constitutes a defect or imperfection. These defects are, sometimes called thermodynamic defects because the number of these defects depends on, the temperature. Crystals may also possess addition defects due to the presence of, impurities. Many properties of crystalline solids such as electrical conductivity and, mechanical strength can be explained in terms of imperfections. Imperfections not only, modify the properties of solids but also give rise to new properties. The defect which arises, due to the irregularity in the arrangement of atoms or ions are called atomic imperfections., These imperfections in the crystalline solid are called defects in crystalline solid. The defects, in crystalline solids are of two types viz.,, a. Point defect, b. Line defect, Point Defect: This defect is produced because of the faulty arrangement of a point i.e., constituent practice like atom, ion or molecules in a crystalline solid., The point defects are classified into three types:, Types of point Defects:, i) Stoichiometric defects. These are those defects in which the stoichiometry of the solid is, not disturbed as a result of the defect., ii) Non-stoichiometry defects. These are those in which the stoichiometry is disturbed due to, the defect., iii) Impurity defect. These arise when some foreign material is added into the crystal., Types of Stoichiometric defect, (i) Vacancy defect is a stoichiometric defect generated during, crystallization, in which some of the places of the, constituent particle remain unoccupied. This defect results, in the decrease of density of the crystal than expected., This defect possibly occurs when a substance is heated., , https://wa.me/919844532971, , Vacancy, , Vacancy defect

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Active site edutech-9844532971, , (ii) Interstitial defect: Interstitial defect is a type of, stoichiometric defect, in which the constituent particles (atoms, or molecules) occupy an interstitial site (occupies the space, between the lattice site). This defect results in the increase, of density of the crystal than expected., , Interstitial defect, , Particle at the, interstitial site, , In case of ionic solids, always electrical neutrality must be maintained. The above two, defects in case of ionic solids can be explained as follows:, a) Schottky defect:, It is due to equal number of cations and anions missing from their lattice sties. As a result,, density decreases. This type of defect is shown by ionic compounds which have high, coordination number and small difference in the size of cations and anions, e.g., NaCl,, KCl, KBr, AgBr and CsCl., , b) Frenkel defect:, It arises when cations are missing from their lattice sites and occupy interstitial sites. As, a result, density remains unchanged. This defect is also called dislocation defect as smaller, ions (usually cations) are dislocated from normal sites to interstitial sites., , Types of Non-stoichiometric Defects:, These are of two types, i) Metal excess: These defects arise when there are excess metal ions in the crystal. these, defects arises in two ways:, https://wa.me/919844532971

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Active site edutech-9844532971, , a) By anion vacancies: It arises due to a negative ion missing from the lattice site leaving, a hole which is occupied by electron thereby maintaining electrical neutrality. The lattice, sites occupied by electrons are called F-centres as they are responsible for colour of, Crystal:, Ex: When NaCl is heated in the atmosphere of sodium vapors, sodium atoms get deposited on, the surface of the crystal. The Cl¯ ions from the crystal lattice leaves their sites and, diffuse to the surface. These Cl¯ ions combine with the sodium atoms and these Na atoms, ionizes and the electrons that are released are trapped by the anion vacancies. These, are called f centers, , (a) Metal excess defect due to anion vacancies, b) By presence of extra cations in the interstitial sites:, Excess metal ions are entrapped into the vacant interstitials sites and electrons in the, neighbouring interstitial sites to maintain electrical neutrality., For example, when ZnO is heated, it loses O2 and turns yellow due to the following reaction:, 1, ZnO → Zn2+ + O2 + 2e−, 2, , The Zn2+ ions occupy certain interstitial sites whereas electrons released will occupy the, neighboring sites in the lattice. On heating the crystal turns yellow, due to transition of, free electrons from a lower energy state., , (b) Metal excess defect due to interstitial cation, , https://wa.me/919844532971

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Active site edutech-9844532971, , ii) Metal Deficiency due to cations vacancies:, This defect occurs when the metal shows variable vacancy, i.e., transition metals, e.g., in, FeO, FeS, NiO etc. This is because in FeO, 3 Fe2+ ions may be replaced by 2 Fe3+ ions, to maintain electrical neutrality. That is why we never have the idea composition FeO., Instead, we have FexO with x = 0.93 to 0.96., , Metal deficiency due to cation vacancy, Types of Impurity defects:, Impurities are added to change the properties of the crystals. The process is called, doping., i) In ionic solids: For example, SrCl2 may be added to NaCl. Two Na+ ions will be replaced, by one Sr2+ ion thereby creating a whole (a cation vacancy) and imparting conductivity., , ii) In covalent solids:, a) Doping with electron rich impurities: For example, Group 14 elements like Si or Ge, (having 4 valence electros) may be doped with Group 15 elements like P or as (having, 5 valence electrons). For every atom of Group 14 replaced by that of Group 15 one, extra electron is present making it n-type semiconductor, b) Doping with electron deficit impurities: For example, when Group 14 elements is doped, with Group 13 elements like B, Al or Ga (having 3 valence electrons), for every atom of, Group 14 replaced by that of Group 13, a hole is created. On applying electric field,, electrons move to occupy these holes. Thus, holes move towards the negative plate as if, they carry positive charge. Hence, we get p-type semiconductors., SESSION – 7, https://wa.me/919844532971

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Active site edutech-9844532971, , AIM - To introduce properties of solids, PROPERTIES OF SOLIDS, (i) Electrical Properties: Solids can be broadly classified into three types, on the basis of, electrical conductivity., (a) Metals (conductors), (b) Insulators, (c) Semi-conductors, –, –, Electrical conductivity of metals is very high and is of the order of 106–108ohm 1cm 1, –, –, –, whereas for insulators, it is of the order of 10 12ohm 1cm 1. Semi-conductors have, –, –, –, intermediate conductivity in the range of 102–10 9ohm 1cm 1. Electrical conductivity of, solids may arise through the motion of electrons and holes (positive) or through the motion, of ions. The conduction through electrons is called n-type conduction and through (positive), holes is called p-type conduction. Pure ionic solids where conduction can take place only, through movement of ions are insulators. The presence of defects in the crystal structure, increases their conductivity., The conductivity of semi-conductors and insulators is mainly due to the presence of, interstitial electrons and positive holes in the solids due to imperfections. The conductivity, of semi-conductors and insulators increases with increase in temperature while that of, metals decrease., (ii) Magnetic Properties:, Diamagnetic Materials: Those materials which are weakly repelled by the magnetic field, are called diamagnetic materials. e.g. Cu+, TiO2, NaCl and benzene. They do not have, unpaired electrons., Paramagnetic Materials: The materials which are weakly attracted by magnetic field, are called paramagnetic materials. These materials have permanent magnetic dipoles due, to presence of atoms, ions or molecules with unpaired electron. e.g. O2, Cu2+, Fe2+ etc., But these materials lose their magnetism in the absence of magnetic field., Ferromagnetic Materials: The materials which show permanent magnetism even in the, absence of magnetic field are called ferromagnetic materials. These materials are strongly, , https://wa.me/919844532971

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Active site edutech-9844532971, , attracted by the magnetic field. e.g. Fe, Co, Ni and CrO2. Ferromagnetism arises due to, spontaneous alignment of magnetic moments of ions or atoms in the same direction., Alignment of magnetic moments in opposite directions in a compensatory manner and, resulting in zero magnetic moment gives rise to anti-ferromagnetism., , Alignment of magnetic moments, Ferromagnetic substances, , Alignment of magnetic moments, Antiferromagnetic substances, , Alignment of magnetic moments, Ferrimagnetic substances, , for example, MnO, Mn2O3 and MnO2., Alignment of magnetic moments in opposite directions resulting in a net magnetic moment, due to unequal number of parallel and anti-parallel magnetic dipoles give rise to ferrimagnetism e.g. Fe3O4., Ferromagnetic and ferrimagnetic substances change into paramagnetic substances at, higher temperature due to randomization of spins. Fe3O4, is ferrimagnetic at room, temperature and becomes paramagnetic at 850 K., (iii) Dielectric Properties:, The electrons in insulators are closely bound to the individual atoms or ions and thus they, do not generally migrate under the applied electric field. However, due to shift in charges,, dipoles are created which results in polarisation. The alignments of these dipoles in, different ways i.e. compensatory way (zero dipole) or non-compensatory way (net dipole), impart certain characteristic properties to solids., If the dipoles align in such a way that there is net dipole moment in the crystals, these, crystals are said to exhibit piezoelectricity or piezoelectric effect i.e. when such crystals, are subjected to pressure or mechanical stress, electricity is produced. Conversely, if an, electric field is applied to such a crystal, the crystal gets deformed due to generation, of mechanical strain. This is called inverse piezoelectric effect., Some crystals which on heating, acquire electric charges on opposite faces, are said to, exhibit pyroelectric effect., https://wa.me/919844532971

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Active site edutech-9844532971, , The solids, in which dipoles are spontaneously aligned in a particular direction, even in the, absence of electric field are called ferroelectric substances and the phenomenon is known, as Ferroelectricity. If the alternate dipoles are in opposite direction, then the net dipole, moment will be zero and the crystal is called anti-ferroelectric., Ferroelectric solids – Barium titanate (BaTiO3), sodium potassium tartrate (Rochelle, salt) and potassium hydrogen phosphate (KH2PO4). Anti-ferroelectric – Lead Zircon ate, (PbZrO3)., Super Conducting Materials: The materials which offer no resistance to the passage of, electricity is called superconductor or super conducting material. In this state, the materials, become diamagnetic and are repelled by the magnets. Most of the metals become super, conducting at low temperatures (2 – 5K). Highest temperature at which super, conductivity is known is 23K in alloys of niobium (e.g. Nb3Ge). Many complex metal oxides, have been found to possess super-conductivity at somewhat higher temperatures.], Material, Temperature, Nb3Ge, 23 K, Bi2Ca2Sr2Cu3O10, 105 K, Ti2Ca2Ba2Cu3O10, 125 K, Band theory of solids:, 1. According to band Theory, the atomic orbitals of atom in the crystal combine to form, molecular orbital which spreads over the complete crystal structure., 2. As the number of atoms in crystal increases, the number of molecular orbital containing, electrons increased. As the number of molecular orbitals increases the energy difference, between the adjacent orbitals decreases., 3. Until finally the energy gap becomes very small and molecular discrete energy levels, merge into one another to form continuous band of molecular orbitals which extend over, the entire length of crystal., 4. All the molecular orbitals are very close to each other and are collectively called a, band., 5. There are two types of bands of molecular orbitals as follows :, , https://wa.me/919844532971

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Active site edutech-9844532971, , 1., , Energy, , 6., , Valence band: The atomic orbitals with filled electrons from the inner shells form, valence bands, where there are no free mobile electrons since they are involved in, bonding., 2. Conduction band: Atomic orbitals which are partially filled or empty on overlapping, form closely placed molecular orbitals giving conduction bands where electrons are, delocalized and can conduct, heat and electricity., In metallic crystals, the valence bands and conduction bands are, Conduction, band, very close to each other and a very little energy is required to, Forbidden zone, excite electrons from valence bond in to the conduction band. In, (large energy gap), conduction band the electron are delocalized and are free to move, Valence, band, from one end to the other end of the metal piece, this migration of, electron makes the metal good conductor of heat and electricity., Insulator, In substance which are bad conductor of heat and electricity, the, spacing between the valence band and conduction band is relatively, Conduction, more so that more energy is required to promote electrons from valence, band, band to conduction bond, hence electrons remains in valence band and, thus cannot move freely thus do not conduct heat and electricity and, Valence, band, act as insulators., Energy, , 7., , If the energy difference between valence band and conduction, band is moderate, then the substance in ordinary condition is, non-conductor, but if heated it becomes conductor due to, transition of electrons into conduction band. Such conductors are, semiconductors., , Metal, Conduction, band, , Energy, , 8., , less energy gap, Valence, band, , Semiconductor, , Conduction of electricity in Semiconductors: The substance which have poor electrical, conductance at low temperature but increases with increase in temperature is called, semiconductor. A substance containing filled band with electrons and a completely empty, band behaves as a semiconductor., Example: Si, Ge, etc., https://wa.me/919844532971

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Active site edutech-9844532971, , In excitation, empty conduction bands contain electrons to conduct electricity. However, electrons can be added to conduction band by adding impurity (like Arsenic with extra, electrons to silicon conduction band) and hence can become conductor of electricity., Electron rich impurity: n-type semiconductor: If the impurity from Group 15 i.e. (Arsenic) is, added to group 14 (i.e. silicon), some of the sites of silicon in the crystal are occupied, by arsenic atoms each with one extra electron in the conduction band and will be available, for transport of electricity. Such type of semiconductor with impurity having extra negative, charge due to extra electron of impurity atom is called n-type semiconductor., Electron deficient impurity: p-type semiconductor: If the impurity from Group 13 i.e. (Boron), added to Group 14 (i.e. silicon) then some atoms of born will occupy some of the sites of, silicon atoms. At all sites of boron atoms one valence electron will be shorter as compared, to silicon atoms and there will be a positive hole in the lattice. Hence an electron from, neighbouring silicon atoms jumps into the electron hole and continues till the electron hole, is transferred to the edge of the crystal lattice and movement of electron takes place., This type of semiconductor is called p-type semiconductor., , Examples for n and p –type semiconductors:, Semiconductor, , Type, , 1, , B doped with Si, , p-type, , 2, , As doped with Si, , n-type, , 3, , P doped with Si, , n-type, , 4, , Ge doped with In, , p-type, , https://wa.me/919844532971

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Active site edutech-9844532971, , WHATS UP US FOR MORE NOTES AND TEST PAPERS-9844532971, Greetings from Active site edutech, Create ur own brand with *copyrights free* materials, Don't go for old copy, Updated 2020 study material *ENGLISH, HINDI, TAMIL MEDIUM* with ur branding., 1) *Foundation 6 to 10*, 2) *CBSE 6 to 12 study material*, 3) *11 &12th NEET and JEE materials & test papers*(soft copy, printed copy), Each topic contains, 1) Detailed theory(session wose), 2) 1000mcqs per chapter(student copy +review copy)*, 3) 3 chapter wise paperS, 4) power point presentation*, 5) *PCMB power point presentation*, 6) *1.38lakh PCMB mcqs*, 7) *KVPY* *NTSE* materials, 8) Android app &website* for online plotform, 9) *School and students accessories, 10) Education related *softwares with Active serial* key, Text us for details, https://wa.me/919844532971, , https://wa.me/919844532971