Subject : CHEMISTRY Topic : SOLID STATE

Transcription

1 fo/u fopkj Hkh# tu] ugha vkjehks dke] foif ns[k NksM+s qja e/;e eu dj ';kea iq#"k flag ladyi dj] lgs foif vusd] ^cuk^ u NksM+s /;s; dks] j?kqcj jk[ks VsdAA jfp% ekuo /kez iz.ksk ln~xq# Jh j.knksm+nklth egkjkt STUDY PACKAGE Subject : CHEMISTRY Topic : SOLID STATE This is TYPE 1 Package please wait fo Type 2 R Index 1. Key Concepts 2. Execise I 3. Execise II 4. Execise III 5. Execise IV 6. Answe Key Ys. Que. fom IIT-JEE Ys. Que. fom AIEEE Student s Name : Class Roll No. : : ADDRESS: R-1, Opp. Raiway Tack, New Cone Glass Building, Zone-2, M.P. NAGAR, Bhopal : (0755) , ,

2 FREE Download Study Package fom website: THE KEY Cystalline solids: Cystalline solids ae those whose atom, molecules o ions have an odeed aangement extending ove a Long Range. example-(rock salt, NaCl). Amophous solids: Amophous solids ae those whose constitutent paticles ae andomly aange and have no odeed long ange stuctue. example: Rubbe, Glass ect. TYPES OF CRYSTALLINE SOLIDS: Type of Solid Intemolecula foces Popeties Examples Ionic Ion-Ion foces Bittle, had high Melting NaCl, KCl, MgCl 2 Molecula Dispesion Soft, low melting nonconducting foces/dipole-dipole /H-bond H 2 O, B 2, CO 2, CH 4 Covalent netwok Covalent bonds Had: High melting C-Diamond SiO 2 Metallic Metallic bonds Vaiable hadness and melting point conducting Na, Zn, Cu, Fe TYPES OF UNIT CELL: Collection of lattice points, whose epetition poduce whole lattice is called a unit cell. The whole lattice can be consideed to be made by epetion of unit cell. 1. Unit Cell: Cystal Systems 1 Cubic 2 Othohombic Bavais Lattice Pimitive, Face Centeed, Body Centeed Pimitive, Face Centeed, Body Centeed, End Centeed Unit Cell Paametes Intecepts Cystal Angles a = b = c α = β = γ = 90 a b c α = β = γ = 90 3 Rhombohedal Pimitive a = b = c α = β = γ 90 4 Monoclinic Pimitive, End Centeed a b c α = γ = 90, β 90 5 Ticlinic Pimitive a b c α β γ 90 6 Tetagonal Pimitive, Body Centeed a = b c α = β = γ = 90 7 Hexagonal Pimitive a = b c α = β = 90, γ = 120 Page 2 of 32 GASOUS STATE

3 1.1 Pimitive o simple cubic (PS/SC) unit cell: Sphees in one laye sitting diectly on top of those in pevious laye, so that all layes ae identical. Each sphee is touched by six othe, hence coodination numbe is 6. 52% of available space occupied by sphees. Example: Polonium cystallises in simple cubic aangement. Z = 1 ; C.N. = 6 Page 3 of 32 GASOUS STATE 1.2 Body Centeed cubic (BCC) unit cell: Sphees in one laye sit in the depession made by fist laye in a-b-a-b manne. Coodination numbe is 8, and 68% of available space is occupied by atoms. Example: Ion, sodium and 14 othe metal cystallises in this manne. FREE Download Study Package fom website: Face centeed cubic (FCC) unit cell: Examples : Al, Ni, Fe, Pd all solid noble gases etc. 2. Density of cubic cystals: TYPE OF PACKING: Z = 2 ; C.N. = 8 Z = 4 ; C.N. = Closest packing of atoms: This is the most efficient way of packing 74% of available space is occupied by sphees and coodination numbe is 12. (i) Hexagonal close pack (A-B-A-B) type packing : Each laye has hexagonal aangement of touching sphee and 3 d laye is simila (exactly on top) of fist laye. (ii) Cubic close pack (A-B-C-A-B-C): AB layes ae simila to HCP aangement but thid laye is offset fom both A and B layes. The fouth laye is exactly on top of fist laye.

4 Hexagonal pimitive unit cell 4. Types of voids 4.1 Tetahedal void Page 4 of 32 GASOUS STATE FREE Download Study Package fom website: Octahedal void 5. Radius atio 5.1 Radius atio fo co-odination numbe 3 (Tiangula Aangement): = 3 3 ; + = = 0.155

5 5.2 Radius atio fo coodination numbe 4 (Tetahedal aangement): + + = + 3 a ; 4 = 2 a = 4 = = Page 5 of 32 GASOUS STATE FREE Download Study Package fom website: Radius atio fo coodination numbe 6: + + = 2 (Octahedal Aangement) o Radius atio fo coodination numbe 4 (Squae planna aangement) 5.4 Radius atio fo coodination numbe 8 : + + = + = 2 1 = a 2 (Body centeed cubic cystal) + + = 3 6. Types of ionic stuctues 6.1 Rock salt stuctue:(nacl) Lage atom fomic ccp aangement and smalle atom filling all octahedal voids. + = 3 1 = 0.732

6 6.2 Zinc blende (sphaleite) stuctue:(zns) Lage atom fomic ccp aangement and smalle atom filling half of altenate tetahedal voids 6.3 Fluoite stuctue:(caf 2 ) Ca 2+ foming ccp aangement and F filling all tetahedal voids. Page 6 of 32 GASOUS STATE 6.4 Antifluoite stuctue :(Li 2 O) O 2 ion foming ccp and Li + taking all tetahedal voids. FREE Download Study Package fom website: Cesium halide stuctue: (CsCl) Cl at the cones of cube and Cs + in the cente. 6.6 Coundum Stuctue: (Al 2 O 3 ) O 2 foming hcp and Al 3+ filling 2/3 octahedal voids. 6.7 Rutile stuctue: (TiO 2 ) O 2 foming hcp while Ti 4+ ions occupy half of the octahedal voids. 6.8 Pevoskite stuctue:(catio 3 ) Ca 2+ in the cone of cube O 2 at the face cente and Ti 4+ at the cente of cube. 6.9 Spinel and invese spinel stuctue: (MgAl 2 O 4 )O 2 foming fcc, Mg 2+ filling 1/8 of tetahedal voids and Al 3+ taking half of octahedal voids.in an invese spinel stuctue, O 2 ion fom FCC lattice, A 2+ ions occupy 1/8 of the tetahedal voids and tivalent cation occupies 1/8 of the tetahedal voids and 1/4 of the octahedal voids. 7. Cystal defects: Point defects: When ions o atoms do not hold the theoetical position, this is called point defect. Point defects ae of two types: (I) Stoichiometic defects: (a) Schottky defect: Due to missing of ions fom lattice point in pais. (b) Fenkel defect: It is caused due to the ceation of lattice vacancy as a esult of misplaced ion in intestitial site. Schottky defect common in ionic solid with high coodination numbe. NaCl, KCl, KB Fenkel defect :- Solid with low coodination numbe ZnS, AgB. (II) Non-Stoichiometic defects: Ratio of positive and negative ion diffe fom that indicated by chemical fomula. Metal-excess defect : (a) A negative ion eplaced by electon. (F-cente) (b) Exta metal ion pesent in lattice and electon also pesent in intestitial site. Metal-deficiency defect caused by : Cation missing fom lattice point, electoneutality maintained by metal ions with highe oxidation state as Fe 0.94 O.

7 THE ATLAS FREE Download Study Package fom website: Page 7 of 32 GASOUS STATE

8 FREE Download Study Package fom website: Fomula of ionic solid fom unit cell desciption EXERCISE I Q.1 A cubic solid is made up of two elements A and B. Atoms B ae at the cones of the cube and A at the body cente. What is the fomula of compound. Q.2 A compound alloy of gold and coppe cystallizes in a cubic lattice in which gold occupy that lattice point at cones of the cube and coppe atom occupy the centes of each of the cube faces. What is the fomula of this compound. Q.3 A cubic solid is made by atoms A foming close pack aangement, B occupying one. Fouth of tetahedal void and C occupying half of the octahedal voids. What is the fomula of compound. Q.4 What is the pecent by mass of titanium in utile, a mineal that contain Titanium and oxygen, if stuctue can be descibed as a closet packed aay of oxide ions, with titanium in one half of the octahedal holes. What is the oxidation numbe of titanium? Q.5 Spinel is a impotant class of oxides consisting of two types of metal ions with the oxide ions aanged in CCP patten. The nomal spinel has one-eight of the tetahedal holes occupied by one type of metal ion and one half of the octahedal hole occupied by anothe type of metal ion. Such a spinel is fomed by Zn 2+, Al 3+ and O 2, with Zn 2+ in the tetahedal holes. Give the fomulae of spinel. Edge length, density and numbe of atoms pe unit cell Q.6 KF cystallizes in the NaCl type stuctue. If the adius of K + ions 132 pm and that of F ion is 135 pm, what is the shotest K F distance? What is the edge length of the unit cell? What is the closet K K distance? Q.7 A closed packed stuctue of unifom sphees has the edge length of 534 pm. Calculate the adius of sphee, if it exist in (a) simple cubic lattice (b) BCC lattice (c) FCC lattice Q.8 Calculate the density of diamond fom the fact that it has face centeed cubic stuctue with two atoms pe lattice point and unit cell edge length of Å. Q.9 An element cystallizes into a stuctue which may be descibed by a cubic type of unit cell having one atom on each cone of the cube and two atoms on one of its body diagonals. If the volume of this unit cell is cm 3 and density of element is 7.2 g cm 3, calculate the numbe of atoms pesent in 200 g of element. Q.10 Silve has an atomic adius of 144 pm and the density of silve is 10.6 g cm 3. To which type of cubic cystal, silve belongs? Q.11 AgCl has the same stuctue as that of NaCl. The edge length of unit cell of AgCl is found to be 555 pm and the density of AgCl is g cm 3. Find the pecentage of sites that ae unoccupied. Page 8 of 32 GASOUS STATE

9 FREE Download Study Package fom website: Q.12 Xenon cystallises in the face-cented cubic lattice and the edge of the unit cell is 620 pm. What is the neaest neighbou distance and what is the adius of xenon atom? Q.13 The two ions A + and B have adii 88 and 200 pm espectively. In the closed packed cystal of compound AB, pedict the co-odination numbe of A +. Q.14 CsCl has the bcc aangement and its unit cell edge length is 400 pm. Calculate the inteionic distance in CsCl. Q.15 Gold cystallizes in a face centeed cubic lattice. If the length of the edge of the unit cell is 407 pm, calculate the density of gold as well as its atomic adius assuming it to be spheical. Atomic mass of gold = 197 amu. Q.16 The density of KB is 2.75 g cm 3. The length of the edge of the unit cell is 654 pm. Show that KB has face centeed cubic stuctue. (N = mol 1, At. mass : K = 39, B = 80) Q.17 An element cystallizes in a stuctue having FCC unit cell of an edge 200 pm. Calculate the density, if 200 g of this element contains atoms. Q.18 The effective adius of the ion atom is 1.42 Å. It has FCC stuctue. Calculate its density (Fe = 56 amu) Q.19 A cystal of lead(ii) sulphide has NaCl stuctue. In this cystal the shotest distance between Pb +2 ion and S 2 ion is 297 pm. What is the length of the edge of the unit cell in lead sulphide? Also calculate the unit cell volume. Q.20 If the length of the body diagonal fo CsCl which cystallises into a cubic stuctue with Cl ions at the cones and Cs + ions at the cente of the unit cells is 7 Å and the adius of the Cs + ion is 1.69 Å, what is the adii of Cl ion? Page 9 of 32 GASOUS STATE

10 PROFICIENCY TEST 1. Cystalline solids ae isotopic. 2. Rhombohedal, ticlinic and hexagonal ae the unit cells, which have only pimitive aangement possible. 3. Packing faction of FCC and HP units cells ae same. 4. The minimum void faction fo any unit cell in any shape having only one type of atom and all voids unfilled is Page 10 of 32 GASOUS STATE 5. Packing faction of a lattice stuctue depends on the adius of the atom cystallizing in it. FREE Download Study Package fom website: 6. The location of tetahedal voids in FCC unit cell ae the centes of 8 minicubes foming a lage cube. 7. Effective numbe of octahedal voids in a unit cell is equal to the effective numbe of atoms in the unit cell. 8. Radius atio fo co-odination numbe 4 having tetahedal and squae plana geomety is same. 9. The adius atio value fo co-odination numbe 4 having squae plana geomety and co-odination numbe 6 having octahedal geomety is same. 10. A metallic element cystallises into a lattice containing a sequence of layes of AB AB AB.... Any packing of sphees leaves out voids in the lattice 26% pecent by volume of this lattice is empty space. 11. The elation between edge length (a) and adius of atom () fo BCC lattice is. 12. The elation between edge length (a) and adius of atom () fo FCC lattice is. 13. ABCABC...layeing patten is called packing, found in lattice. 14. ABABAB...layeing patten is called packing, found in lattice. 15. Height (c) of the hexagonal pimitive unit cell in tems of adius of atom () is. 16. Anions would be in contact with each othe only if the cation to anion adius fo a given co-odination numbe is. 17. The numbe of tetahedal voids in hexagonal pimitive unit cell is. 18. The limiting adius fo co-odination numbe 8 is. 19. Fo cesium chloide stuctue, the inteionic distance (in tems of edge length, a) is equal to. 20. Density of a cystal due to Schottky defect and due to Fankel defect.

11 FREE Download Study Package fom website: EXERCISE II Q.1 Ion has body centeed cubic lattice stuctue. The edge length of the unit cell is found to be 286 pm. What is the adius of an ion atom? Q.2 Cesium chloide foms a body centeed cubic lattice. Cesium and chloide ions ae in contact along the body diagonal of the unit cell. The length of the side of the unit cell is 412 pm and Cl ion has a adius of 181 pm. Calculate the adius of Cs + ion. Q.3 In a cubic closed packed stuctue of mixed oxides the lattice is made up of oxide ions, one eighth of tetahedal voids ae occupied by divalent ions (A 2+ ) while one half of the octahedal voids occupied tivalent ions (B 3+ ). What is the fomula of the oxide? Q.4 A solid A + and B had NaCl type closed packed stuctue. If the anion has a adius of 250 pm, what should be the ideal adius of the cation? Can a cation C + having a adius of 180 pm be slipped into the tetahedal site of the cystal of A + B? Give easons fo you answe. Q.5 Calculate the value of Avogado s numbe fom the following data: Density of NaCl = cm 3 Distance between Na + and Cl in NaCl = 281 pm. Q.6 If the adius of Mg 2+ ion, Cs + ion, O 2 ion, S 2 ion and Cl ion ae 0.65 Å, 1.69 Å, 1.40 Å, 1.84 Å, and 1.81 Å espectively. Calculate the co-odination numbes of the cations in the cystals of MgS, MgO and CsCl. Q.7 Ion occus as bcc as well as fcc unit cell. If the effective adius of an atom of ion is 124 pm. Compute the density of ion in both these stuctues. Na+ Q.8 KCl cystallizes in the same type of lattice as does NaCl. Given that = 0. 5 Na+ and = 0. 7 Calculate: Cl + K (a) The atio of the sides of unit cell fo KCl to that fo NaCl and (b) The atio of densities of NaCl to that fo KCl. Q.9 An element A (Atomic weight = 100) having bcc stuctue has unit cell edge length 400 pm. Calculate the density of A and numbe of unit cells and numbe of atoms in 10 gm of A. Q.10 Pove that the void space pecentage in zinc blende stuctue is 25%. Q.11 A unit cell of sodium chloide has fou fomula units. The edge of length of the unit cell is nm. What is the density of sodium chloide. Q.12 In a cubic cystal of CsCl (density = 3.97 gm/cm 3 ) the eight cones ae occupied by Cl ions with Cs + ions at the cente. Calculate the distance between the neighbouing Cs + and Cl ions. Q.13 KF has NaCl stuctue. What is the distance between K + and F in KF if density of KF is 2.48 gm/cm 3. Q.14 The composition of a sample of wustite is Fe 0.93 O 1.0. What pecentage of ion is pesent in the fom of Fe(III)? Page 11 of 32 GASOUS STATE

12 FREE Download Study Package fom website: Q.15 BaTiO 3 cystallizes in the pevoskite stuctue. This stuctue may be descibed as a cubic lattice with baium ions occupying the cone of the unit cell, oxide ions occupying the face-centes and titanium ion occupying the cente of the unit cell. (a) If titanium is descibed as occupying holes in BaO lattice, what type of holes does it occupy? (b) What faction of this type hole does it occupy? Q.16 Rbl cystallizes in bcc stuctue in which each Rb + is suounded by eight iodide ions each of adius 2.17 Å. Find the length of one side of RbI unit cell. Q.17 If NaCl is dopped with 10 3 mol % SCl 2, what is the numbes of cation vacancies? Q.18 Find the size of lagest sphee that will fit in octahedal void in an ideal FCC cystal as a function of atomic adius ''. The insetion of this sphee into void does not distot the FCC lattice. Calculate the packing faction of FCC lattice when all the octahedal voids ae filled by this sphee. Q.19 A cubic unit cell contains manganese ions at the cones and fluoide ions at the cente of each edge. (a) What is the empiical fomula of the compound? (b) What is the co-odination numbe of the Mn ion? (c) Calculate the edge length of the unit cell, if the adius of Mn ion is 0.65 Å and that of F ion is 1.36 Å. Q.20 NaH cystallizes in the same stuctue as that of NaCl. The edge length of the cubic unit cell of NaH is 4.88 Å. (a) Calculate the ionic adius of H, povided the ionic adius of Na + is 0.95 Å. (b) Calculate the density of NaH. Q.21 Metallic gold cystallises in fcc lattice. The length of the cubic unit cell is a = 4.07 Å. (a) What is the closest distance between gold atoms. (b) How many neaest neighbous does each gold atom have at the distance calculated in (a). (c) What is the density of gold? (d) Pove that the packing faction of gold is Q.22 Ice cystallizes in a hexagonal lattice. At the low tempeatue at which the stuctue was detemined, the lattice constants wee a = 4.53 Å, and b = 7.60 Å(see figue). How many molecules ae contained in a given unit cell? [density (ice) = 0.92 gm/cm 3 )] Q.23 Using the data given below, find the type of cubic lattice to which the cystal belongs. Fe V Pd a in pm ρ in gm cm Q.24 Potassium cystallizes in a body-centeed cubic lattice with edge length, a = 5.2 Å. (a) What is the distance between neaest neighbous? (b) What is the distance between next-neaest neighbous? (c) How many neaest neighbous does each K atom have? (d) How many next-neaest neighbous does each K atom have? (e) What is the calculated density of cystalline potassium? Q.25 Pove that void space in fluoite stuctue pe unit volume of unit cell is Q.26 A compound fomed by elements X & Y, Cystallizes in a cubic stuctue, whee X is at the cones of the cube and Y is at six face centes. What is the fomula of the compound? If side length is 5Å, estimate the density of the solid assuming atomic weight of X and Y as 60 and 90 espectively. Page 12 of 32 GASOUS STATE

13 FREE Download Study Package fom website: Q.27 The metal nickel cystallizes in a face cented cubic stuctue. Its density is 8.9 gm/cm 3. Calculate (a) the length of the edge of the unit cell. (b) the adius of the nickel atom. [Atomic weight of Ni = 58.89] Q.28 The olivine seies of mineals consists of cystals in which Fe and Mg ions may substitute fo each othe causing substitutional impuity defect without changing the volume of the unit cell. In olivine seies of mineals, oxide ion exist as FCC with Si 4+ occupying 4 1 th of octahedal voids and divalent ions occupying 1 th of tetahedal voids. The density of fosteite (magnesium silicate) is 3.21 g/cc and that of fayalite 4 (feous silicate )is 4.34 g/cc. Find the fomula of fosteite and fayalite mineals and the pecentage of fayalite in an olivine with a density of 3.88 g/cc. Q.29 The mineal hawleyite, one fom of CdS, cystallizes in one of the cubic lattices, with edge length 5.87Å. The density of hawleyite is 4.63 g cm 3. (i) In which cubic lattice does hawleyite cystallize? (ii) Find the Schottky defect in g cm 3. Q.30 A stong cuent of tivalent gaseous boon passed though a gemanium cystal deceases the density of the cystal due to pat eplacement of gemanium by boon and due to intestitial vacancies ceated by missing Ge atoms. In one such expeiment, one gam of gemanium is taken and the boon atoms ae found to be 150 ppm by weight, when the density of the Ge cystal deceases by 4%. Calculate the pecentage of missing vacancies due to gemanium, which ae filled up by boon atoms. Atomic wt. Ge = 72.6, B = 11 Page 13 of 32 GASOUS STATE

14 FREE Download Study Package fom website: EXERCISE III Q.1 A solid has a stuctue in which W atoms ae located at the cones of a cubic lattice, O atom at the cente of the edges and Na atom at cente of the cubic. The fomula fo the compound is (A) NaWO 2 (B) NaWO 3 (C) Na 2 WO 3 (D) NaWO 4 Q.2 The density of CaF 2 (fluoite stuctue) is 3.18 g/cm 3. The length of the side of the unit cell is (A) 253 pm (B) 344 pm (C) 546 pm (D) 273 pm Q.3 Which of the following statements is coect in the ock-salt stuctue of an ionic compounds? (A) coodination numbe of cation is fou wheeas that of anion is six. (B) coodination numbe of cation is six wheeas that of anion is fou. (C) coodination numbe of each cation and anion is fou. (D) coodination numbe of each cation and anion is six. Q.4 The coodination numbe of cation and anion in Fluoite CaF 2 and CsCl ae espectively (A) 8:4 and 6:3 (B) 6:3 and 4:4 (C) 8:4 and 8:8 (D) 4:2 and 2:4 Q.5 The intestitial hole is called tetahedal because (A) It is fomed by fou sphees. (B) Patly same and patly diffeent. (C) It is fomed by fou sphees the centes of which fom a egula tetahedon. (D) None of the above thee. Q.6 The tetahedal voids fomed by ccp aangement of Cl ions in ock salt stuctue ae (A) Occupied by Na + ions (B) Occupied by Cl ions (C) Occupied by eithe Na + o Cl ions (D) Vacant Q.7 The numbe of neaest neighbous aound each paticle in a face-cented cubic lattice is (A) 4 (B) 6 (C) 8 (D) 12 Q.8 If the anions (A) fom hexagonal closest packing and cations (C) occupy only 2/3 octahedal voids in it, then the geneal fomula of the compound is (A) CA (B) CA 2 (C) C 2 A 3 (D) C 3 A 2 Q.9 A solid is fomed and it has thee types of atoms X, Y, Z. X foms a FCC lattice with Y atoms occupying all the tetahedal voids and Z atoms occupying half the octahedal voids. The fomula of the solid is: (A) X 2 Y 4 Z (B) XY 2 Z 4 (C) X 4 Y 2 Z (D) X 4 YZ 2 Q.10 The intemetallic compound LiAg cystallizes in cubic lattice in which both lithium and silve have coodination numbe of eight. The cystal class is (A) Simple cubic (B) Body cented cubic (C) Face cented cubic (D) None Q.11 A compound XY cystallizes in BCC lattice with unit cell edge lenght of 480 pm. If the adius of Y is 225 pm, then the adius of X + is (A) pm (B) pm (C) 225 pm (D) 255 pm Q.12 The mass of a unit cell of CsCl coesponds to (A) 1 Cs + and 1 Cl (B) 1 Cs + and 6 Cl (C) 4 Cs + and 4 Cl (D) 8 Cs + and 1 Cl Page 14 of 32 GASOUS STATE

15 FREE Download Study Package fom website: Q.13 In the closest packing of atoms A (adius : a ), the adius of atom B that can be fitted into tetahedal voids is (A) a (B) a (C) a (D) a Q.14 Which one of the following schemes of odeing closed packed sheets of equal sized sphees do not geneate close packed lattice. (A) ABCABC (B) ABACABAC (C) ABBAABBA (D) ABCBCABCBC Q.15 An ionic compound AB has ZnS type stuctue. If the adius A + is 22.5 pm, then the ideal adius of B would be (A) pm (B) 100 pm (C) pm (D) none of these Q.16 NH 4 Cl cystallizes in a body-centeed cubic type lattice with a unit cell edge length of 387 pm. The distance between the oppositively chaged ions in the lattice is (A) pm (B) pm (C) pm (D) pm Q.17 + = 95 pm and =181 pm in NaCl (ock salt) stuctue. What is the shotest distance between Na Cl Na + ions? (A) pm (B) 276 pm (C) pm (D) pm Q.18 In diamond, cabon atom occupy FCC lattice points as well as altenate tetahedal voids. If edge length of the unit cell is 356 pm, then adius of cabon atom is (A) pm (B) pm (C) pm (D) 89 pm Q.19 Which of the following will show schottky defect (A) CaF 2 (B) ZnS (C) AgCl (D) CsCl Q.20 Give the coect ode of initials T (tue) o F (false) fo following statements. I. In an anti-fluoite stuctue anions fom FCC lattice and cations occupy all tetahedal voids. II. If the adius of cations and anions ae 0.2 Å and 0.95 Å then coodinate numbe of cation in the cystal is 4. III An atom/ion is tansfeed fom a lattice site to an intestitial position in Fenkel defect. IV. Density of cystal always inceases due to substitutinal impuity defect. (A) TFFF (B) FTTF (C) TFFT (D) TFTF Page 15 of 32 GASOUS STATE

16 FREE Download Study Package fom website: EXERCISE IV Q.1 The edge length of unit cell of a metal having atomic weight 75 g/mol is 5 Å which cystallizes in cubic lattice. If the density is 2 g/cc then find the adius of metal atom. (N A = ). Give the answe in pm. [JEE 2006] Q.2 An element cystallises in FCC lattice having edge length 400 pm. Calculate the maximum diamete which can be placed in intestital sites without distubing the stuctue. [JEE 2005] Q.3 Which of the following FCC stuctue contains cations in altenate tetahedal voids? (A) NaCl (B) ZnS (C) Na 2 O (D) CaF 2 [JEE 2005] Q.4(i) AB cystallizes in a ock salt stuctue with A : B = 1 : 1. The shotest distance between A and B is Y 1/3 nm. The fomula mass of AB is Y amu whee Y is any abitay constant. Find the density in kg m- 3. (ii) If measued density is 20 kg m- 3. Identify the type of point defect. [JEE 2004] Q.5 Mables of diamete 10 mm each ae to be aanged on a flat suface so that thei centes lie within the aea enclosed by fou lines of length each 40 mm. Sketch the aangement that will give the maximum numbe of mables pe unit aea, that can be enclosed in this manne and deduce the expession to calculate it. [JEE 2003] Q.6 A substance A x B y cystallises in a FCC lattice in which atoms A occupy each cone of the cube and atoms B occupy the centes of each face of the cube. Identify the coect composition of the substance A x B y. (A) AB 3 (B) A 4 B 3 (C) A 3 B (D) composition cannot be specified [JEE-2002] Q.7 The figues given below show the location of atoms in thee cystallogaphic planes in FCC lattice. Daw the unit cell fo the coesponding stuctue and identify these planes in you diagam. [JEE-2000] Q.8 In a solid AB having NaCl stuctue A atoms occupy the cones of the cubic unit cell. If all the face-cented atoms along one of the axes ae emoved, then the esultant stoichiomety of the solid is (A) AB 2 (B) A 2 B (C) A 4 B 3 (D) A 3 B 4 [JEE-2000] Q.9 In any ionic solid [MX] with schottky defects, the numbe of positive and negative ions ae same.[t/f] [JEE-2000] Q.10 The coodination numbe of a metal cystallising in a hcp stuctue is [JEE-2000] (A) 12 (B) 4 (C) 8 (D) 6 Q.11 A metal cyatallises into two cubic phases, FCC and BCC whose unit cell lengths ae 3.5 and 3.0 Å espectively. Calculate the atio of densities of FCC and BCC. [JEE-1999] Page 16 of 32 GASOUS STATE

17 Q.12 Which of the following statements ae coect : (A) The coodination numbe of each type of ion in CsCl is 8. (B) A metal that cystallises in BCC stuctue has a coodination numbe 12. (C) A unit cell of an ionic cystal shaes some of its ions with othe unit cells (D) The length of the unit cell in NaCl is 552 pm. = 95 pm ; = 181 pm ] [JEE-1998] [ + Na Cl Q.13 In the sodium chloide stuctue, each Na + ion is suounded by six Cl neaest neighbous and Na + ions next neaest neighbous. [JEE-1997] Page 17 of 32 GASOUS STATE Q.14 A unit cell of sodium chloide has fou fomula units. The edge length of the unit cell is nm. What is the density of sod. chloide. [JEE-1997] FREE Download Study Package fom website: Q.15 Chomium cystallises with bcc lattice. The unit cell length is 287 pm. Calculate atomic ad. What would be the density of chomium. [JEE-1997]

18 ANSWER KEY EXERCISE I Q.1 A-B Q.2 AuCu 3 Q.3 A 4 B 2 C 2 Q %, +4 Q.5 ZnAl 2 O 4 Q pm, 534 pm, 378 pm Q pm, pm, pm Q g cm 3 Q atoms Q.10 FCC Page 18 of 32 GASOUS STATE Q % Q pm, pm Q.13 6 FREE Download Study Package fom website: Q pm Q g/cm 3, pm Q g cm 3 Q g cm 3 Q.19 a = cm, V= cm 3 Q Å PROFICIENCY TEST 1. F 2. T 3. T 4. T 5. F 6. T 7. T 8. F 9. T 10. T a = a = 4] 13. cubic close, FCC 14. hexagonal close, HP 15. c = least o minimum a deceases, emains constant EXERCISE II Q pm Q pm Q.3 AB 2 O 4 Q pm, No Q Q.6 4, 6, 8 Q g/cc, 8.59 gm/cm 3 Q.8 (a) 1.143, (b) Q gm/cm 3, atoms of A, unit cells Q gm/cm 3 Q Å Q Å Q Q.15 (a) octahedal, (b) 1/4 Q Å Q mol 1 Q , 79.3% Q.19 (a) MnF 3, (b) 6, (c) 4.02Å Q.20 (a) 1.49 Å, (b) 1.37 g/cm 3

19 Q.21 (a) 2.88 Å, (b) 12, (c) 19.4 g/cc Q.22 4 molecules of H 2 O Q.23 fo Fe is bcc, fo V is bcc, fo Pd is face centeed Q.24 (a) 4.5 Å, (b) 5.2 Å, (c) 8, (d) 6, (e) 0.92 g/cm 3 Q.26 XY 3, 4.38 g/cm 3 Q.27 (a) 3.52 Å,(b) 1.24 Å Q.28 Mg 2 SiO 4, Fe 2 SiO 4, 59% Q.29 (i) 3.90, (ii) g/cc Q % EXERCISE III Q.1 B Q.2 C Q.3 D Q.4 C Q.5 C Q.6 D Q.7 D Q.8 C Q.9 A Q.10 B Q.11 B Q.12 A Q.13 B Q.14 C Q.15 B Q.16 A Q.17 D Q.18 A Q.19 D Q.20 D EXERCISE IV Q pm Q pm Q.3 B Q.4 (i) = 5 kg m 3 (ii) Thee is huge diffeence in theoetically calculated density and obseved density. It is only possible if some foeign species occupies intestitial space i.e. substitution defect. Q.5 Discuss Q.6 A Q.7 Discuss Q.8 D Q.9 Tue Q.10 A Q Q.12 A, C, D Q Q g/cm 3 Q.15 (i) pm, (ii) 7.30 g/cm 3