Solid State Chemistry Iit

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com This file was last updated on 5th January, 2010. For the latest updates, visit http://www.adichemistry.com

1

1)

CRYSTAL SYSTEMS The number of basic crystal systems based on their symmetry elements and crystallographic parameters is 1) 14 2) 7 3) 230 4) 32 Note : In the seven basic or primitive crystal systems, the lattice points are present only at the corners of unit cell. But in case of fourteen Bravais lattices, the lattice points are also present at the centre or at the edges or at the centre of faces of unit cell.

2)

Match the following Crystal system

Parallelopiped dimensions

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TYPES OF SOLIDS 1) The characteristics of crystalline solids 1) Definite shape 2) Long range orders 3) Anisotropic 4) All 2) Choose the incorrect statement 1) Amorphous solids are isotropic and have only short range orders. 2) Crystalline solids have sharp melting points. 3) Amorphous solids have sharp melting points. 4) Amorphous solids are also called as super cooled liquids. 3) Match the following. A) Ionic crystals 1) Diamond, Silicon etc., B) Molecular crystals 2) Cu, Zn, Na etc., C) Covalent crystals 3) Solid CO2, I2 etc., D) Metallic crystals 4) KCl, Na2SO4 etc., The correct match is A B C D 1) 1 2 4 3 2) 4 3 2 1 3) 4 3 1 2 4) 3 4 1 2 4) The substance which exhibits electrical conductivity in the solid state is 1) NaCl 2) Diamond 3) Silver 4) Both 1 & 3 5) The molecular crystal which shows electrical conductivity is 1) Diamond 2) Silica 3) Silver 4) Graphite 6) Conversion of amorphous substances into crystalline state by slow cooling of liquids of amorphous substances is called 1) Crystallization 2) Annealing 3) Racemization 4) None 7) Low melting points, bad electrical conductivity and softness are the characteristics of 1) Ionic crystals 2) Covalent crystals 3) Metallic crystals 4) Molecular crystals 8) The type of attractions present between molecules in ice are 1) vander Waal’s attractions 2) Covalent bonds 3) Hydrogen bonds 4) Both vander Waal’s attractions and Hydrogen bonds 9) Ionic solids are generally 1) Good conductors of electricity 2) Quite hard 3) Quite brittle 4) Volatile 10) The units which occupy lattice points in covalent solids are 1) Molecules 2) Ions 3) Atoms 4) covalent bonds

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SOLID STATE CHEMISTRY

2) a = b = c;       900

C) Orthorhombic

3) a = b  c;       900

D) Triclinic 4) a  b  c;       900 Correct Matching is A B C D 1) 2 3 1 4 2) 2 3 4 1 3) 2 4 3 1 4) 4 2 1 3 Which of the following crystal system has not been correctly characterized ?

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3)

B) Tetragonal

1) Rhombohedral ; a = b = c ;       900

2) Monoclinic ; a  b  c ;     900 ;   900 3) Hexagonal ; a = b  c ;  = =900 ,   1200 4)

5)

4) Orthorhombic ; a = b = c;      Match the following A) Triclinic B) Cubic C) Orthorhombic D) Monoclinic Correct matching is A B C D 1) 3 1 4 2 2) 2 3 4 1 3) 1 2 3 4 4) 4 3 2 1 Rhombohedral crystal system is present in 1) KMnO4 2) Calcite

1) NaCl, diamond & ZnS 2) KNO3,  - S & MgSO4.7H2O 3) CuSO4. 5H2O, K2Cr2O7 & H3BO3 4)  -S, NaHCO3 & FeSO4.7H2O

3) Bi

4) Calcite

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Note: Other examples are KMnO 4,Bi, As, Sb, NaNO 3 etc.,

6)

7)

Choose the incorrect statement (s) 1) Ice and quartz can crystallise in either hexagonal or trigonal forms 2) Cinnabar has hexagonal crystal system 3) Tetragonal crystal system is present in CaF2 4) 1 & 2 only. The substance with monoclinic crystal system is 1) Glauber’s salt 2)  - sulfur 3) K2Cr2O7 4) All Note:  - sulfur, Monoclinic gypsum, NaHCO 3, FeSO 4.7H 2O etc.,

8,) The parameters of crystal system in graphite are 1) a = b  c ;     900 ;   1200

2) a = b = c ;     

3) a  b  c ;     

4) All

Note : Other examples with hexagonal arrangement are Mg, SiO 2 and ZnO

9)

The crystal system present in white tin is 1) Hexagonal 2) Tetragonal

3) Triclinic

Note : Other examples with tetragonal arrangement are TiO 2 , NiSO 4 , SnO 2 and K4 [Fe(CN) 6 ]

4) Cubic

2

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com A) Cubic 1) a  b  c;       900

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 10) The crystal system without any rotational axis of symmetry is 1) Triclinic 2) Cubic 3) Hexagonal 4) None 11) The relation between crystallographic angles in monoclinic crystal system is 2)       900

3)      4)     900 ;   1200 12) The correct parallelopiped dimensions for the crystal system in baryta (BaSO4) are 1) a  b  c;       900

2) a  b  c;       900

3) a  b  c;       900

4) a  b  c;     

Hint :

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13) The crystal system with the crystallographic angles       900 is 1) Cubic 2) Tetragonal 3) Orthorhombic 4) All 14) The relation between crystallographic axes in Na2B4O7.10H2O and H3BO3 is 1) a  b  c 2) a = b = c 3) a  b = c 4) a = b  c Na2B 4O 7.10H 2O

- Monoclinic

H 3BO 3

- Triclinic

15) The changes in the crystallographic parameters in the following conversion are Sα  Sβ

1) a  b  c  a = b = c

2)           900 ;   900

3)            4) a  b  c  a  b  c 16) The unit cell present in the crystal lattice of diamond is 1) Cubic 2) Tetragonal 3) Hexagonal 4) Trigonal 17) CuSO4.5H2O belongs to 1) Triclinic system 2) Cubic system 3) Tetragonal system 4) Hexagonal system 18) The number of bravais lattices possible in a cubic crystal system is equal to 1) 1 2) 2 3) 3 4) 4 Note : Simple cube (P), fcc (F) and bcc ( I ) are possible for cubic system.

19) In which of the following bravais systems, only the primitive arrangement of lattice points in the unit cell is possible ? 1) Hexagonal 2) Trigonal 3) Triclinic 4) All Key is available from http://www.adichemistry.com

Note : In the primitive unit cell, the lattice points are present only at the corners.

20) The types of bravais lattices possible for orthorhombic system are 1) P only 2) P & I 3) P, I & F 4) P, I, F & C Note :

P - Primitive I - Body - centred F - Face - centred C - End - centred

21) The number of C3 axes (three fold axes) of symmetry present in a cubic system 1) 2 2) 3 3) 4 4) No C3 axis of symmetry Note : C 3 axis of symmetry passes through the diagonally opposite corners

22) Which of the following crystal system possesses C6 axis of symmetry ? 1) Trigonal 2) Hexagonal 3) Cubic 4) All

1)

PACKING OF ATOMS & TYPES OF UNIT CELLS The type of unit cell obtained when two dimensional square close packed layers are arranged over each other such that the spheres in the second layer are present exactly over the spheres of first layer is 1) Body centred cubic 2) Primitive cubic 3) Face centred cubic 4) Hexagonal

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1)     900 ;   900

3

4

The two dimensional square close packed layers are arragenged such that the spheres in evey next layer are arraged over the voids of the first layer. The unit cell obtained is 1) BCC 2) FCC 3) HCP 4) CCP

3)

The unit cell present in ABAB.... type of closest packing of atoms is 1) Tetragonal 2) Hexagonal 3) Face centred cube 4) Primitive cube

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2)

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Note : There are two types of closest packing layers in three dimensional hexagonal close packing arrangement. The spheres in the second layer (B) are present over the voids of one type in first layer (A)

4)

The unit cell present in ABCABC... type of closest packing of atoms is 1) Hexagonal 2) Primitive cube 3) Body centred cube

4) Face centred cube

Note : In the face centred cube or cubic close packing, the closest packing layers are arranged in ABCABC pattern. The spheres in the second layer (B) are arranged over one type of voids in the first layer (A). whereas the spheres in the third layer (C) are placed over the second type of voids of first layer (A)

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com

The co-ordination number in body centred cubic lattice is 1) 6 2) 8 3) 12 4) 4

6)

The number of nearest atoms surrounding a given atom in a metallic crystal containing primitive cubic unit cell is 1) 6 2) 8 3) 12 4) 4

7)

The co-ordination number in hcp and ccp type of metallic crystals is 1) 4 2) 8 3) 12 4) 6

8)

The number of atoms per a single primitive cubic unit cell is 1) 8 2) 4 3) 2

4) 1

5

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5)

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com

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Note : The atom at the corner is shared amongst eight unit cell 1

9)

The number of atoms per a single body centred unit cell is 1) 1 2) 2 3) 4

4) 9

Hint : There is one atom at the centre of the unit cell along with atoms at eight corners 1

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 no. of atoms per unit cell = 1+ (8 x 8 ) =2

10) The number of atoms per a single face centred cubic unit cell is 1) 2 2) 4 3) 8

4) 12

Hint : In the face cented cubic unit cell, there are atoms at of 6 faces along with atoms at 8 corners. 1

1

 no. of atoms = (8 x 8 ) + (6 x 2 ) = 4

11) The number of atoms in an end centred cubic unit cell is 1) 2 2) 1 3) 4

4) 8

Hint : In the end centred cubic unit cell, there are two atoms at the centres of two opposite faces along with atoms at eight corners. 1

1

 no. of atoms = (8 x 8 ) + (2x 2 ) = 2

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12) The number of atoms in hexagonal prismatic unit cell is 1) 2 2) 4 3) 6

Note :

1

4) 12

1

contribution from top & bottom layers  2x[(6x 6 )  2 ]  3 contribution from middle layer = 3  Total no.of atoms = 3 + 3 = 6

13) The relation between radius (r) of atom and edge length (a) in the primitive cubic unit cell of closest packed atoms is 1) r = 2a 2) r = a / 2 3) r = a 4) r = 4a

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 no. of atoms per unit cell = 8 x 8 =1

1) r =

3 a 4

2) r =

2 a 4

3) r =

3 a 2

4) r =

2a

Derivation : In BCD 2

2

2

2

2

BC  BD  DC  a  a  2 a

2

In ABC AC

2

2

 AB  BC

2

2

 a  BC

2

2

 a  2a

2

 3a

2

But AC  4 r  AC  4 r 

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3a 3 r  a 4

15) The relation between radius (r) of atom and edge length (a) in the face centred cubic unit cell is 1) r =

3 a 4

2) r =

2 a 4

3) r =

4) r =

2a

3 a 2

Derivation : In ABC 2

2

AC  AB  BC

4r 

2

 a a

 4r  r 

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2

16) The metal which crystallises in simple cubic arrangement is 1) Po 2) Al 3) Mg 17) The type of unit cell present in sodium metal is 1) BCC 2) FCC 3) HCP

2

2

 2a

2

2a 2 a 4

4) All

4) none

Note : Other examples with bcc structure are K, Rb, Cs, Ba, Cr, Mo and W

18) The metal which has fcc arrangement in its crystal is 1) Cs 2) Al 3) Zn

4) W

Note : Other examples with fcc arrangement are Cu, Au, Pb, Pt, Pd, Ni and Ca

19) The metal which has hcp arrangement 1) Be 2) Mg

3) Zn

4) All

3) bcc structure

4) rhombic structure

Note : Other examples are Cd, Co, Ti & Tl

20) All the noble gases, except helium, crystallise in 1) hcp structure 2) ccp structure Note : Helium crystallises in hcp structure

21) The crystal structure in solid H2 is 1) hcp 2) ccp 3) bcc 4) All 22) If the atomic radius of ‘Cs’ is 235 pm, then the edge length of unit cell in ‘Cs’ metal will be 1) 54.27 pm 2) 542.7.A0 3) 54.27 X 10-10m 4) 5.427.A0 Note : 1 Picometer (pm) = 10 -12 . meters

= 10-2A0

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 7 14) The relation between radius (r) of atom and edge length (a) in the body centred cubic unit cell of closest packed atoms is

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 23) The edge length of unit cell in ‘Cu’ metal is 3.62 A0. The atomic radius of ‘Cu’ will be 1) 1.28 A0 2) 3.62 A0 3) 1.81 A0 4) 1.52 A0

8

24) The length of a face diagonal of a simple cubic unit cell is 120 pm. The radius of the atom is 1) 60 pm 2) 42.4 pm 3) 72 pm 4) 47.3 pm 25) The edge length of unit cell in potassium metal, which crystallises in body centred cubic lattice, is‘y’ cm. The length of body diagonal of the unit cell is 1)

2 y cm

3 y cm

2)

3)

3 y cm 4

4) 4 2 y cm

Hint : There are three atoms touching each other along the body diagonal of the body centred cubic unit cell.

 Length of body digonal = 4r =

3 a.

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26) Chromium is crystallised in body centred cubic structure. The edge length of unit cell in chromium is 293.3 pm. The distance between two nearest atoms in the unit cell is 1) 63 pm 2) 293.3 pm 3) 127 pm 4) 254 pm Hint : The two nearest atoms in bcc are present along the body diagonal.

3

 Nearest distance = d = 2r =

a

2

27) The nearest distance (d) between two atoms in Nickel metal is 248 pm. The edge length (a) of the unit cell will be 1) 124 pm 2) 350.6 pm 3) 68 pm 4) 412 pm Hint : The two nearest atoms in fcc are arranged along the face diagonal of the unit cell.

3

 Nearest distance (d) = 2r =

a (  4r =

2 a)

2

Note: Nickel crystallises in face centred cubic lattice.

28) A metal crystallises into a lattice containing a sequence of layers of ABC ABC-----. If the radius of metal atoms is 174 pm, then the distance between the two successive layers (i.e., A and B) is 1) 348 pm 2) 174 pm 3) 284. 2 pm 4) 492. 2 pm Hint : ABCABC ---- pattern gives rise to face centred cubic lattice. The layers (ABCA) are present perpendicular to the body diagonal of the unit cell.

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 The distance between two successive layers

=

length of body diagonal 3

3a

=

3

3

4

.

=

3

r

2

2

 2r 3

29) Magnesium crystallises into a lattice containing closely packed layers in ABAB____ pattern. The distance between each successive layers is 217 pm. What is the radius of magnesium atom? 1) 133 pm 2) 217 pm 3) 108.5 pm 4) 266 pm Hint: ABAB---- pattern of arrangement of layers is otherwise known as hexagonal cubib packing. The distance between two successive layers in this type of packing is same as that of cubic close packing i.e.,

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Note : Cu crystallises in fcc structure

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com

9

2  2r 3

3

3

3

3

3

4 3 4  3  4  2  2) 2 x   3) 4 x   4)  r a a   3 3  4  3  4  31) The volume occupied by atoms in a body centred cubic unit cell is (where ‘a’ is edge length) 4 a 1)    3 2

3

4 a 1)    3 2

3

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4 3 4  3  4  2  2) 2 x   3) 4 x   4)  r a a   3 3  4  3  4  32) The volume occupied by atoms in a face centred cubic unit cell is (where ‘a’ is edge length) 4 a 1)    3 2

3

4  3  4  2  2) 2 x   3) 4 x   a a  3  4  3  4  33) The percentage of packing of a simple cubic unit cell is 1) 52.4% 2) 47.6% 3) 74% Hint: The packing fraction of a unit cell =

3

4)

4 3 r 3

4) 68%

The volume occupied by the atoms in a single unit cell The volume of the unit cell

4  a 3 4 3   r  3  2 3  The packing fraction of body centred cubic unit cell = =  = 0.5238 3 3 6 a a  The percentage of packing = 0.5238 X 100  52.38%

34) The percentage of void volume in a simple cubic unit cell is 1) 47.6% 2) 68% 3) 52.4% 35) The percentage of packing of a body centred cubic unit cell is 1) 74% 2) 68% 3) 52.4%

4) 20% 4) 47.6%

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3 4  3  4 3 2 X  a   2 X r 3  4  3 3 Hint:  The packing fraction of body centred cubic unit cell = =   = 0.68 3 3 8 a a  The percentage of packing = 0.68 X 100  68%

36) The percentage of packing of hcp and ccp type of unit cells is 1) 74% 2) 52.4% 3) 92%

4) none

3 4  2  4 3 4 X  a   4 X r 3  4  2 3 Hint:  The packing fraction of cubic close packed unit cell = =   = 0.74 3 6 a a3  The percentage of packing = 0.74 X 100  74%

Note: The packing fraction of hexagonal cubic packed unit cell is also 0.74

37) The percentage of void volume in face centred cubic lattice is 1) 26% 2) 0% 3) 32% 4) 12% 38) The atomic radius of aluminium is 1.26A0. The density of it in the solid state is 1) 3.33 g.cm-2 2) 3.7g.cm-3 3) 2.31g.cm-3 4) 3.96g.cm-3 Formula : M

1

density (  ) = Z. N . 3 a

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30) The volume occupied by atoms in a primitive cubic unit cell is (where ‘a’ is edge length)

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com where

10

Z = number of atoms in a unit cell M = Molar mass N = Avogadro number a3 = Volume of the unit cell

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39) The cubic unit cell of a metal ( molar mass 63.55g.mol-1) has an edge length of 362 pm. Its density is 8.92 g.cm-3. The type of unit cell is 1) primitive 2) face centred 3) body centred 4) end centred 40) A metal has a density of 1.984 g.cm-3 and it crystallises in face centred cubic crystal with edge length equal to 630 pm. The molar mass of the metal is 1) 37.35 g.mol-1 2) 56.02 g.mol-1 3) 74.70 g.mol-1 4) 65.36 g.mol-1 41) The numbers of tetrahedral and octahedral voids respectively present in closest packed crystals containing ‘X’ number of spheres are 1) 2X and X 2) X and 2X 3) 4X and 2X 4) 4X and X Note: The number of trigonal voids is equal to 8X.

42) The ratio of radius of trigonal void to the radius of the spheres in closest packed arrangement is 1) 0.414 2) 0.155 3) 0.225 4) 0.732 Derivation:

BE

In BDE, cosDBE =

BD rsphere

o

cos30 =

rsphere  rvoid

rsphere  rvoid 

rsphere

o

 2.

cos30

rsphere

3

rvoid =1.155 rsphere  rsphere  0.155 rsphere rvoid

 0.155 rsphere

rsphere

43) The ratio of radius of tetrahedral void to the radius of the sphere in closest packed arrangement is 1) 0.414 2) 0.225 3) 0.732 4) None Derivation:

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AC

In OAC ,

sinAOC = o

109 28

sin

,

AO

rsphere

=

2

(  AOB  109o 28, )

rsphere  rvoid

rsphere  rvoid 

rsphere o

sin 54 44

,



rsphere

0.8164

rvoid =1.225 rsphere  rsphere  0.225 rsphere rvoid

rsphere

 0.225 rsphere

44) The ratio of radius of octahedral void to the radius of the spheres in closest packed arrangement is 1) 0.414 2) 0.155 3) 0.225 4) 0.732

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a = edge length Note : Aluminium crystallises in fcc structure.

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com

11

Derivation: cosABD = o

cos45 =

AB rsphere rsphere  rvoid

rsphere  rvoid 

rsphere

cos45

o



2

rsphere

rvoid =1.414 rsphere  rsphere  0.414 rsphere rvoid

 0.414 rsphere

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rsphere

45) The ratio of radius of cubic void to the radius of surrounding closely packed atoms whose centres lie at the corners of a cube is 1) 0.414 2) 0.155 3) 0.225 4) 0.732

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1)

IONIC CRYSTALS In the following diagram, the circles filled with black color represent the cations, whereas the big circles represent the anions.

which of the following is the correct statement about the given diagrams 1) The cation in diagram A is unstable. 2) The cation in diagram B is stable. 3) The cations in both the diagrams A & C are stable. 4) All

Note: The state of the atom or ion occupying any void in a crystal lattice is stable only when it is touching the surrounding atoms or ions.

2)

Match the following Limiting radius ratio A) 0.155 - 0.225 B) 0.225 - 0.414 C) 0.414 - 0.732 D) 0.732-0.999 The correct matching is A B 1) 1 3 2) 3 2

Geometry 1) Tetrahedral 2) Octahedral 3) Trigonal 4) Body centred cubic

C 2 4

D 4 1

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BD In ABD ,

Note: The cation can touch the anions when it occupies trigonl or tetrahedral voids, but it will be more stable in octahedral void as it is surrounded by more number of anions. It will be less stable in body centred cubic void, even though it is surrounded by even more anions, as it cannot touch the anions

5)

The Cl- ions are arranged in expanded cubic close packing in NaCl crystal. The radii of Na+ and Cl- ions are 95pm and 181 pm respectively. The type of voids occupied by Na+ ions is 1) Octahedral 2) Tetrahedral 3) Trigonal 4) All Hint:

6)

r  Na r   0.5248 Cl

The crystal structure present in NaCl is called 1) Fluorite structure 2) Rock-salt structure 3) Anti-fluorite structure

4) Spinel structure

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Note : In Rock-salt structure, the bigger anions occupy the lattice points of expanded face centred cubic lattice. The smaller cations occupy all the octahedral holes. The limiting radius ratio is in between 0.414 and 0.732. The co-ordination numbers cation and anion are (6:6). The general formula of ionic compounds having this structure is AB. Examples : NaCl, KCl, MgO, CaO, SrO etc.,

7) 8) 9)

The number of NaCl units present in a single unit cell of NaCl crystal is 1) 1 2) 2 3) 4 4) 6 + The number of octahedral holes occupied by Na ions in a single unit cell of NaCl is 1) 4 2) 8 3) 2 4) Zero Which of the following does not crystallise in the rock salt structure 1) NaCl 2) KCl 3) CsCl 4) MgO Note : Usually halides of Cesium assume BCC structures as the limiting radius ratio is greater than 0.732

10) The number of nearest Cl- ions around an Na+ ion in NaCl crystal is 1) 8 2) 6 3) 4 4) 12 11) The number of nearest Cl- ions arround a Cl- ion in NaCl crystal is 1) 8 2) 6 3) 4 4) 12 12) The radii of Na+ and Cl- ions are 95 pm and 181 pm respectively. The edge length of unit cell in NaCl is

Key is available from http://www.adichemistry.com

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 12 3) 3 1 2 4 4) 1 2 4 3 3) Match the following Co-ordination number Limiting radius ratio A)3 1) 0.155-0.225 B) 4 2) 0.225-0.414 C) 8 3) 0.414-0.732 D) 6 4) 0.732-0.999 Correct matching is A B C D 1) 1 2 3 4 2) 1 2 4 3 3) 1 3 2 4 4) 2 3 4 1 4) The limiting radius ratio for an ionic compound AB is 0.427. The smaller cation A+ will be more stable when it occupies 1) Tetrahedral voids 2) Octahedral voids 3) Trigonal voids 4) Body centred cubic voids

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 1) 457 pm 2) 552 pm 3) 190 pm 4) 362 pm

13

Note : edge length in NaCl = 2rc+ 2ra

4) None

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Note : BCC structure is present when the limiting radius ratio isgreater than 0.732. The anions occupy the lattice points of simple cubic lattice. The cations occcupy centred cubic voids. This structure can be considered as interpenetrating primitive cubic lattices of cation and anion. The co-ordination numbers are (8:8). The number of formula units present per a single unit cell is one (one cation and one anion). The general formula is AB. Examples : CsCl, CsBr, CsI, CsCN, TlCl, TlBr, TlI, TlCN etc.,

14) The number of nearest Cl- ions present around a Cs+ ions in CsCl crystal is 1) 6 2) 8 3) 12 4) 4 15) The number of nearest Cs+ ions present around a Cs+ ion in CsCl crystal is 1) 8 2) 6 3) 4 4) 12 Hint : If only Cs+ ions are considered they occupy lattice points of primitive cubic lattice

16) The number of second nearest Cs+ ions present around a Cs+ ion in CsCl is 1) 4 2) 8 3) 12 4) 6 + 17) The radii of Cs and Cl ions are 1.69 Å and 1.81 Å respectively. The edge length of the unit cell in CsCl will be 1) 7 Å 2) 3.38 Å 3) 4.04 Å 4) 3.5 Å Hint : In BCC, the ions touch along the body diagonal  Length of body diagonal = 2rc+2ra =

3a

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18) The ionic compound which crystallises in anti-fluorite structure is 1) NaCl 2) Na2O 3) CaF2

4) Al2O3

Note : In the anti-fluorite structure, anions are arranged in cubic closest packing and cations occupy all the tetrahedral voids. There are four anions and eight cations per unit cell of this structure and hence, the general formula of an ionic compound is A8B4 or A2B. The ideal radius ratio is between 0.225 - 0.414. But this ratio is not always maintained.The co-ordination numbers of cation and anion are (4:8). Examples : Na2O, K2O, Li2O, Rb2O, K2S, Cl2O, Na2S etc.,

19) In a unit cell of an ionic crystal, anions (Y) occupy the lattice points of face centred cubic lattice and cations (X) occupy all the tetrahedral voids. The formula of the ionic compound will be 1) XY2 2) X2Y2 3) X2Y 4) XY 20) The number of anions per a single unit cell in antifluorite structure is 1) 2 2) 4 3) 8 4) 1

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13) The crystal structure present in CsCl is referred to as 1) FCC 2) BCC 3) HCP

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Note : In the fluroite structure, the cations are arranged into cubic close packing and the anions occupy all the tetrahedral voids. Thus there are four cations and eight anions per a unit cell. Hence the formula of ionic compound is A4B8 or AB2. The co-ordination numbers of cation and anion are (8:4). Examples : CaF2, ZrO2, UO2, ThO2, BaF2, BaCl2, SrCl2, PbCl2 etc.,

26) The number of anions per a single unit cell in fluorite structure is 1) 2 2) 4 3) 8 4) 1 27) The type of voids occupied by anions in fluorite structure is 1) Octahedral 2) Tetrahedral 3) Trigonal 4) Body centred cubic 2+ 28) The co-ordination number of Ca ions in CaF2 is 1) 2 2) 4 3) 8 4) None 29) The type of voids occupied by Ca2+ ions in CaF2 crystal is 1) Tetrahedral 2) Octahedral 3) Body centred cubic 4) Trigonal 30) The number of Ca2+ ions present per a single unit cell in CaF2 crystal is 1) 4 2) 2 3) 8 4) 12 2+ 31) The radii of Ca and F ions respectively are 100 pm and 131 pm. The edge length of the unit cell in CaF2 is 1) 231 pm 2) 533.5 pm 3) 462 pm 4) 362.5 pm Hint: The Fluoride ions are present along the body diagonal at one fourth distance from the corner of the cube. Hence the distance between calcium and fluoride ions is 1/4th of length of body diagonal.

32) The substance containing zinc-blende crystal structure is 1) NaCl 2) ZnCl2 3) BeO

4) CsCl

Note: In zinc-blende or sphalerite structure, anions occupy the face centred cubic lattice points and cations occupy half of the tetrahedral holes (of one type). The ideal radius ratio is in between 0.225 to 0.414. There are four anions and four cations in the unit cell. Therefore the formula is A4B4 or AB. The co-ordination numbers of cation and anion are (4:4). Examples: ZnS, BeO etc.,

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 14 21) The type of voids occupied by cations in antifluorite structure is 1) Octahedral 2) Tetrahedral 3) Trigonal 4) Body centred cubic 22) The co-ordination number of Na+ ions in Na2O is 1) 2 2) 4 3) 8 4) None 23) The type of voids occupied by O2- ions in Na2O crystal is 1) Tetrahedral 2) Octahedral 3) Body centred cubic 4) Trigonal + 24) The number of Na ions present per a single unit cell in Na2O crystal is 1) 4 2) 2 3) 8 4) 12 25) The fluorite crystal structure is present in 1) NaF 2) CaF2 3) AlF3 4) CsF

15

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33) The number of anions per a single unit cell in zinc-blende structure is 1) 2 2) 4 3) 8 4) 1 34) The type of voids occupied by cations in zinc-blende structure is 1) Octahedral 2) Tetrahedral 3) Trigonal 4) Body centred cubic 2+ 35) The co-ordination number of Zn ions in ZnS is 1) 2 2) 4 3) 8 4) None 236) The type of voids occupied by S ions in ZnS crystal is 1) Tetrahedral 2) Octahedral 3) Body centred cubic 4) Trigonal 2+ 37) The number of Zn ions present per a single unit cell in ZnS crystal is 1) 4 2) 2 3) 8 4) 12 38) The co-ordination number of S2- ions in ZnS is 1) 2 2) 4 3) 8 4) None 39) The compound containing spinel structure is 1) MgAl2O4 2) Fe2O3 3) ThO2 4) KCl Note: In spinel structure, the oxide ions are arranged in cubical closest packing and one eighth of the tetrahedral holes are occupied by divalent metal ion (A2+) and one half of the octahedral holes are occupied by trivalent metal ions (B3+). Thus in a unit cell there are four oxide ions, one divalent metal ion(A2+) and two trivalent metal ions (B3+). The general formula of the compound is AB2O4.

Examples: MgAl2O4,ZnAl2O4, ZnFe2O4 etc.,

40) The crystal structure present in Al2O3 is called as 1) corundum structure 2) spinel structure 3) rock-salt structure

4) Fluorite structure

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Note: In the corundum structure, anions form hexagonal closest packing and cations are present in 2/3 of the octahedral holes. The general formula of the compound is M2O3. Examples: Fe2O3, Al2O3, Cr2O3 etc.,

41) Inverse spinel structure is found in 1) Chromite 2) Magnetite

1)

3) Spinel

4) Corundum

X-RAY DIFFRACTION AND BRAGG’S EQUATION The diffraction of barium with X - radiation of wavelength 2.29A0 gives a first order diffraction at 300. What is the distance between diffracted planes ? 1) 2.29 A0 2) 2.73 A0 3) 4.58 A0 4) None Formula : nλ=2d sin

2)

3)

4)

At λ what angles for the first order diffraction, spacing between two planes respectively are λ and ? 2 0 1) 90 & 300 2) 300 & 900 3) 900 & 00 4) 00 & 900 An X - ray beam of wavelength 71pm was scattered by a solid. The angle of diffraction (2 θ ) for a second order reflection is 140661. The inter planar distance in the crystal will be 1) 710 pm 2) 559 pm 3) 142 pm 4) 71 pm The interplanar distance in a crystal used for X-ray diffraction is 0.2nm. The angle of incidence ( θ ) of X-rays is 90. If the diffraction is of first order, Find the wavelength of the X-rays.

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com

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1)

DEFECTS IN CRYSTALS MAGNETIC & ELECTRICAL PROPERTIES The incorrect statement related to schottky defect is 1) It is a stoichiometric point defect 2) Equal number of cations and anions are missing from their lattice points. 3) Shown by strongly ionic crystals with high co-ordination number. 4) Density & covalent nature are increased.

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Note: In Schottky defect, pair of holes are formed as both the cations and anions (with equal but opposite charge) leave the lattice points and move out of the crystal. This is a stoichiometric point defect. The defected crystal is electrically neutral. But density and covalent nature are decreased. Dielectric constant and hence ionic nature are increased. Defected crystals show little electrical conductivity. Schottky defects are shown by ionic compounds with high co-ordination numbers. The difference in the sizes of oppositely charged ions is small. Usually these defects are shown by compounds of big sized alkali and alkaline earth metals. Eg., NaCl, CsCl etc., It is a thermodynamic defect. The number of defects increase with increase in temperature.

2)

Creation of holes due to transfer of a cation from its lattice point to the interstitial space is called 1) Schottky defect 2) Metal excess defect 3) Frenkel defect 4) F-centre formation Note: In Frenkel defect, the cations, being small can move from the lattice points to interstitial spaces and thus by creating holes. This is a stoichiometric point defect. The defected crystal is electrically neutral. But density and covalent nature are decreased. Dielectric constant and hence ionic nature are increased. Defected crystals show little electrical conductivity. This defect is shown by ionic compounds with low co-ordination numbers. The difference in the sizes of oppositely charged ions must be large. Usually these defects are shown by compounds of small sized transition metals. Eg., AgCl, AgBr, ZnS etc., It is also a thermodynamic defect. The number of defects increase with increase in temperature.

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 16 1) 0.062 nm 2) 0.23nm 3) 0.43nm 4) 0.11nm 5) A first order diffraction of an X-radiation by crystal planes, separated by a distance of 231 pm, in a solid is observed at a reflection angle of 300. By using same radiation the first order diffraction is observed at 600 in another solid. The interplanar distance in the second solid will be 1) 462 pm 2) 400 pm 3) 115.5 pm 4) 322 pm 6) A first order diffraction by a crystal plane is observed at an angle of 150. by using x - rays of wavelength of 258 pm. If the interplanar distance is 500 pm, the second order of diffraction will be observed at 1) 7.280 2) 10.50 3)31.170 4) 9.20

9)

In which of the following non-stoichiometric defect, the cation occupies the interstitial site 1) Schottky defect 2) Frenkel defect 3) Metal excess defect 4) Metal deficiency defect 10) LiCl shows pink color when heated in Li vapour due to 1) Metal deficiency defect 2) Schottky defect 3) F-Centre formation 4) Frenkel defect Note : F-Centres are formed when an electron occupies anion vacancty in the crystal. They import color and paramagnetic nature to the crystals Eg : KCl in K vapours is blue lilac in color NaCl in Na vapour is yellow is color.

11) ZnO turns yellow upon heating because of 1) Metal excess defect 2) Metal deficiency defect

3) Frenkel defect

4) All

Note : When heated ZnO loses oxide ions reversibly. Excess Zn2+ ion and electrons are accomodated interstitially. Due to presence of odd electrons, ZnO turns yellow. The electrical conductivity is also improved. This type of defect due to pressence of extra cation and electtrons is also shown by CdO, Cr2O3 and Fe2O3.

12) The formula of wustite ranges from Fe0.93O to Fe0.96O instead of FeO. It is due to presence of 1) Frenkel defect 2) Schottky defect 3) Metal deficiency defect 4) Metal excess defect Note : Some compounds cannot be prepared in ideal stiochimetric proportions due to metal dificiency defect. This defect arises when a metal cation is missing from its lattice points and the cahrge is balanced by an adjacent metal ion with extra

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 17 3) Frenkel defect is not possible in 1) AgCl 2) ZnS 3) CsCl 4) AgBr 4) Which of the following is not common for Schottky and Frenkel defects? 1) Stoichiometric 2) Increase in the number of defects with temperature 3) Decrease in density 4) Low lattice energy and stability of defected crystal 5) Consider the following statements. a) Both Schottky and Frenkel defects are non stiochiometric defects b) Crystals with Schottky and Frenkel defects show little electrical conductivity c) Frenkel defect is shown by ionic compounds with high co-ordination numbers and with big sized cations. d) Crystals with Schottky and Frenkel defects are electrically neutral The correct statements are 1) a & b 2) b & d 3) c & d 4) b, c & d 6) Which of the following point defect causes decrease in density of crystal without disturbing the stoichiometric ratio ? 1) Frenkel defect 2) Schottky defect 3) Metal excess defect 4) All 7) The stoichiometric point defect possible in AgBr is 1) Schottky defect 2) Frenkel defect 3) Both 1 & 2 4) Metal excess defect 8) Consider the following statements related to metal excess defect. a) Metal excess arises due to extra cation and electrons present at interstitial voids in a crystal b) Metal excess defect arises when anions leave the crystal from their lattice points . c) Crystal with metal excess defect is not neutral. d) Metal excess defect is a non-stiochiometric defect. The correct statement(s) is/are 1) a & c 2) b, c, & d 3) a, b & d 4) All

Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com

18

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13) Following are the statements relating to defects in crystals a) Frenkel defect is shown by ionic compounds where there is large difference in size between positive and negative ions. b) Zinc oxide turns yellow upon heating due to formation of metal deficiency defect c) The vacant anion sites occupied by electrons are called F-Centres d) The number of schottky and Frenkel defects decreases with increase in temperature The correct statements are 1) a only 2) a & c 3) a, b & c 4) a, c & d 14) Select the incorrect statement. 1) Schottky defect is shown by CsCl 2) Frenkel defect is shown by ZnS 3) F-Centres are formed due to leaving of metal ion from the lattice point. 4) Metal deficiencies defect is formed when the metal can exhibit variable oxidation number. 15) The composition of a sample of wustite is Fe0.93O. What percentage of iron is present as Fe(III)? 1) 7% 2) 15.05% 3) 30% 4) 26.3% 16) Addition of little SrCl2 to NaCl produces 1) Cation vacancies 2) Anion vacancies 3) Both cation & anion vacancies 4) None

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Note : When NaCl is doped with SrCl2, Sr2+ ions displace Na+ ions from their lattice points. Also at the same time, equal number of Na+ ions from other lattice sites move out of the crystal and thus by creating cation vacancies. Thus formed solids are called substitutional solids other examples:- AgCl doped by CdCl2.

17) If NaCl is doped with 10-4 mole% of SrCl2, the concentration of cation vacancies would be 1) 10-4 mole-1 2) 6.022 x 1017 mole-1 3) 6.002 x 10-4mole-1 4) 6.022 x 10-8 mole-1 18) Which one of the following is the correct statement ? 1) Brass is an interstitial alloy, while steel is a substitutional alloy. 2) Brass is a substitutional alloy, while steel is an interstitial alloy. 3) Brass & steel are both substitutional alloys. 4) Brass & steel are both interstitial alloys. 19) AgCl is crystallised from molten AgCl containing little CdCl2. The solid obtained will have 1) Cationic vacancies equal to number of Cd2+ ions incorporated

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exhibited by compounds of transition metals which can exhibit variable valency. As a result, there compounds show non stoichiometric formulae. Eg : VOX (x can be 0.6 - 1.3), Fe0.95O

Note : Ferroelectric substances are piezoelectric crystals with permanent dipoles.

32) Piezo-electric crystals with zero net dipole moment are called 1) Ferro electric 2) Pyro electric 3) Antiferro electric 33) The substance which exhibits anti-ferroelectricity is 1) BaTiO3 2) PbZrO3 3) KH2PO4 34) The crystals which produce electricity upon heating are referred to as

4) None 4) All

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 19 2) Cationic vacannies equal to double the number of Cd2+ ions incorporated. 3) Anionic vacancies 4) Neither cationic nor anionic vacancies. 20) The type of electrical conductivity shown by crystals with F - Centres is 1) n-type semiconductivity 2) p-type semiconductivity 3) Super conductivity 4) None 21) The conductivity of semiconductors is in the range of 1) 10-20 ohm-1 cm-1 2) 107 ohm-1 cm-1 3) 10-6 to 104 ohm-1 cm-1 4) None 22) Choose the correct statement 1) The energy gap between conduction band and valence band in metallic conductors is very large. 2) The energy gap between conduction band and valence band in semiconductors is very large. 3) Electrical conductivity of semiconductors increases with increasing temperature. 4) Electrical conductivity of conductors increases with increasing temperature. 23) Which of the following is an intrinsic semiconductor 1) Si 2) Si doped with As 3) Fe 4) Both 1 & 2 24) Silicon doped with III A group elements exhibit 1) n-type semi conductivity 2) p-type semi conductivity 3) Both 1 & 2 4) None 25) Germanium doped with phosphorus acts as 1) n-type semiconductors 2) p-type semiconductor 3) super conductor 4) Intrinsic conductor. 26) Solar photovoltaic cell used to convert radiant energy into electrical energy consists of 1) a ‘pnp’ triode 2) a ‘pn’ diode 3) an ‘npn’ triode 4) None 27) Which of the following is incorrect statement about super conductivity. 1) Super conductors show zero resistance to electrical conductivity. 2) The electrical resistance becomes zero at absolute zero temperature for all the substance 3) Super conductors are good insulators 4) None 28) Match the following A) Ferro magnetic 1) MnO, MnO2, FeO, NiO etc., B) Dia magnetic 2) Fe3O4, MgFeO4 etc., C) Anti ferri magnetic 3) ZnO, TiO2, NaCl etc., D) Ferri magnetic 4) Fe, Co, Ni etc., The correct matching is A B C D 1) 4 3 2 1 2) 4 3 1 2 3) 3 4 1 2 4) 4 2 3 1 29) The temperature above which the ferromagnetism is lost is called 1) Transition temperature 2) Bohr temperature 3) Curie temperature 4) none 30) The phenomenon of production of electricity by a polar crystal when mechanical stress is applied to it is called. 1) Antiferro electricity 2) Piezoelectricity 3) Magnetic electricity 4) None 31) A ferro electric substance is 1) KH2PO4 2) BaTiO3 3) Rochelle salt 4) All

20

REVISION

2.

3.

4. 5.

An AB2 type structure is found in : a) N2O b) NaCl c) Al2O3 d) CaF2 If the number of atoms per unit in a crystal is 2, the structure of crystal is : a) Simple cubic b) body centred cubic ( bcc ) c) octahedral d) face centred cubic ( fcc ) The intermetallic compound LiAg crystallizes in cubic lattice in which both lithium and silver have co - ordination number of eight. The crystal class is : a) Simple cubic b) body centred cube c) face centred cube d) none of these The vacant space in the bcc unit cell is : a) 23% b) 26% c) 32% d) none of these Potassium fluoride has NaCl type structure. What is the distance between K+ and F- ions if cell edge is a cm ? a a cm b) cm 2 4 Bragg’s law is given by the equation :

a) 6.

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1.

a) n  2  sin  b) n  2 d sin  7.

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9. 10.

11.

12.

13. 14.

15. 16.

d) 4a cm

c) 2 n  d sin 

d) n

 d  sin  2 2

The inter-ionic distance for Cesium chloride crystal will

2a a 3a c) d) 3 2 2 Sodium metal crystallizes as a body centred cubic lattice with the cell edge 4.29A0. what is the radius of sodit atom ? a) 1.857 x 10-8 cmb) 2.371 x 10-7 cm c) 3.817 x 10-8 cm d) 9.312 x 10-7 cm The edge of unit cell of fcc crystal of Xe is 620 pm. The radius of Xe atom is : a) 189.37 pm b) 209.87 pm c) 219.25 pm d) 235.16 pm 0 A metal has bcc structure and the egde length of its unit cell is 3.04 A . The volume of the unit cell in cm3 will be : a) 1.6 x 1021cm3 b) 2.81 x 10-23 cm3 c) 6.02 x 10-23 cm3 d) 6.6 x 10-24 cm3 A compound is formed by elements ‘A’ and ‘B’. This crystallizes in the cubic structure when atoms ‘A’ are at the corners of the cube and atoms ‘B’ are at the centre of the body. The simplest formula of the compound is : a) AB b) AB2 c) A2B d) AB4 In a cubic structure of compound which is made from X ad Y, where X atoms are at the corners of the cube. The molecular formula of the compound is : a) X2Y b) XY2 c) XY3 d) X3Y The structure of MgO is similar to NaCl. what would be the co-ordination number of magnesium? a) 2 b) 4 c) 6 d) 8 Most crystals show good cleavage because their atoms, ions or molecules are : a) weakly bonded together b) strongly bonded together c) spherically symmetrical d) arranged in planes An example of a non - stoichiometric compound is : a) PbO b) NiO2 c) Al2O3 d) Fe3O4 Doping of silicon ( Si ) with boron ( B ) leads to : a) a

8.

c) 2a cm

b)

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 1) Ferro electric 2) Pyro electric 3) Antiferro electric 4) None 35) The Ferro magnetic substance used in audio and video tapes is 1) FeO 2) CrO2 3) MnO 4) BaTiO3.

23. The number of atoms in 100g of an fcc crystal with density, d 

10g and cell edge equal to100 cm 3

pm, is equal to : a) 1 x 1025 b) 2 x 1025 c) 3 x 1025 d) 4 x 1025 24. Potassium has a bcc structure with nearest neighbour distance 4.52 A0. Its atomic weight is 39. Its

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density ( in kg m 3 ) will be : a) 454 b) 804 c) 852 d) 908 25. In orthorhombic, the value of a , b and c are respectively 4.2 A0, 8.6A0 and 8.3 A0.Given the molecular mass of the solute is 155 g mol 1 and that of density is 3.3 g / cc, the number of formula units per unit cell is a) 2 b) 3 c) 4 d) 6 26. A solid has a structure in which ‘ W ‘ atoms are located at the corners of a cubic lattic ‘ O ‘ atoms at the cube. The formula for the compound is a) Na2WO3 b) Na2WO2 c) NaWO2 d) NaWO3 27. In a solid ‘ AB ‘ having the NaCl structure, ‘A’ atoms occupy the corners of the cubic unit cell. If all the centre of the face - centred atoms along one of the axes are removed, then the resultant stoichiometry of the solid is : a) AB2 b) A2B c) A3B4 d) A4B3 28. The pyknometric density of sodium chloride crystal is 2.16 x 103 kg m-3, while its X - rays density is 2.178 x 103 kg m-3. The fraction of unoccupied sites in sodium chloride crystal is : a) 5.96 b) 5.96 x 101 c) 5.96 x 102 29. What type of crystal defect is indicated in the diagram below ? Na+ Cl- Na+ Cl- Na+ ClCl-  Cl- Na+  Na+ Na+ Cl- Na+  Na+ Cl-

d) 5.96 x 103

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 21 a) n - type semiconductor b) p - type semiconductor c) metal d) insulator 17. In the laboratory, sodium chloride is made by burning the sodium in the atmosphere of chlorine which is yellow in colour. The cause of yellow colour is : a) presence of electrons in the crystal lattice b) presence of Na+ ions in the crystal lattice c) presence of Cl- ions in the crystal lattice d) presence of face centred cubic crystal lattice 18. Frenkel defect is caused due to : a) the shift of a positive ion from its normal lattice site to an interstitial site. b) An ion missing from the normal lattice site creating a vacancy c) An extra positive ion occupying an interstitial position in the lattice d) An extra negative ion occupying an interstitial position in the lattic 19. Schottky defect generally appears in : a) KCl b) NaCl c) CsCl d) all of these 20. Due to Frenkel defect, the density of ionic solids : a) increases b) decreases c) does not change d) change 21. Na and Mg crystallize in bcc and fcc type crystals respectively, then the number of atoms of Na and Mg present in the unit cell of their respective crystal is : a) 2 and 4 b) 4 and 2 c) 9 and 14 d) 14 and 9 22. An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound a) AB b) A2B c) A3B d) AB3

20 3 r 3

24 3 r 3

12 3 r 3

b)

c)

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16 3 r 3

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a)

d)

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Solid State Chemistry: Prepared by V. Aditya vardhan, adichemadi(at)gmail(dot)com 22 Cl- Na+ Cl- Na+ Cl-  a) Schottky defect b) Frenkel defect c) Interstitial defect d) Frenkel and Schottky defect 30. Assertion : In any ionic solid ( MX ) with schottky defects, the number of positive and negative ions are same Reason : Equal number of cation and anion vacancies are present. Choose the correct answer. a) Both assertion and reason are true and the reason the correct explanation of the assertion b) Both assertion and reason are true but reason is reason the correct explanation of the assertion c) Assertion is true but reason is false d) Assertion is false but reason is true 31. Total volume of atoms present in a face - centred cubic cell of a metal is ( r is atomic radius ) :