solid state chemistry i it

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

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1This file was last updated on 5th December, 2009. For the latest updates, visit

http://www.adichemadi.com

SOLID STATE CHEMISTRY

TYPES OF SOLIDS1) The characteristics of crystalline solids

1) Definite shape 2) Long range orders 3) Anisotropic 4) All2) 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 D1) 1 2 4 32) 4 3 2 13) 4 3 1 24) 3 4 1 2

4) The substance which exhibits electrical conductivity in the solid state is1) NaCl 2) Diamond 3) Silver 4) Both 1 & 3

5) The molecular crystal which shows electrical conductivity is1) Diamond 2) Silica 3) Silver 4) Graphite

6) Conversion of amorphous substances into crystalline state by slow cooling of liquids ofamorphous substances is called1) Crystallization 2) Annealing 3) Racemization 4) None

7) Low melting points, bad electrical conductivity and softness are the characteristics of1) Ionic crystals 2) Covalent crystals 3) Metallic crystals 4) Molecular crystals

8) The type of attractions present between molecules in ice are1) vander Waal’s attractions 2) Covalent bonds3) Hydrogen bonds 4) Both vander Waal’s attractions and Hydrogen bonds

9) Ionic solids are generally1) Good conductors of electricity 2) Quite hard 3) Quite brittle 4) Volatile

10) The units which occupy lattice points in covalent solids are1) Molecules 2) Ions 3) Atoms 4) covalent bonds

CRYSTAL SYSTEMS1) The number of basic crystal systems based on their symmetry elements and crystallographic

parameters is1) 14 2) 7 3) 230 4) 32Note : 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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2A) Cubic 1) a b c; 090

B) Tetragonal 2) a = b = c; 090

C) Orthorhombic 3) a = b c; 090

D) Triclinic 4) a b c; 090 Correct Matching is

A B C D1) 2 3 1 42) 2 3 4 13) 2 4 3 14) 4 2 1 3

3) Which of the following crystal system has not been correctly characterized ?1) Rhombohedral ; a = b = c ; 090

2) Monoclinic ; a b c ; 0 090 ; 90

3) Hexagonal ; a = b c ; 0= =90 , 0120 4) Orthorhombic ; a = b = c;

4) Match the followingA) Triclinic 1) NaCl, diamond & ZnSB) Cubic 2) KNO3, - S & MgSO4.7H2OC) Orthorhombic 3) CuSO4. 5H2O, K2Cr2O7 & H3BO3

D) Monoclinic 4) -S, NaHCO3 & FeSO4.7H2OCorrect matching is

A B C D1) 3 1 4 22) 2 3 4 13) 1 2 3 44) 4 3 2 1

5) Rhombohedral crystal system is present in1) KMnO4 2) Calcite 3) Bi 4) CalciteNote: Other examples are KMnO4,Bi, As, Sb, NaNO3 etc.,

6) Choose the incorrect statement (s)1) Ice and quartz can crystallise in either hexagonal or trigonal forms2) Cinnabar has hexagonal crystal system3) Tetragonal crystal system is present in CaF24) 1 & 2 only.

7) The substance with monoclinic crystal system is1) Glauber’s salt 2) - sulfur 3) K2Cr2O7 4) AllNote: - sulfur, Monoclinic gypsum, NaHCO3, FeSO4.7H2O etc.,

8,) The parameters of crystal system in graphite are1) a = b c ; 090 ; 0120 2) a = b = c ;

3) a b c ; 4) AllNote : Other examples with hexagonal arrangement are Mg, SiO2 and ZnO

9) The crystal system present in white tin is1) Hexagonal 2) Tetragonal 3) Triclinic 4) CubicNote : Other examples with tetragonal arrangement are TiO2, NiSO4, SnO2 and K4 [Fe(CN)6]

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310) The crystal system without any rotational axis of symmetry is

1) Triclinic 2) Cubic 3) Hexagonal 4) None11) The relation between crystallographic angles in monoclinic crystal system is

1) 090 ; 090 2) 090

3) 4) 0 090 ; 120 12) The correct parallelopiped dimensions for the crystal system in baryta (BaSO4) are

1) 0; 90a b c 2) 0; 90a b c

3) 0; 90a b c 4) ;a b c

13) The crystal system with the crystallographic angles 090 is1) Cubic 2) Tetragonal 3) Orthorhombic 4) All

14) The relation between crystallographic axes in Na2B4O7.10H2O and H3BO3 is1) a b c 2) a = b = c 3) a b = c 4) a = b cHint : Na2B4O7.10H2O - Monoclinic

H3BO3 - Triclinic

15) The changes in the crystallographic parameters in the following conversion are

α βS S

1) a b ca = b = c 2) 090 ; 090

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) Trigonal17) CuSO4.5H2O belongs to

1) Triclinic system 2) Cubic system 3) Tetragonal system 4) Hexagonal system18) The number of bravais lattices possible in a cubic crystal system is equal to

1) 1 2) 2 3) 3 4) 4Note : 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 unitcell is possible ?

1) Hexagonal 2) Trigonal 3) Triclinic 4) AllNote : In the primitive unit cell, the lattice points are present only at the corners.

20) The types of bravais lattices possible for orthorhombic system are1) P only 2) P & I 3) P, I & F 4) P, I, F & CNote : P - Primitive

I - Body - centredF - Face - centredC - End - centred

21) The number of C3 axes (three fold axes) of symmetry present in a cubic system1) 2 2) 3 3) 4 4) No C3 axis of symmetryNote : C3 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

PACKING OF ATOMS & TYPES OF UNIT CELLS1) 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 firstlayer is1) Body centred cubic 2) Primitive cubic 3) Face centred cubic 4) Hexagonal

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2) The two dimensional square close packed layers are arragenged such that the spheres in evey nextlayer are arraged over the voids of the first layer. The unit cell obtained is1) BCC 2) FCC 3) HCP 4) CCP

3) The unit cell present in ABAB.... type of closest packing of atoms is1) Tetragonal 2) Hexagonal 3) Face centred cube 4) Primitive cubeNote : There are two types of closest packing layers in three dimensional hexagonal close packing arrangement. The spheres inthe 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 is1) Hexagonal 2) Primitive cube 3) Body centred cube 4) Face centred cubeNote : 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 thirdlayer (C) are placed over the second type of voids of first layer (A)

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5) The co-ordination number in body centred cubic lattice is1) 6 2) 8 3) 12 4) 4

6) The number of nearest atoms surrounding a given atom in a metallic crystal containing primitivecubic unit cell is1) 6 2) 8 3) 12 4) 4

7) The co-ordination number in hcp and ccp type of metallic crystals is1) 4 2) 8 3) 12 4) 6

8) The number of atoms per a single primitive cubic unit cell is1) 8 2) 4 3) 2 4) 1

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6Note : The atom at the corner is shared amongst eight unit cell

no. of atoms per unit cell = 8 x 18 =1

9) The number of atoms per a single body centred unit cell is1) 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

no. of atoms per unit cell = 1+ (8 x 18 ) =2

10) The number of atoms per a single face centred cubic unit cell is1) 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.

no. of atoms = (8 x 18 ) + (6 x

12 ) = 4

11) The number of atoms in an end centred cubic unit cell is1) 2 2) 1 3) 4 4) 8Hint : In the end centred cubic unit cell, there are two atoms at the centres of two opposite faces along with atoms at eightcorners.

no. of atoms = (8 x 18 ) + (2x

12 ) = 2

12) The number of atoms in hexagonal prismatic unit cell is1) 2 2) 4 3) 6 4) 12

Note : contribution from top & bottom layers 1 1

) ] 36 22x[(6x

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 ofclosest packed atoms is1) r = 2a 2) r = a / 2 3) r = a 4) r = 4a

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714) The relation between radius (r) of atom and edge length (a) in the body centred cubic unit cell of

closest packed atoms is

1) 3r =

4a 2)

2r = 4

a 3) r = 2 a 4) 3r =

2a

2 2 2 2 2 2

2 2 2 2 2 2 2 2

2

2 3

4

4 33

4

:

BD DC a a a

In ABC

AC AB BC a BC a a a

But AC r

AC r a

r a

DerivationIn BCDBC

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

1) 3r =

4a 2)

2r = 4

a 3) r = 2 a 4) 3r =

2a

2 2 2

2 2 2 24 2

4 22

4

:

AB BC

r a a a

r a

r a

DerivationIn ABCAC

16) The metal which crystallises in simple cubic arrangement is1) Po 2) Al 3) Mg 4) All

17) The type of unit cell present in sodium metal is1) BCC 2) FCC 3) HCP 4) noneNote : Other examples with bcc structure are K, Rb, Cs, Ba, Cr, Mo and W

18) The metal which has fcc arrangement in its crystal is1) Cs 2) Al 3) Zn 4) WNote : Other examples with fcc arrangement are Cu, Au, Pb, Pt, Pd, Ni and Ca

19) The metal which has hcp arrangement1) Be 2) Mg 3) Zn 4) AllNote : Other examples are Cd, Co, Ti & Tl

20) All the noble gases, except helium, crystallise in1) hcp structure 2) ccp structure 3) bcc structure 4) rhombic structureNote : Helium crystallises in hcp structure

21) The crystal structure in solid H2 is1) 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 be1) 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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823) 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

Note : Cu crystallises in fcc structure

24) The length of a face diagonal of a simple cubic unit cell is 120 pm. The radius of the atom is1) 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 2) 3 y cm 3) 34

y cm 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.

26) Chromium is crystallised in body centred cubic structure. The edge length of unit cell in chromiumis 293.3 pm. The distance between two nearest atoms in the unit cell is1) 63 pm 2) 293.3 pm 3) 127 pm 4) 254 pmHint : The two nearest atoms in bcc are present along the body diagonal.

Nearest distance = d = 2r = 3

2a

27) The nearest distance (d) between two atoms in Nickel metal is 248 pm. The edge length (a) of theunit cell will be1) 124 pm 2) 350.6 pm 3) 68 pm 4) 412 pmHint : The two nearest atoms in fcc are arranged along the face diagonal of the unit cell.

Nearest distance (d) = 2r = 3

2a ( 4r = 2 a)

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) is1) 348 pm 2) 174 pm 3) 284. 2 pm 4) 492. 2 pmHint : ABCABC ---- pattern gives rise to face centred cubic lattice. The layers (ABCA) are present perpendicular to the bodydiagonal of the unit cell.

The distance between two successive layers = length of body diagonal

3

=3

3

a = .

3 4

3 2r

22

3r

29) Magnesium crystallises into a lattice containing closely packed layers in ABAB____ pattern. Thedistance 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 pmHint: ABAB---- pattern of arrangement of layers is otherwise known as hexagonal cubib packing. The distance between twosuccessive layers in this type of packing is same as that of cubic close packing i.e.,

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9

22

3r

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

1) 34

3 2a

2) 3

4 32 x 3 4

a

3) 3

4 24 x 3 4

a

4) 343

r

31) The volume occupied by atoms in a body centred cubic unit cell is (where ‘a’ is edge length)

1) 34

3 2a

2) 3

4 32 x 3 4

a

3) 3

4 24 x 3 4

a

4) 343

r

32) The volume occupied by atoms in a face centred cubic unit cell is (where ‘a’ is edge length)

1) 34

3 2a

2) 3

4 32 x 3 4

a

3) 3

4 24 x 3 4

a

4) 343

r

33) The percentage of packing of a simple cubic unit cell is1) 52.4% 2) 47.6% 3) 74% 4) 68%

The volume occupied by the atoms in a single unit cellHint: The packing fraction of a unit cell =

The volume of the unit cell

The packing fraction of body centred cubic unit cell =

4 33 = 3a

r

The percentage of packing =

343 2 = 0.52383 6a

0.5238 X 100 52.38%

a

34) The percentage of void volume in a simple cubic unit cell is1) 47.6% 2) 68% 3) 52.4% 4) 20%

35) The percentage of packing of a body centred cubic unit cell is1) 74% 2) 68% 3) 52.4% 4) 47.6%

Hint: The packing fraction of body centred cubic unit cell =


34 34 3 2 X 2 X 3 4 33 = = 0.683 3 8a a

0.68 X 100 68%

ar

36) The percentage of packing of hcp and ccp type of unit cells is1) 74% 2) 52.4% 3) 92% 4) none

Hint: The packing fraction of cubic close packed unit cell =


Note: The packing fraction of hexagon

34 24 3 4 X 4 X 3 4 23 = = 0.743 3 6a a

0.74 X 100 74%

ar

al cubic packed unit cell is also 0.74

37) The percentage of void volume in face centred cubic lattice is1) 26% 2) 0% 3) 32% 4) 12%

38) The atomic radius of aluminium is 1.26A0. The density of it in the solid state is1) 3.33 g.cm-2 2) 3.7g.cm-3 3) 2.31g.cm-3 4) 3.96g.cm-3

Formula :

density ( ) = 3M 1

.N aZ.

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10where Z = number of atoms in a unit cell

M = Molar massN = Avogadro numbera3 = Volume of the unit cella = edge length

Note : Aluminium crystallises in fcc structure.

39) The cubic unit cell of a metal ( molar mass 63.55g.mol-1) has an edge length of 362 pm. Its densityis 8.92 g.cm-3. The type of unit cell is1) 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 edgelength equal to 630 pm. The molar mass of the metal is1) 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 crystalscontaining ‘X’ number of spheres are1) 2X and X 2) X and 2X 3) 4X and 2X 4) 4X and XNote: 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 is1) 0.414 2) 0.155 3) 0.225 4) 0.732

o

o

cos30

Derivation:BE

In BDE, cos = BD

cos30 =

2.3

1.155 0.155

=

sphere spheresphere void

void

sphere

sphere void

sphere sphere sphere

r r

DBE

r

r r

r r

r r r r

0.155voidsphere

sphere

r

rr

43) The ratio of radius of tetrahedral void to the radius of the sphere in closest packed arrangement is1) 0.414 2) 0.225 3) 0.732 4) None

o ,o ,

,

Derivation:AC

In , sin = AO

109 28 sin = 109 28

2

sin 54 44 0.8164

( )

sphere spheresphere void

void

sphere

sphere void

o

r r

OAC AOC

rAOB

r r

r r

r

1.225 0.225

0.225

= sphere sphere sphere

voidsphere

sphere

r

r

r r r

r

44) The ratio of radius of octahedral void to the radius of the spheres in closest packed arrangement is1) 0.414 2) 0.155 3) 0.225 4) 0.732

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o

o

Derivation:BD

In , cos = AB

cos45 =

cos45

2

1.414 0.414

=

spheresphere void

void

sphere

sphere void

sphere

sphere sphere

r

ABD ABD

r

r r

r r

r

r

r r

0.414

sphere

voidsphere

sphere

r

r

r

r

45) The ratio of radius of cubic void to the radius of surrounding closely packed atoms whose centreslie at the corners of a cube is1) 0.414 2) 0.155 3) 0.225 4) 0.732

IONIC CRYSTALS1) 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 diagrams1) 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) AllNote: The state of the atom or ion occupying any void in a crystal lattice is stable only when it is touching the surroundingatoms or ions.

2) Match the followingLimiting radius ratio GeometryA) 0.155 - 0.225 1) TetrahedralB) 0.225 - 0.414 2) OctahedralC) 0.414 - 0.732 3) TrigonalD) 0.732-0.999 4) Body centred cubicThe correct matching is

A B C D1) 1 3 2 42) 3 2 4 1

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123) 3 1 2 44) 1 2 4 3

3) Match the followingCo-ordination number Limiting radius ratioA)3 1) 0.155-0.225B) 4 2) 0.225-0.414C) 8 3) 0.414-0.732D) 6 4) 0.732-0.999Correct matching is

A B C D1) 1 2 3 42) 1 2 4 33) 1 3 2 44) 2 3 4 1

4) The limiting radius ratio for an ionic compound AB is 0.427. The smaller cation A+ will be morestable when it occupies1) Tetrahedral voids 2) Octahedral voids 3) Trigonal voids 4) Body centred cubic voidsNote: The cation can touch the anions when it occupies trigonl or tetrahedral voids, but it will be more stable in octahedralvoid as it is surrounded by more number of anions. It will be less stable in body centred cubic void, even though it issurrounded 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+ andCl- ions are 95pm and 181 pm respectively. The type of voids occupied by Na+ ions is1) Octahedral 2) Tetrahedral 3) Trigonal 4) All

Hint: 0.5248rNarCl

6) The crystal structure present in NaCl is called1) Fluorite structure 2) Rock-salt structure 3) Anti-fluorite structure 4) Spinel structureNote : In Rock-salt structure, the bigger anions occupy the lattice points of expanded face centred cubic lattice. The smallercations occupy all the octahedral holes. The limiting radius ratio is in between 0.414 and 0.732. The co-ordination numberscation and anion are (6:6). The general formula of ionic compounds having this structure is AB.Examples : NaCl, KCl, MgO, CaO, SrO etc.,

7) The number of NaCl units present in a single unit cell of NaCl crystal is1) 1 2) 2 3) 4 4) 6

8) The number of octahedral holes occupied by Na+ ions in a single unit cell of NaCl is1) 4 2) 8 3) 2 4) Zero

9) Which of the following does not crystallise in the rock salt structure1) NaCl 2) KCl 3) CsCl 4) MgONote : 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 is1) 8 2) 6 3) 4 4) 12

11) The number of nearest Cl- ions arround a Cl- ion in NaCl crystal is1) 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 inNaCl is

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131) 457 pm 2) 552 pm 3) 190 pm 4) 362 pmNote : edge length in NaCl = 2rc+ 2ra

13) The crystal structure present in CsCl is referred to as1) FCC 2) BCC 3) HCP 4) NoneNote : BCC structure is present when the limiting radius ratio isgreater than 0.732. The anions occupy the lattice points ofsimple cubic lattice. The cations occcupy centred cubic voids. This structure can be considered as interpenetrating primitivecubic 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 andone 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 is1) 6 2) 8 3) 12 4) 4

15) The number of nearest Cs+ ions present around a Cs+ ion in CsCl crystal is1) 8 2) 6 3) 4 4) 12Hint : 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 is1) 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 inCsCl will be1) 7 Å 2) 3.38 Å 3) 4.04 Å 4) 3.5 ÅHint : In BCC, the ions touch along the body diagonal

Length of body diagonal = 2rc+2ra = 3a

18) The ionic compound which crystallises in anti-fluorite structure is1) NaCl 2) Na2O 3) CaF2 4) Al2O3Note : In the anti-fluorite structure, anions are arranged in cubic closest packing and cations occupy all the tetrahedralvoids. There are four anions and eight cations per unit cell of this structure and hence, the general formula of an ioniccompound 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 ofcation 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 latticeand cations (X) occupy all the tetrahedral voids. The formula of the ionic compound will be1) XY2 2) X2Y2 3) X2Y 4) XY

20) The number of anions per a single unit cell in antifluorite structure is1) 2 2) 4 3) 8 4) 1

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1421) The type of voids occupied by cations in antifluorite structure is

1) Octahedral 2) Tetrahedral 3) Trigonal 4) Body centred cubic22) The co-ordination number of Na+ ions in Na2O is

1) 2 2) 4 3) 8 4) None23) The type of voids occupied by O2- ions in Na2O crystal is

1) Tetrahedral 2) Octahedral 3) Body centred cubic 4) Trigonal24) The number of Na+ ions present per a single unit cell in Na2O crystal is

1) 4 2) 2 3) 8 4) 1225) The fluorite crystal structure is present in

1) NaF 2) CaF2 3) AlF3 4) CsFNote : In the fluroite structure, the cations are arranged into cubic close packing and the anions occupy all the tetrahedralvoids. 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 is1) 2 2) 4 3) 8 4) 1

27) The type of voids occupied by anions in fluorite structure is1) Octahedral 2) Tetrahedral 3) Trigonal 4) Body centred cubic

28) The co-ordination number of Ca2+ ions in CaF2 is1) 2 2) 4 3) 8 4) None

29) The type of voids occupied by Ca2+ ions in CaF2 crystal is1) Tetrahedral 2) Octahedral 3) Body centred cubic 4) Trigonal

30) The number of Ca2+ ions present per a single unit cell in CaF2 crystal is1) 4 2) 2 3) 8 4) 12

31) The radii of Ca2+ and F- ions respectively are 100 pm and 131 pm. The edge length of the unit cell

in CaF2 is1) 231 pm 2) 533.5 pm 3) 462 pm 4) 362.5 pmHint: The Fluoride ions are present along the body diagonal at one fourth distance from the corner of the cube. Hence thedistance between calcium and fluoride ions is 1/4th of length of body diagonal.

32) The substance containing zinc-blende crystal structure is1) NaCl 2) ZnCl2 3) BeO 4) CsClNote: In zinc-blende or sphalerite structure, anions occupy the face centred cubic lattice points and cations occupy half ofthe tetrahedral holes (of one type). The ideal radius ratio is in between 0.225 to 0.414. There are four anions and fourcations 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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15

33) The number of anions per a single unit cell in zinc-blende structure is1) 2 2) 4 3) 8 4) 1

34) The type of voids occupied by cations in zinc-blende structure is1) Octahedral 2) Tetrahedral 3) Trigonal 4) Body centred cubic

35) The co-ordination number of Zn2+ ions in ZnS is1) 2 2) 4 3) 8 4) None

36) The type of voids occupied by S2- ions in ZnS crystal is1) Tetrahedral 2) Octahedral 3) Body centred cubic 4) Trigonal

37) The number of Zn2+ ions present per a single unit cell in ZnS crystal is1) 4 2) 2 3) 8 4) 12

38) The co-ordination number of S2- ions in ZnS is1) 2 2) 4 3) 8 4) None

39) The compound containing spinel structure is1) MgAl2O4 2) Fe2O3 3) ThO2 4) KClNote: In spinel structure, the oxide ions are arranged in cubical closest packing and one eighth of the tetrahedral holes areoccupied by divalent metal ion (A2+) and one half of the octahedral holes are occupied by trivalent metal ions (B3+). Thus ina unit cell there are four oxide ions, one divalent metal ion(A2+) and two trivalent metal ions (B3+). The general formula ofthe compound is AB2O4.Examples: MgAl2O4,ZnAl2O4, ZnFe2O4 etc.,

40) The crystal structure present in Al2O3 is called as1) corundum structure 2) spinel structure 3) rock-salt structure 4) Fluorite structureNote: In the corundum structure, anions form hexagonal closest packing and cations are present in 2/3 of the octahedralholes. The general formula of the compound is M2O3.Examples: Fe2O3, Al2O3, Cr2O3 etc.,

41) Inverse spinel structure is found in1) Chromite 2) Magnetite 3) Spinel 4) Corundum

X-RAY DIFFRACTION AND BRAGG’S EQUATION1) 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) NoneFormula : nλ=2d sin

2) At what angles for the first order diffraction, spacing between two planes respectively areλ andλ2 ?1) 900 & 300 2) 300 & 900 3) 900 & 00 4) 00 & 900

3) An X - ray beam of wavelength 71pm was scattered by a solid. The angle of diffraction (2θ ) fora second order reflection is 140661. The inter planar distance in the crystal will be1) 710 pm 2) 559 pm 3) 142 pm 4) 71 pm

4) 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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161) 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, ina solid is observed at a reflection angle of 300. By using same radiation the first order diffraction isobserved at 600 in another solid. The interplanar distance in the second solid will be1) 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 ofwavelength of 258 pm. If the interplanar distance is 500 pm, the second order of diffraction will beobserved at1) 7.280 2) 10.50 3)31.170 4) 9.20

DEFECTS IN CRYSTALS MAGNETIC & ELECTRICAL PROPERTIES

1) The incorrect statement related to schottky defect is1) It is a stoichiometric point defect2) 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.Note: In Schottky defect, pair of holes are formed as both the cations and anions (with equal but opposite charge) leave thelattice points and move out of the crystal. This is a stoichiometric point defect. The defected crystal is electrically neutral. Butdensity and covalent nature are decreased. Dielectric constant and hence ionic nature are increased. Defected crystals showlittle electrical conductivity. Schottky defects are shown by ionic compounds with high co-ordination numbers. The differencein the sizes of oppositely charged ions is small. Usually these defects are shown by compounds of big sized alkali and alkalineearth 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 called1) Schottky defect 2) Metal excess defect 3) Frenkel defect 4) F-centre formationNote: In Frenkel defect, the cations, being small can move from the lattice points to interstitial spaces and thus by creatingholes. This is a stoichiometric point defect. The defected crystal is electrically neutral. But density and covalent nature aredecreased. Dielectric constant and hence ionic nature are increased. Defected crystals show little electrical conductivity. Thisdefect is shown by ionic compounds with low co-ordination numbers. The difference in the sizes of oppositely charged ionsmust 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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173) Frenkel defect is not possible in

1) AgCl 2) ZnS 3) CsCl 4) AgBr4) Which of the following is not common for Schottky and Frenkel defects?

1) Stoichiometric 2) Increase in the number of defects with temperature3) 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 defectsb) Crystals with Schottky and Frenkel defects show little electrical conductivityc) Frenkel defect is shown by ionic compounds with high co-ordination numbers and with big sizedcations.d) Crystals with Schottky and Frenkel defects are electrically neutralThe correct statements are1) 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 sto-ichiometric ratio ?1) Frenkel defect 2) Schottky defect 3) Metal excess defect 4) All

7) The stoichiometric point defect possible in AgBr is1) 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 crystalb) 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/are1) a & c 2) b, c, & d 3) a, b & d 4) All

9) In which of the following non-stoichiometric defect, the cation occupies the interstitial site1) Schottky defect 2) Frenkel defect3) Metal excess defect 4) Metal deficiency defect

10) LiCl shows pink color when heated in Li vapour due to1) Metal deficiency defect 2) Schottky defect 3) F-Centre formation 4) Frenkel defectNote : F-Centres are formed when an electron occupies anion vacancty in the crystal. They import color and paramagneticnature to the crystalsEg : KCl in K vapours is blue lilac in color NaCl in Na vapour is yellow is color.

11) ZnO turns yellow upon heating because of1) Metal excess defect 2) Metal deficiency defect 3) Frenkel defect 4) AllNote : When heated ZnO loses oxide ions reversibly. Excess Zn2+ ion and electrons are accomodated interstitially. Due topresence 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 of1) Frenkel defect 2) Schottky defect 3) Metal deficiency defect 4) Metal excess defectNote : Some compounds cannot be prepared in ideal stiochimetric proportions due to metal dificiency defect. This defectarises 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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18exhibited by compounds of transition metals which can exhibit variable valency. As a result, there compounds show nonstoichiometric formulae. Eg : VOX (x can be 0.6 - 1.3), Fe0.95O

13) Following are the statements relating to defects in crystalsa) Frenkel defect is shown by ionic compounds where there is large difference in size between posi-tive and negative ions.b) Zinc oxide turns yellow upon heating due to formation of metal deficiency defectc) The vacant anion sites occupied by electrons are called F-Centresd) The number of schottky and Frenkel defects decreases with increase in temperatureThe correct statements are1) a only 2) a & c 3) a, b & c 4) a, c & d

14) Select the incorrect statement.1) Schottky defect is shown by CsCl2) Frenkel defect is shown by ZnS3) 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 produces1) Cation vacancies 2) Anion vacancies 3) Both cation & anion vacancies 4) NoneNote : When NaCl is doped with SrCl2, Sr2+ ions displace Na+ ions from their lattice points. Also at the same time, equal numberof Na+ ions from other lattice sites move out of the crystal and thus by creating cation vacancies. Thus formed solids are calledsubstitutional solids other examples:- AgCl doped by CdCl2.

17) I f NaCl is doped with 10-4 mole% of SrCl2, the concentration of cation vacancies would be1) 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 have1) Cationic vacancies equal to number of Cd2+ ions incorporated

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192) Cationic vacannies equal to double the number of Cd2+ ions incorporated.3) Anionic vacancies4) Neither cationic nor anionic vacancies.

20) The type of electrical conductivity shown by crystals with F - Centres is1) n-type semiconductivity 2) p-type semiconductivity 3) Super conductivity 4) None

21) The conductivity of semiconductors is in the range of1) 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 statement1) 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 semiconductor1) Si 2) Si doped with As 3) Fe 4) Both 1 & 2

24) Silicon doped with III A group elements exhibit1) n-type semi conductivity 2) p-type semi conductivity 3) Both 1 & 2 4) None

25) Germanium doped with phosphorus acts as1) n-type semiconductors 2) p-type semiconductor3) super conductor 4) Intrinsic conductor.

26) Solar photovoltaic cell used to convert radiant energy into electrical energy consists of1) 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 substance3) Super conductors are good insulators4) None

28) Match the followingA) 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 D1) 4 3 2 12) 4 3 1 23) 3 4 1 24) 4 2 3 1

29) The temperature above which the ferromagnetism is lost is called1) 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 toit is called.1) Antiferro electricity 2) Piezoelectricity 3) Magnetic electricity 4) None

31) A ferro electric substance is1) KH2PO4 2) BaTiO3 3) Rochelle salt 4) AllNote : Ferroelectric substances are piezoelectric crystals with permanent dipoles.

32) Piezo-electric crystals with zero net dipole moment are called1) Ferro electric 2) Pyro electric 3) Antiferro electric 4) None

33) The substance which exhibits anti-ferroelectricity is1) BaTiO3 2) PbZrO3 3) KH2PO4 4) All

34) The crystals which produce electricity upon heating are referred to as

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201) Ferro electric 2) Pyro electric 3) Antiferro electric 4) None

35) The Ferro magnetic substance used in audio and video tapes is1) FeO 2) CrO2 3) MnO 4) BaTiO3.

REVISION1. An AB2 type structure is found in :

a) N2O b) NaCl c) Al2O3 d) CaF22. 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 )

3. The intermetallic compound LiAg crystallizes in cubic lattice in which both lithium and silver haveco - ordination number of eight. The crystal class is :a) Simple cubic b) body centred cubec) face centred cube d) none of these

4. The vacant space in the bcc unit cell is :a) 23% b) 26% c) 32% d) none of these

5. Potassium fluoride has NaCl type structure. What is the distance between K+ and F- ions if celledge is a cm ?

a) 2a cm b) 4

a cm c) 2a cm d) 4a cm

6. Bragg’s law is given by the equation :

a) 2 sinn b) 2 sinn d c) 2 sinn d d) sin2 2

dn

7. The inter-ionic distance for Cesium chloride crystal will

a) a b) 2a

c) 2

3a

d) 32

a

8. Sodium metal crystallizes as a body centred cubic lattice with the cell edge 4.29A0. what is theradius 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

9. 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

10. A metal has bcc structure and the egde length of its unit cell is 3.04 A0. The volume of the unit cellin 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

11. 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 formulaof the compound is :a) AB b) AB2 c) A2B d) AB4

12. In a cubic structure of compound which is made from X ad Y, where X atoms are at the corners ofthe cube. The molecular formula of the compound is :a) X2Y b) XY2 c) XY3 d) X3Y

13. 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

14. Most crystals show good cleavage because their atoms, ions or molecules are :a) weakly bonded together b) strongly bonded togetherc) spherically symmetrical d) arranged in planes

15. An example of a non - stoichiometric compound is :a) PbO b) NiO2 c) Al2O3 d) Fe3O4

16. Doping of silicon ( Si ) with boron ( B ) leads to :

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21a) n - type semiconductor b) p - type semiconductorc) metal d) insulator

17. In the laboratory, sodium chloride is made by burning the sodium in the atmosphere of chlorinewhich is yellow in colour. The cause of yellow colour is :a) presence of electrons in the crystal latticeb) presence of Na+ ions in the crystal latticec) presence of Cl- ions in the crystal latticed) 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 vacancyc) An extra positive ion occupying an interstitial position in the latticed) 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 Naand 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 thecentres of the faces of the cube. The empirical formula for this compounda) AB b) A2B c) A3B d) AB3

23. The number of atoms in 100g of an fcc crystal with density, 3

10gdcm

and cell edge equal to100

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. Itsdensity ( in kg 3m ) 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 themolecular mass of the solute is 1155 g mol and that of density is 3.3 g / cc, the number offormula units per unit cell isa) 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 ‘ atomsat the cube. The formula for the compound isa) 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. Ifall the centre of the face - centred atoms along one of the axes are removed, then the resultantstoichiometry 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 densityis 2.178 x 103 kg m-3. The fraction of unoccupied sites in sodium chloride crystal is :a) 5.96 b) 15.96 10x c) 25.96 10x d) 35.96 10x

29. What type of crystal defect is indicated in the diagram below ?Na+ Cl- Na+ Cl- Na+ Cl-Cl- Cl- Na+ Na+

Na+ Cl- Na+ Na+ Cl-

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22Cl- Na+ Cl- Na+ Cl- a) Schottky defect b) Frenkel defectc) Interstitial defect d) Frenkel and Schottky defect

30. Assertion : In any ionic solid ( MX ) with schottky defects, the number of positive and negativeions are sameReason : 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 assertionb) Both assertion and reason are true but reason is reason the correct explanation of the assertionc) Assertion is true but reason is falsed) 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 ) :

a) 3203

r b) 3243

r c) 3123

r d) 3163

r

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