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Right answer is (d) 2.3%

To explain I would say: Given,

Edge length (a) = 350 pm = 3.5 x 10^-8 cm

Atomic mass (M) = 7 amu

Avogadro’s NUMBER (N0) = 6.02 x 10^23

Density (ρ) = (Z x M)/(a^3 x N0)

= (2 x 7)/((3.5 x 10^-8)^3 x 6.02 x 10^23)

= 0.542 G cm^-3

% of lithium atoms occupied = (Experimental density/Theoretical density) x 100

= 0.53/0.542 x 100

= 97.7%

% of unoccupied lattice SITES = 100 – 97.7

= 2.3%.

Right ANSWER is (b) Anti-ferromagnetism

Easiest EXPLANATION: On increasing the TEMPERATURE, the MAGNETIC susceptibility of diamagnetic substances do not change, that of paramagnetic and ferromagnetic substances decrease and that of antiferromagnetic substances INCREASE.

The correct choice is (a) Packing FACTOR

For explanation: Packing factor is a fraction of TOTAL space of the unit CELL occupied by the CONSTITUENT particles.

Correct choice is (a) Unit cell

For explanation I would say: Unit cell is the smallest entity of a crystal lattice which, when repeated in space (3 dimensions) generates the ENTIRE crystal lattice. Lattice comprises of the unit cells which hold all the PARTICLES in a particular arrangement in 3 dimensions. Crystal is a piece of homogenous solid and Bravais indices are USED to define planes in crystal LATTICES in the HEXAGONAL system.

The correct choice is (a) dipole-dipole interaction

For EXPLANATION I WOULD SAY: The force responsible for holding TOGETHER the molecules of polar molecular solids is dipole-dipole force of attraction. Polar molecular solids are non-conductors of ELECTRICITY.

Right option is (d) Metallic

Explanation: Metallic crystals consist of METAL cations surrounded by a SEA of mobile valence ELECTRONS. These electrons are capable of moving through the ENTIRE crystal. The metallic crystals conduct heat and ELECTRICITY due to the presence of these mobile electrons in them.

Right OPTION is (c) Unit cell

For explanation: Crystalline solids are composed of many small crystals, each of which is CALLED a unit cell. It is a SPECIFIC term. MONOMER is the basic unit for a polymer, and ATOMS make up molecules, which can further arrange themselves to form solids, liquids or gases.

Correct answer is (a) Body-Centred Cubic (BCC)

For explanation I would say: Given,

Edge length (a) = 288 pm

Density (ρ) =7.2 g cm^-3

Atomic mass (M) = 51.8 g mol^-1

Avogadro’s number (N0) = 6.02 X 10^23

We know, (ρ) = (Z x M)/(a^3 x N0)

Or Z =(ρ x a^3 x N0)/M = (7.2 x (288 x 10^-10) ^3 x 6.02 x 10^23)/51.8

Z = 2

Therefore, the ELEMENT has Body-Centred Cubic (BCC) type of structure.

Correct choice is (a) Fe > Co > Ni > Cu

The explanation: MAGNETIC strength depends on the NUMBER of UNPAIRED electrons possessed by the element. Iron, Cobalt, Nickel and Copper have 4, 3, 2 and 1unpaired electron respectively. Hence, the correct ORDER of magnetic strength is: Fe > Co > Ni > Cu.

Correct answer is (d) S = 8d^2

Explanation: For BCC unit CELL the relation between radius of a particle ‘r’ and edge length of unit cell, a, is r = \(\FRAC{\sqrt{3}}{4}\)a.

We know that diameter, d = 2r = \(\frac{\sqrt{3}}{2}\)a

Implying d^2 = \(\frac{3}{4}\)a^2

Therefore, 4d^2/3=a^2

 Multiplying by 6 on both sides gives S = 6a^2 = 8d^2, where S is the surface area of the CUBE = 6a^2.

Right answer is (a) eight unit cells

Explanation: The unit cell in which the CONSTITUENT atoms are present only at the corner is known as SIMPLE CUBIC cell. It is also referred to as a primitive cubic cell. In the simple cubic cell, each corner atom is shared by eight different unit cells.

Correct answer is (a) 12

Easiest explanation: For a crystal LATTICE, if there are N close-packed SPHERES the NUMBER of tetrahedral voids are 2N and number octahedral voids are N. For N=6, number of tetrahedral voids = 2 × 6 = 12.

The CORRECT option is (a) BAD conductors of ELECTRICITY

Best explanation: In polar MOLECULAR solids, the molecules are formed by covalent bonds and held together by strong dipole-dipole interaction. Therefore, polar molecular solids are non-conductors of electricity.

Correct option is (b) M^0L^0T^0

The explanation: Packing fraction is a dimensionless quantity which is the ratio of space OCCUPIED to TOTAL CRYSTAL space available. SINCE both the quantities have the same units the ratio renders dimensionless.

Right CHOICE is (c) 4

The explanation is: In face-centered cubic unit cell, atoms are present at each of the corners and at the CENTRE of the face of the cube.

• 8 corners × \(\frac{1}{8}\)th of an ATOM = 1

• 6 FACES × \(\frac{1}{2}\) of an atom = 3

Thus, the total number of atoms in face-centered cubic unit cell: 1+3=4 atoms.

The correct answer is (B) Homogeneous, anisotropic

To EXPLAIN I would say: Homogeneity REFERS to uniformity in composition, which is a characteristic property of crystalline solids. Isotropy is when the VALUES of physical PROPERTIES do not change with direction throughout the body of the solid. Crystalline solids are anisotropic because the composition of the solid changes with direction, hence the physical properties also change with direction.

The CORRECT CHOICE is (B) Quartz glass

Easy explanation: Quartz glass does not have a perfectly ORDERED structure, HENCE it is classified as an amorphous solid. The rest are crystalline solids due to ordered structures.

The correct ANSWER is (B) 0.0235

Easiest explanation: Density, d of unit cell is GIVEN by d = \(\frac{zM}{a^3N_A}\)

Given,

Density, d = 9.0 g/cm^3

Atomic mass, M = 63.5 g/mole

Edge length = a

NA = Avogadro’s number = 6.022 x 10^23

z = 4 atoms/cell

On REARRANGING the equation for density we get a^3 = \(\frac{zM}{dN_A}\)

SUBSTITUTING the given values:

a^3 = \(\frac{4 \times 63.5}{9 \times 6.022 \times 10^{23}}\)

Therefore, a = 360.5 pm

 The relation of edge length ‘a’ and radius of particle ‘r’ for FCC packing i.e. a = 2\(\sqrt{2}\)r.

On substituting the value of ‘a’ in the given relation, r = \(\frac{360.5}{2\sqrt{2}}\)=127.46 pm

Now, for spherical particles volume, V = 4πr^3/3 and surface area, S = 4πr^2

Required ratio = S/V=4πr^2/(4πr^3/3) = 3/r (after simplifying)

Thus, S/V = 3/127.46 = 0.0235.

Correct choice is (C) PbZrO3

For explanation: In the given LIST: NIO and V2O3 are ANTIFERROMAGNETIC substances, Fe3O4 is Ferrimagnetic and PbZrO3 is antiferroelectric. Antiferroelectric materials are those materials having ions which can polarize without external field (spontaneous polarization).

The correct answer is (a) True

The explanation is: Pyroelectricity is the ABILITY of CERTAIN materials to generate a temporary POTENTIAL difference when HEATED or cooled. Ferroelectrics form a subset of PYROELECTRICS. Hence, all Ferroelectrics are Pyroelectrics.

Right choice is (a) True

For EXPLANATION: Piezoelectrics are SUBSTANCES whose polarization CHANGES under the influence of stress. Ferro ELECTRIC substances are considered as Piezoelectric since their polarization can change under the influence of an electric FIELD.

Correct CHOICE is (d) They are ISOTROPIC

Explanation: Amorphous solids are isotropic that is they have IDENTICAL PROPERTIES in all DIRECTIONS. The remaining options are the characteristics of crystalline solids.

Right CHOICE is (a) True

The best EXPLANATION: Amorphous solids behave like fluids and flow very slowly under the influence of gravity. HENCE, they are said to be super COOLED LIQUIDS.

Right answer is (b) 0.37 Å

Easy explanation: Given,

Edge length of FCC crystal (aFCC) = 4.0 Å

For FCC structure, Z = 4

For BCC structure, Z=2

Avogadro’s number (N0) = 6.02 x 10^23

The DENSITY of a crystal (ρ)=(Z x M)/(a^3 x N0)

 Therefore, the RATIO of Densities= ρFCC/ρBCC = (ZFCC x a^3BCC) / (ZBCC x a^3FCC)

1.5 = (4 x (ABCC)^3) / ( 2 x (4 x 10^-10)^3)

(aBCC)^3 = (1.5 x 2 x 64 x 10^-30)/ 4= 48 x 10^-30

Therefore aBCC = 3.63 Å

Difference in Unit Cell Length = 4.0 – 3.63 = 0.37 Å.

Correct answer is (b) 4

The explanation is: In a two-dimensional square close packed STRUCTURE, each sphere is in contact with 4 of its ADJACENT spheres. HENCE, it has coordination NUMBER 4.

Right answer is (a) X2Y3

The best explanation: The NUMBER of tetrahedral voids form is EQUAL to twice the number of atoms of ELEMENT X. Number of atoms of Y is 3/4^th the number of tetrahedral voids i.e. 3/2 times the number of atoms of X. THEREFORE, the ratio of NUMBERS of atoms of X and Y are 2:3, hence X2Y3.

Right CHOICE is (C) Ice

The best explanation: The density of ice is about 0.92 g/cm^3 while that of water is 1 g/cm^3. Mercury has density 14.184 g/cm^3 as solid and 13.69 g/cm^3 as liquid. CARBON dioxide has density 1.56 g/cm^3 as solid and 1.10 g/cm^3 as liquid. NaCl has density 2.71 g/cm^3 as solid and 1.556 g/cm^3 in molten state. Therefore only ice has LESSER density as a solid than as a liquid.

The CORRECT answer is (b) increase

To elaborate: The band theory assumes that ATOMIC orbitals of the atoms of the crystal combine to form molecular orbitals which are SPREAD over the whole crystal STRUCTURE. HENCE, the number of atoms is directly proportional to the number of molecular orbitals formed.

The correct answer is (b) 0.144 nm

The best explanation: Given,

EDGE length of the Gold unit cell (a) = 0.407 x 10^-7m

For FCC unit cell, the ATOMIC radius (R) = a/(2\(\SQRT{2}\))

 = 0.407 x 10^-9/(2\(\sqrt{2}\))

 = 0.144 nm.

Correct CHOICE is (c) HCP < BCC < Simple cubic

Best explanation: HCP and CCP have the HIGHEST packing EFFICIENCY of 74% followed by BCC which is 68%. The simple cubic structure has a packing efficiency of 54%.

The correct ANSWER is (d) Free and mobile ELECTRONS

Explanation: Each ATOM of a metal gives one or more electrons TOWARDS the sea of mobile electrons it is surrounded by which ultimately contributes to the electrical and thermal conductivity of the metal.

The correct CHOICE is (c) METAL

To explain I would say: Metal is SAID to be an orderly collection of POSITIVE ions SURROUNDED and held together by a sea of delocalized electrons. These delocalized electrons are mobile and are responsible for the conduction of electricity.

Right ANSWER is (d) Mn

To elaborate: MnO, Mn2O3, and MNO2 are Anti-ferromagnetic. Mn is paramagnetic in NATURE. PARAMAGNETISM is when a substance is weakly attracted to a magnetic field.

The correct OPTION is (C) semiconductor

Easy explanation: Semiconductors have completely filled valence bands and completely empty conduction bands. The energy gap between the TWO bands is relatively small and can be OVERCOME by supplying HEAT, which excites some electrons to the conduction band, thus allowing the conduction of electricity.

The correct option is (d) Hydrogen bonded molecular solids

Explanation: In hydrogen bonded molecular SOLID, the intermolecular FORCES are strong hydrogen bonds. Hence, it tends to be VOLATILE LIQUIDS or soft solids at room temperature and pressure.

Correct CHOICE is (d) crystalline and amorphous SOLIDS

Explanation: BASED on their crystal structures, solids are CLASSIFIED as crystalline and amorphous solids. In crystalline solids, the CONSTITUENT particles are arranged in a regular manner. In amorphous solids, the constituent particles are not arranged in any regular manner.

Correct answer is (a) BATIO3

To explain I would say: At the Curie TEMPERATURE (AROUND 120 ºC) paraelectric BaTiO3 transforms into a ferroelectric STRUCTURE. Ferroelectricity is the characteristic of certain substances that possess a SPONTANEOUS electric field which can be reversed by applying an external electric field.

The correct choice is (d) Nitrogen

The explanation: Only Diamagnetic substances SHOW a negative value of MAGNETIC susceptibility. In the GIVEN list: OXYGEN and aluminium are paramagnetic, iron is ferromagnetic and nitrogen is diamagnetic. Therefore, Nitrogen has a negative value of magnetic susceptibility.

Correct ANSWER is (a) Poor conductors of heat and electricity

To EXPLAIN: Metalloids have PROPERTIES INTERMEDIATE to those of metals and non-metals. They are non-malleable, non-ductile and brittle. They are poor conductors of heat and electricity as compared to metals, but are BETTER conductors than non-metals.

The correct answer is (a) 1.32 × 10^6 pm^2

To EXPLAIN: ABCABC arrangement is found in CCP.

In closed CUBIC packing, relation between edge length of unit CELL, a, and RADIUS of particle, r, is given as a=2\(\sqrt{2}\)r.

 Surface area (S.A.) = 6a^2

From the RELATIONSHIP,

a^2 = 8r^2

S.A. = 6a^2 = 48r^2

 When r = 166 pm, S.A. = 48(166pm) = 1.32 x 10^6 pm^2.

Right OPTION is (b) IONIC SOLIDS

Easy explanation: Ionic solids are MADE up of THREE dimensional arrangement of cations and anions bound by strong electrostatic force.