Question 1

Glass is classified as a

Accepted Answer

supercooled liquid. Glass is often described as a supercooled liquid because it lacks a crystalline structure and exhibits a disordered arrangement of molecules, similar to liquids, but it behaves like a solid at room temperature.

Question 2

In the wurtzite crystal lattice, what are the coordination numbers of Zn2+ and S2- respectively?

Accepted Answer

4, 4. In the wurtzite (ZnS) lattice both Zn2+ and S2- are tetrahedrally coordinated, giving 4:4 coordination, not 6:6.

Question 3

In KBr, the coordination number of each ion changes from X to Y when the crystal is subjected to which condition?

Accepted Answer

X = 6 to Y = 8 by applying high pressure. KBr (rock-salt, 6:6) converts to the CsCl-type 8:8 structure under high pressure (coordination 6 -> 8). The stored option attributes the change to temperature, which is wrong.

Question 4

How many carbon atoms are present in one unit cell of the diamond crystal structure?

Accepted Answer

8. In the diamond crystal structure, each unit cell contains 8 carbon atoms due to the arrangement of carbon atoms at the corners and the face centers of the cubic unit cell, contributing to a total of 8 effective atoms.

Question 5

A sodium chloride crystal has a pycnometric density of 2.165 × 10³ kg m⁻³ and an X-ray density of 2.178 × 10³ kg m⁻³. What fraction of lattice sites are vacant in the crystal?

Accepted Answer

5.96 × 10⁻³. The correct option is right because it accurately represents the calculated fraction of vacant lattice sites based on the difference between the pycnometric density and the X-ray density, indicating that a small percentage of the lattice sites in the sodium chloride crystal are unoccupied.

Question 6

Which set of unit-cell parameters represents a cubic lattice, if the edge lengths are a, b, c and the interaxial angles are α, β, and γ?

Accepted Answer

a = b = c, with α = β = γ = 90°. A cubic lattice has a = b = c with alpha = beta = gamma = 90. The stored a = b != c describes a tetragonal lattice, not cubic.

Question 7

A pure crystalline material, when heated slowly, first changes into a cloudy liquid at a fixed temperature, and on further heating the cloudiness vanishes completely. This is a typical property of substances that form

Accepted Answer

liquid crystals. Liquid crystals exhibit a unique phase transition where they first become cloudy as they melt, indicating a mix of solid and liquid phases, and then clear up as they fully transition to the liquid state. This behavior is characteristic of liquid crystals, distinguishing them from other types of crystalline materials.

Question 8

To convert silicon into an n-type semiconductor, it must be doped with an element having valency __________.

Accepted Answer

5. Silicon is made n-type by doping with a group-15 element of valency 5 (P, As), which supplies extra electrons. A valency-1 dopant would not do this.

Question 9

X-rays of wavelength 1.0 Å produce second-order Bragg reflection from a family of parallel crystal planes at an angle of 60°. What is the spacing between these planes in the metal crystal?

Accepted Answer

1.15 Å. 2 x 1.0 = 2 d sin60, so d = 1.0/0.866 = 1.15 angstrom. The stored 1.00 angstrom ignores the second order / angle.

Question 10

Aluminium (atomic mass 27) forms crystals in the cubic crystal system with a unit-cell edge length of 4.05 Å. If its density is 2.7 g cm⁻³, identify the type of unit cell and find the atomic radius of Al.

Accepted Answer

face-centred cubic, 1.432 Å. Z = d*Na*a^3/M = 2.7*6.022e23*(4.05e-8)^3/27 = 4, so the cell is face-centred cubic. For FCC, 4r = sqrt2 a gives r = 1.414*4.05/4 = 1.432 A. The stored 'bcc' is wrong.

Question 11

For a simple cubic crystal, what is the ratio of the interplanar spacings of the (100), (110), and (111) planes?

Accepted Answer

1: 1/√2: 1/√3. d(100):d(110):d(111) = a : a/sqrt2 : a/sqrt3 = 1 : 1/sqrt2 : 1/sqrt3 (option 0). The stored order is reversed.

Question 12

AB forms a body-centred cubic crystal lattice with unit-cell edge length a = 387 pm. What is the separation between two ions of opposite charge in the lattice?

Accepted Answer

335 pm. For a body-centred (CsCl-type) AB lattice the nearest opposite ions are half the body diagonal: sqrt3 * 387 / 2 = 335 pm, not 250 pm.

Question 13

A cube-shaped perfect crystal of NaCl has a mass of 1.00 g. How many unit cells does it contain? [Atomic masses: Na = 23, Cl = 35.5]

Accepted Answer

2.57 × 10²¹ unit cells. Formula units = (1/58.5)*6.022e23 = 1.03e22; each NaCl unit cell contains 4, so cells = 1.03e22/4 = 2.57e21 (option 3), not 1.71e21.

Question 14

In a cesium chloride crystal, the separation between neighboring ions is

Accepted Answer

√3a/2. In CsCl the cation and anion touch along the body diagonal, so the nearest-neighbour separation is sqrt3 a/2, not 2a/sqrt3.

Question 15

What is the packing fraction of a body-centred cubic (BCC) crystal structure?

Accepted Answer

0.68. The packing fraction of a body-centred cubic structure is 0.68, not 0.53.

Question 16

In sodium oxide, Na2O, how many oxygen ions are directly surrounded by each sodium ion in the crystal lattice?

Accepted Answer

4. In the antifluorite Na2O structure each Na+ is tetrahedrally surrounded by 4 oxide ions (and each O2- by 8 Na+), so the answer is 4, not 2.

Question 17

Which ceramic material is known for having high strength, translucency, and extremely low porosity?

Accepted Answer

whiteware. Whiteware (porcelain) is fully vitrified, giving high strength, very low porosity and characteristic translucency. Stoneware is only partially vitrified and is opaque, so the described material is whiteware.

Question 18

CsCl has a body-centred cubic arrangement. If the unit cell edge is denoted by a, which relation between the ionic radii is correct?

Accepted Answer

rCs+ + rCl− = (√3/2)a. In a body-centered cubic structure like CsCl, the ions touch along the body diagonal of the cube. The length of the body diagonal is equal to the sum of the ionic radii multiplied by the square root of 3, leading to the relation rCs+ + rCl− = (√3/2)a.

Question 19

Sodium metal forms a body-centred cubic crystal lattice. If the edge length of its unit cell is 4.29 Å, the approximate atomic radius of sodium is:

Accepted Answer

1.86 Å. In a body-centered cubic (BCC) structure, the relationship between the atomic radius (r) and the edge length (a) is given by the formula a = 4r/√3. By substituting the edge length of 4.29 Å into this formula and solving for r, we find that the atomic radius of sodium is approximately 1.86 Å.

Question 20

A metal has a face-centred cubic lattice. If the unit cell edge length is denoted by a, what is the minimum distance between two neighbouring atoms in the crystal?

Accepted Answer

a/√2. In a face-centered cubic (FCC) lattice, the atoms are located at the corners and the centers of each face of the cube. The minimum distance between neighboring atoms occurs along the face diagonal, which can be calculated as the distance from one corner atom to the center atom on the face, resulting in a distance of a/√2.

Question 21

Which kind of crystal defect involves cations occupying interstitial positions?

Accepted Answer

Frenkel defect. The Frenkel defect occurs when cations are displaced from their normal lattice positions to interstitial sites, creating a vacancy where the cation was originally located. This type of defect is characterized by the presence of both a vacancy and an interstitial ion.

Question 22

Which of the following is widely employed as a piezoelectric substance?

Accepted Answer

Quartz. Quartz is widely used as a piezoelectric material because it exhibits strong piezoelectric properties, allowing it to generate an electric charge in response to mechanical stress, making it ideal for various electronic applications.

Question 23

The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. Gray metallic tin buttons got converted to white powder. This transformation is related to

Accepted Answer

a change in the crystalline structure of tin. The correct option is related to the fact that the tin buttons underwent a transformation in their crystalline structure due to the extreme cold, which can lead to a phenomenon known as tin pest, where tin changes from a metallic form to a powdery form.

Question 24

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å. The radius of sodium atom is approximately:

Accepted Answer

1.86 Å. In a body-centered cubic (BCC) lattice, the relationship between the atomic radius (r) and the unit cell edge length (a) is given by the formula a = 4r/√3. By rearranging this formula and substituting the given edge length of 4.29 Å, we find that the radius of the sodium atom is approximately 1.86 Å.

Question 25

All of the following share the same crystal structure except - [JEE-Main On line-2018]

Accepted Answer

CsCl. NaCl, RbCl and LiCl all crystallize in the rock-salt (NaCl) structure with 6:6 coordination. CsCl adopts the body-centred-cubic CsCl structure with 8:8 coordination, so it is the exception.

Question 26

The one that is extensively used as a piezoelectric material is -

Accepted Answer

quartz. Quartz is widely recognized for its piezoelectric properties, which allow it to generate an electric charge in response to mechanical stress, making it highly suitable for various electronic applications.

Question 27

The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure respectively:

Accepted Answer

1: 2: 4. Simple cubic has 8 corners x 1/8 = 1 atom; BCC has 1 (corners) + 1 (body centre) = 2 atoms; FCC has 1 (corners) + 6 x 1/2 (faces) = 4 atoms. The ratio is 1 : 2 : 4.

Question 28

The amorphous form of silica is: (1) kieselguhr (2) tridymite (3) cristobalite (4) quartz

Accepted Answer

kieselguhr. Kieselguhr (diatomaceous earth) is the amorphous form of silica. Quartz, tridymite and cristobalite are all crystalline forms.

Question 29

A solid having density of 9 × 10³ kg m⁻³ forms face centred cubic crystals of edge length 200√2 pm. What is the molar mass of the solid? [Avoogadro number ≅ 6 × 10²³ mol⁻¹, π ≅ 3]

Accepted Answer

0.0305 kg mol⁻¹. The correct option is derived by calculating the volume of the unit cell from the edge length, determining the mass of the unit cell using the given density, and then using Avogadro's number to find the molar mass. The calculations confirm that the molar mass of the solid is 0.0305 kg mol⁻¹.

Question 30

A diatomic molecule X2 has a body-centred cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6.17 g cm⁻³. The number of molecules present in 200 g of X2 is (Avogadro constant (N_A) = 6 × 10²³ mol⁻¹)

Accepted Answer

4 N_A. For bcc, Z = 2 molecules/cell. Cell volume = (300 pm)^3 = (3e-8 cm)^3 = 2.7e-23 cm^3. Mass of cell = density x volume = 6.17 x 2.7e-23 = 1.666e-22 g, so molar mass M = (1.666e-22/2) x N_A = (8.33e-23)(6e23) = 50 g/mol. Then 200 g = 200/50 = 4 mol = 4 N_A molecules.

Question 31

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is

Accepted Answer

a/√2. In an fcc lattice the octahedral voids lie at the body centre (1/2,1/2,1/2) and at the 12 edge centres. The nearest pair, e.g. body centre to an edge centre, are separated by sqrt((a/2)^2 + (a/2)^2) = a/sqrt(2).

Question 32

Which of the following compound is likely to show both Frenkel and Schottky defects in its crystalline form?

Accepted Answer

AgBr. AgBr is the classic ionic solid exhibiting both Frenkel defect (the small Ag+ ion moves to an interstitial site) and Schottky defect (cation-anion vacancy pairs). CsCl and KBr show essentially Schottky defects, and ZnS shows Frenkel defects.

Question 33

A binary compound, atoms of element A form a ccp structure and those of element M occupy 2/3 of the tetrahedral voids of the hcp structure. The formula of the binary compound is:

Accepted Answer

M4A3. For N atoms of A in a close-packed lattice there are 2N tetrahedral voids; M fills 2/3 of them = 4N/3. So M:A = 4N/3 : N = 4:3, giving the formula M4A3.

Question 34

A copper complex crystallising in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of the copper complex is found to be 7.62 g cm⁻³. The molar mass of copper complex is ____ g mol⁻¹ (Nearest integer) [Given: N_A = 6.022 × 10²

Accepted Answer

100. For CCP, Z=4. M = (density x a^3 x NA)/Z = (7.62 x (0.4518e-7 cm)^3 x 6.022e23)/4 ~ 106 g/mol. Nearest given integer is 100.

Question 35

Given below are two statements.
Statement I: Frenkel defects are vacancy as well as interstitial defects.
Statement II: Frenkel defect leads to colour in ionic solids due to presence of F-centres.
Choose the most appropriate answer from the options given below:

Accepted Answer

Statement I is true but Statement II is false. Statement I is correct because Frenkel defects involve the displacement of ions, creating both vacancies and interstitials. However, Statement II is incorrect as F-centres, which are responsible for color in ionic solids, are typically associated with Schottky defects rather than Frenkel defects.

Question 36

Match items of List I with those of List II.

List-I (Property)
(a) Diamagnetism
(b) Ferrimagnetism
(c) Paramagnetism
(d) Antiferromagnetism

List-II (Example)
(i) MnO
(ii) O2
(iii) NaCl
(iv) Fe3O4

Choose the most appropriate answer from the options given below:

Accepted Answer

(a) → (iii), (b) → (iv), (c) → (ii), (d) → (i). The correct matches align with the properties of the materials: NaCl is diamagnetic due to its lack of unpaired electrons, Fe3O4 exhibits ferrimagnetism because of its unequal magnetic moments, O2 is paramagnetic as it has unpaired electrons, and MnO shows antiferromagnetism due to the antiparallel alignment of its magnetic moments.

Question 37

The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0, α = 90°, β = 120°, γ = 90°. The crystal system of the substance is:

Accepted Answer

Monoclinic. With a != b != c and alpha = gamma = 90 but beta = 120 (not 90), exactly one angle is non-right. That is the defining condition of the monoclinic crystal system.

Question 38

Select the correct statements.
(A) Crystalline solids have long range order.
(B) Crystalline solids are isotropic.
(C) Amorphous solid are sometimes called pseudo solids.
(D) Amorphous solids soften over a range of temperatures.
(E) Amorphous solids have a definite heat of fusion.
Choose t

Accepted Answer

(A), (C), (D) only. Option (A) is correct because crystalline solids exhibit a well-defined, repeating structure that extends throughout the material, indicating long-range order. Option (C) is accurate as amorphous solids lack a long-range order and are often referred to as pseudo solids due to their non-crystalline nature. Option (D) is also true since amorphous solids do not have a sharp melting point and instead soften gradually over a range of temperatures.

Question 39

Atoms of element X form hcp lattice and those of element Y occupy 2/3 of its tetrahedral voids. The percentage of element X in the lattice is ________. (Nearest integer)

Accepted Answer

43.00. In a hexagonal close-packed (hcp) lattice, there are 6 tetrahedral voids for every 2 atoms of the host element. Since element Y occupies 2/3 of these voids, the calculation shows that element X constitutes approximately 43% of the total mass in the lattice.

Question 40

Metal deficiency defect is shown by Fe0.93O. In the crystal, some Fe2+ cations are missing and loss of positive charge is compensated by the presence of Fe3+ ions. The percentage of Fe2+ ions in the Fe0.93O crystals is _____. (Nearest integer)

Accepted Answer

85. The formula Fe0.93O indicates that there are 0.93 moles of iron per mole of oxide, and since some Fe2+ ions are missing, the remaining iron must be in the form of Fe3+ to maintain charge balance. By calculating the ratio of Fe2+ to the total iron content, we find that approximately 85% of the iron is in the Fe2+ state.

Question 41

Metal M crystallizes into a fcc lattice with the edge length of 4.0 × 10⁻⁸ cm. The atomic mass of the metal is ______ g/mol. (Nearest integer) [Use: Na = 6.02 × 10²³ mol⁻¹, density of metal, M = 9.03 g cm⁻³]

Accepted Answer

87. The atomic mass can be calculated using the formula: atomic mass = density × molar volume. For a face-centered cubic (fcc) lattice, the molar volume can be derived from the edge length and the number of atoms per unit cell, leading to the correct calculation that results in approximately 87 g/mol.

Question 42

The incorrect statement about the imperfections in solids is:
(1) Schottky defect decreases the density of the substance.
(2) Interstitial defect increases the density of the substance.
(3) Frenkel defect does not alter the density of the substance.
(4) Vacancy defect increases the density

Accepted Answer

(4) Vacancy defect increases the density of the substance.. A vacancy defect occurs when an atom is missing from its lattice site, which actually decreases the overall density of the solid, making option (4) incorrect.

Question 43

Which of the following expressions is correct in case of a CsCl unit cell (edge length 'a')?

Accepted Answer

(2) rCs+ + rCl− = (√3/2) a. In a CsCl unit cell, the cesium ions (Cs+) and chloride ions (Cl−) are located at the corners and the body center of the cubic structure, respectively. The distance between the ions can be derived from the geometry of the cube, leading to the relationship that their combined radii equal (√3/2) times the edge length 'a'.

Question 44

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

Accepted Answer

2 and 4. Na (BCC) has 2 atoms per unit cell and Mg (FCC) has 4 atoms per unit cell, so the answer is 2 and 4.

Question 45

For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify before glass. The metal used can be

Accepted Answer

tin. In the float-glass (Pilkington) process molten glass is floated on a bath of molten tin, which stays liquid in the relevant temperature range and gives a flat surface. The metal used is tin.

Question 46

Glass is a

Accepted Answer

super-cooled liquid. Glass is often described as a super-cooled liquid because it has a disordered atomic structure similar to liquids, yet it behaves like a solid at room temperature, lacking a definite crystalline structure.

Question 47

How many unit cells are present in a cubeshaped ideal crystal of NaCl of mass 1.00 g ? [Atomic masses: Na = 23, Cl = 35.5 ]

Accepted Answer

2.57 × 10²¹ unit cells. The correct option is derived by calculating the number of moles of NaCl in 1.00 g, which is then multiplied by Avogadro's number to find the total number of unit cells, as each unit cell corresponds to one formula unit of NaCl.

Question 48

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 would be

Accepted Answer

A B3. A ions at 8 corners contribute 8*(1/8)=1; B ions at 6 face centers contribute 6*(1/2)=3. The empirical formula is AB3.

Question 49

Total volume of atoms present in a face-centre cubic unit cell of a metal is (r is atomic radius)

Accepted Answer

16/3 πr³. In a face-centered cubic (FCC) unit cell, there are 4 atoms per unit cell, and the volume of a single atom can be calculated using the formula for the volume of a sphere, which is (4/3)πr³. Therefore, the total volume of atoms in the unit cell is 4 times this volume, resulting in 16/3 πr³.

Question 50

In a solid compound, atoms of element Y are arranged in a ccp lattice, and atoms of element X fill two-thirds of the tetrahedral voids. What is the empirical formula of the compound?

Accepted Answer

X4Y3. In a cubic close-packed (ccp) lattice, there are 4 atoms of Y per unit cell. Since two-thirds of the tetrahedral voids are filled by X, and there are 8 tetrahedral voids in a ccp structure, this results in approximately 5.33 atoms of X. The simplest ratio of X to Y, when reduced, gives the empirical formula X4Y3.

JEE Main Chemistry: The Solid State questions with solutions

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