Question 1: Palette 1/46

JEE Mains 2023 MCQ

Which of the following expressions is correct in case of a $\mathrm{CsCl}$ unit cell (edge length 'a')?

A

$\mathrm{r}_{\mathrm{Cs}^{+}}+\mathrm{r}_{\mathrm{Cl}^{-}}=\frac{\sqrt{3}}{2} \mathrm{a}$

B

$\mathrm{r}_{\mathrm{Cs}^{+}}+\mathrm{r}_{\mathrm{Cl}^{-}}=\frac{\mathrm{a}}{\sqrt{2}}$

C

$\mathrm{r}_{\mathrm{Cs}^{+}}+\mathrm{r}_{\mathrm{Cl}^{-}}=\mathrm{a}$

D

$\mathrm{r}_{\mathrm{Cs}^{+}}+\mathrm{r}_{\mathrm{Cl}^{-}}=\frac{\mathrm{a}}{2}$

Question 2: Palette 2/46

JEE Mains 2023 MCQ

The correct relationships between unit cell edge length '$a$' and radius of sphere '$r$' for face-centred and body-centred cubic structures respectively are :

A

$r=2 \sqrt{2} a$ and $\sqrt{3} r=4 a$

B

$r=2 \sqrt{2} a$ and $4 r=\sqrt{3} a$

C

$2 \sqrt{2} r=a$ and $\sqrt{3} r=4 a$

D

$2 \sqrt{2} r=a$ and $4 r=\sqrt{3} a$

Question 3: Palette 3/46

JEE Mains 2023 MCQ

A compound is formed by two elements $\mathrm{X}$ and $\mathrm{Y}$. The element $\mathrm{Y}$ forms cubic close packed arrangement and those of element $\mathrm{X}$ occupy one third of the tetrahedral voids. What is the formula of the compound?

A

$\mathrm{XY}_{3}$

B

$\mathrm{X_3Y}_{2}$

C

$\mathrm{X_3Y}$

D

$\mathrm{X_2Y}_{3}$

Question 4: Palette 4/46

JEE Mains 2023 MCQ

Which of the following represents the lattice structure of $\mathrm{A_{0.95}O}$ containing $\mathrm{A^{2+},A^{3+}}$ and $\mathrm{O^{2-}}$ ions?

A

B only

B

A and B only

C

A only

D

B and C only

Question 5: Palette 5/46

JEE Mains 2023 MCQ

A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. Y is at $\frac{1}{3}^{\mathrm{rd}}$ of the total faces. The empirical formula of the compound is :

A

$\mathrm{{X_2}{Y_{1.5}}}$

B

$\mathrm{{X_{3}}{Y_2}}$

C

$\mathrm{X{Y_{2.5}}}$

D

$\mathrm{{X_{2.5}}Y}$

Question 6: Palette 6/46

JEE Mains 2022 MCQ

An element X has a body centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm^$-$3. The number of atoms present in 300 g of the element X is _______________.

Given : Avogadro constant, N_A = 6.0 $\times$ 10²³ mol^$-$1.

A

5 N_A

B

6 N_A

C

15 N_A

D

25 N_A

Question 7: Palette 7/46

JEE Mains 2022 MCQ

The incorrect statement about the imperfections in solids is :

A

Schottky defect decreases the density of the substance.

B

Interstitial defect increases the density of the substance.

C

Frenkel defect does not alter the density of the substance.

D

Vacancy defect increases the density of the substance.

Question 8: Palette 8/46

JEE Mains 2021 MCQ

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 for the statements from the options given below :

A

Statement I is false but Statement II is true

B

Both Statement I and Statement II are true

C

Statement I is true but Statement II is false

D

Both Statement I and Statement II are false

Question 9: Palette 9/46

JEE Mains 2021 MCQ

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 the most appropriate answer from the options given below.

A

(A), (B), (E) only

B

(B), (D) only

C

(C), (D) only

D

(A), (C), (D) only

Question 10: Palette 10/46

JEE Mains 2021 MCQ

The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0, $\alpha$ = 90$^\circ$, $\beta$ = 120$^\circ$, $\gamma$ = 90$^\circ$. The crystal system of the substance is :

A

Hexagonal

B

Orthorhombic

C

Monoclinic

D

Triclinic

Question 11: Palette 11/46

JEE Mains 2021 MCQ

Given below are two statements. One is labelled as Assertion A nd the other is labelled as Reason R.

Assertion A : Sharp glass edge becomes smooth on heating it upto its melting point.

Reason R : The viscosity of glass decreases on melting.

Choose the most appropriate answer from the options given below.

A

A is true but R is false

B

Both A and R are true but R is NOT the correct explanation of A.

C

A is false but R is true.

D

Both A and R are true and R is the correct explanation of A.

Question 12: Palette 12/46

JEE Mains 2021 MCQ

A hard substance melts at high temperature and is an insulator in both solid and in molten state. This solid is most likely to be a/an :

A

Covalent solid

B

Molecular solid

C

Ionic solid

D

Metallic solid

Question 13: Palette 13/46

JEE Mains 2021 MCQ

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

A

M₂A₃

B

M₄A₃

C

M₄A

D

MA₃

Question 14: Palette 14/46

JEE Mains 2020 MCQ

A crystal is made up of metal ions 'M₁' and 'M₂' and oxide ions. Oxide ions form a ccp lattice structure. The cation 'M₁' occupies 50% of octahedral voids and the cation 'M₂' occupies 12.5% of tetrahedral voids of oxide lattice. The oxidation numbers of 'M₁' and 'M₂' are, respectively :

A

+ 3, + 1

B

+ 4, + 2

C

+ 1, + 3

D

+ 2, + 4

Question 15: Palette 15/46

JEE Mains 2020 MCQ

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 :

A

$a$

B

${a \over 2}$

C

${a \over {\sqrt 2 }}$

D

${\sqrt 2 a}$

Question 16: Palette 16/46

JEE Mains 2020 MCQ

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 $ \times $ 10²³ mol^–1 )

A

8 N_A

B

40 N_A

C

4 N_A

D

2 N_A

Question 17: Palette 17/46

JEE Mains 2020 MCQ

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

A

CsCl

B

AgBr

C

ZnS

D

KBr

Question 18: Palette 18/46

JEE Mains 2019 MCQ

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

A

8 : 1 : 6

B

4 : 2 : 1

C

1 : 2 : 4

D

4 : 2 : 3

Question 19: Palette 19/46

JEE Mains 2019 MCQ

An element has a face-centred cubic (fcc) structure with a cell edge of $a$. The distance between the centres of two nearest tetrahedral voids in the lattice is :

A

$a$

B

${3 \over 2}a$

C

${a \over 2}$

D

$\sqrt 2 a$

Question 20: Palette 20/46

JEE Mains 2019 MCQ

10 mL of 1mM surfactant solution forms a monolayer covering 0.24 cm² on a polar substrate. If the polar head is approximated as cube, what is its edge length?

A

1.0 pm

B

2.0 nm

C

0.1 nm

D

2.0 pm

Question 21: Palette 21/46

JEE Mains 2019 MCQ

Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?

A

45%

B

90%

C

75%

D

65%

Question 22: Palette 22/46

JEE Mains 2019 MCQ

0.27 g of a long chain fatty acid was dissolved in 100 cm³ of hexane. 10 mL of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is 10 cm. What is the height of the monolayer?
[Density of fatty acid = 0.9 g cm^–3, $\pi $ = 3]

A

10^–8 m

B

10^–2 m

C

10^–4 m

D

10^–6 m

Question 23: Palette 23/46

JEE Mains 2019 MCQ

Element 'B' forms ccp structure and 'A' occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids, The structure of bimetallic oxide is :

A

AB₂O₄

B

A₂BO₄

C

A₄B₂O

D

A₂B₂O

Question 24: Palette 24/46

JEE Mains 2019 MCQ

The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by 'a')

A

0.134 a

B

0.067 a

C

0.047 a

D

0.027 a

Question 25: Palette 25/46

JEE Mains 2019 MCQ

A solid having density of 9$ \times $10³ kg m^–3 forms face centred cubic crystals of edge length $200\sqrt 2 $ pm. What is the molar mass of the solid?
[Avogadro constant $ \cong $ 6 $ \times $ 10²³ mol^–1 , $\pi $ $ \cong $ 3]

A

0.0305 kg mol^–1

B

0.4320 kg mol^–1

C

0.0216 kg mol^–1

D

0.0432 kg mol^–1

Question 26: Palette 26/46

JEE Mains 2019 MCQ

A compound of formula A₂B₃ has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms :

A

hcp lattice - A, ${1 \over 3}$ Tetrahedral voids-B

B

hcp lattice - B, ${1 \over 3}$ Tetrahedral voids - A

C

hcp lattice - A, ${2 \over 3}$ Tetrahedral voids - B

D

hcp lattice - B, ${2 \over 3}$ Tetrahedral voids - A

Question 27: Palette 27/46

JEE Mains 2019 MCQ

Which premitive unit cell has unequal edge lengths (a $ \ne $ b $ \ne $ c) and all axial angles different from 90^o?

A

Hexagonal

B

Tetragonal

C

Triclinic

D

Monoclinic

Question 28: Palette 28/46

JEE Mains 2019 MCQ

At 100^oC, copper (Cu) has FCC unit cell structure with cell edge length of x $\mathop A\limits^o $. What is the approximate density of Cu (in g cm^$-$3) at this temperature?
[Atomic Mass of Cu = 63.55 u]

A

${{205} \over {{x^3}}}$

B

${{105} \over {{x^3}}}$

C

${{211} \over {{x^3}}}$

D

${{422} \over {{x^3}}}$

Question 29: Palette 29/46

JEE Mains 2018 MCQ

Which type of ‘defect’ has the presence of cations in the interstitial sites?

A

Metal deficiency defect

B

Schottky defect

C

Vacancy defect

D

Frenkel defect

Question 30: Palette 30/46

JEE Mains 2018 MCQ

All of the following share the same crystal structure except :

A

LiCl

B

NaCl

C

RbCl

D

CsCl

Question 31: Palette 31/46

JEE Mains 2018 MCQ

Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance ?

A

B

C

D

Question 32: Palette 32/46

JEE Mains 2017 MCQ

A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal will be :

A

$2\sqrt 2 a$

B

$\sqrt 2 a$

C

${a \over {\sqrt 2 }}$

D

2a

Question 33: Palette 33/46

JEE Mains 2015 MCQ

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 :

A

5.72 Å

B

0.93 Å

C

1.86 Å

D

3.22 Å

Question 34: Palette 34/46

JEE Mains 2014 MCQ

CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following expressions is correct?

A

${r_{C{s^ + }}} + {r_{C{l^ - }}} = {{\sqrt 3 } \over 2}a$

B

${r_{C{s^ + }}} + {r_{C{l^ - }}} = {3 \over 2}a$

C

${r_{C{s^ + }}} + {r_{C{l^ - }}} = \sqrt 3 a$

D

${r_{C{s^ + }}} + {r_{C{l^ - }}} = 3a$

Question 35: Palette 35/46

JEE Mains 2013 MCQ

Which of the following exists as covalent crystals in the solid state?

A

Silicon

B

Sulphur

C

Phosphorous

D

Iodine

Question 36: Palette 36/46

JEE Mains 2012 MCQ

Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be :

A

75 pm

B

300 pm

C

240 pm

D

152 pm

Question 37: Palette 37/46

JEE Mains 2011 MCQ

In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is :

A

AB₂

B

A₂B₃

C

A₂B₅

D

A₂B

Question 38: Palette 38/46

JEE Mains 2010 MCQ

Percentages of free space in cubic close packed structure and in body centred packed structure are respectively :

A

30% and 26%

B

26% and 32%

C

32% and 48%

D

48% and 26%

Question 39: Palette 39/46

JEE Mains 2010 MCQ

The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is :

A

288 pm

B

398 pm

C

618 pm

D

144 pm

Question 40: Palette 40/46

JEE Mains 2009 MCQ

Copper crystallizes in fcc with a unit cell length of 361 pm. What is the radius of copper atom?

A

108 pm

B

127 pm

C

157 pm

D

181 pm

Question 41: Palette 41/46

JEE Mains 2008 MCQ

In a compound atoms of element Y from ccp lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be :

A

X₄Y₃

B

X₂Y₃

C

X₂Y

D

X₃Y₄

Question 42: Palette 42/46

JEE Mains 2006 MCQ

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

A

20/3 $\pi r^3$

B

24/3 $\pi r^3$

C

16/3 $\pi r^3$

D

12/3 $\pi r^3$

Question 43: Palette 43/46

JEE Mains 2005 MCQ

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 :

A

AB

B

A₂B

C

AB₃

D

A₃B

Question 44: Palette 44/46

JEE Mains 2004 MCQ

What type of crystal defect is indicated in the diagram below?

A

Interstitial defect

B

Schottky defect

C

Frenkel defect

D

Frenkel and Schottky defects

Question 45: Palette 45/46

JEE Mains 2003 MCQ

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]

A

5.14 $\times$ 10²¹ unit cells

B

1.28 $\times$ 10²¹ unit cells

C

1.71 $\times$ 10²¹ unit cells

D

2.57 $\times$ 10²¹ unit cells

Question 46: Palette 46/46

JEE Mains 2002 MCQ

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

4 and 2

B

9 and 14

C

14 and 9

D

2 and 4