Solid State — JEE Previous Year Questions

Every Solid State question asked in JEE Main and JEE Advanced across the last 186 papers — 63 questions, each with its correct answer. Free to read, no account needed.

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63/186

Appearance rate

34%

All 63 Solid State questions

Most recent papers first.

Q1·ChemistryNumericalJEE Advanced 2025

The density (in g cm

^{-3}

) of the metal which forms a cubic close packed (ccp) lattice with an axial distance (edge length) equal to 400 pm is ______. Use: Atomic mass of metal = 105.6 amu and Avogadro's constant = 6

\times

^{23}

mol

^{-1}

Q2·ChemistrySingle correctJEE Advanced 2024

In a metal deficient oxide sample,

M_xY_2O_4

(

M

and

Y

are metals),

M

is present in both +2 and +3 oxidation states and

Y

is in +3 oxidation state. If the fraction of

M^{2+}

ions present in

M

\frac{1}{3}

, the value of

X

is______.

(A)0.25
(B)0.33
(C)0.67
(D)0.75

Q3·ChemistrySingle correctJEE Main 2024

Which of the following material is not a semiconductor?

(A)Germanium
(B)Graphite
(C)Silicon
(D)Copper oxide

Q4·ChemistryNumericalJEE Main 2024

The values of conductivity of some materials at 298.15 K in S m

^{-1}

are

2.1\times10^3

1.2\times10

, 3.91,

1.5\times10^{-2}

1\times10^{-7}

1.0\times10^3

. The number of conductors among the materials is ______.

Q5·ChemistryMultiple correctJEE Advanced 2023

Atoms of metals x, y, and z form face-centred cubic (fcc) unit cell of edge length

L_x

, body-centred cubic (bcc) unit cell of edge length

L_y

, and simple cubic unit cell of edge length

L_z

, respectively. If

r_z = \frac{\sqrt{3}}{2} r_y

;

r_y = \frac{8}{\sqrt{3}} r_x

;

M_z = \frac{3}{2} M_y

and

M_Z = 3M_x

. then the correct statement(s) is(are) [Given:

M_x

M_y

, and

M_z

are molar masses of metals x, y, and z, respectively.

r_x

r_y

, and

r_z

are atomic radii of metals x, y, and z, respectively.]

(A)Packing efficiency of unit cell of x > Packing efficiency of unit cell of y > Packing efficiency of unit cell of z
(B) $L_y > L_z$
(C) $L_x > L_y$
(D)Density of x > Density of y

Q6·ChemistrySingle correctJEE Main 2023

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

(A) $r_{Cs^+} + r_{Cl^-} = \dfrac{a}{\sqrt{2}}$
(B) $r_{Cs^+} + r_{Cl^-} = a$
(C) $r_{Cs^+} + r_{Cl^-} = \dfrac{\sqrt{3}}{2}a$
(D) $r_{Cs^+} + r_{Cl^-} = \dfrac{a}{2}$

Q7·ChemistryNumericalJEE Main 2023

Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4 Å. The radius of sodium atom is ____

\times 10^{-1}

Å (Nearest integer)

Q8·ChemistrySingle correctJEE Main 2023

Which one of the following pairs is an example of polar molecular solids?

(A) $SO_2(s),\ NH_3(s)$
(B) $SO_2(s),\ CO_2(s)$
(C) $HCl(s),\ AlN(s)$
(D) $MgO(s),\ SO_2(s)$

Q9·ChemistryNumericalJEE Main 2023

An atomic substance A of molar mass

12

mol^{-1}

has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is __________. (Nearest integer) Given the density of A is

3.0

mL^{-1}

and

N_A = 6.02 \times 10^{23}

mol^{-1}

Q10·ChemistrySingle correctJEE Main 2023

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

(A) $r=2\sqrt{2}a$ and $\sqrt{3}r=4a$
(B) $r=2\sqrt{2}a$ and $4r=\sqrt{3}a$
(C) $2\sqrt{2}r=a$ and $4r=\sqrt{3}a$
(D) $2\sqrt{2}r=a$ and $\sqrt{3}r=4a$

Q11·ChemistrySingle correctJEE Main 2023

A compound is formed by two elements

X

and

Y

. The element

Y

forms cubic close packed arrangement and those of element

X

occupy one third of the tetrahedral voids. What is the formula of the compound?

(A) $X_2Y_3$
(B) $X_3Y$
(C) $X_3Y_2$
(D) $XY_3$

Q12·ChemistryNumericalJEE Main 2023

Number of crystal systems from the following where body centred unit cell can be found, is ____. Cubic, orthorhombic, tetragonal, hexagonal, rhombohedral, monoclinic, triclinic.

Q13·ChemistrySingle correctJEE Main 2023

Which of the following represents the lattice structure of

\text{A}_{0.95}\text{O}

containing

\text{A}^{2+}

\text{A}^{3+}

and

\text{O}^{2-}

ions (structures A, B and C shown in the figure)?

(A)A only
(B)B and C only
(C)A and B only
(D)B only

Q14·ChemistryNumericalJEE Main 2023

A metal M crystallizes into two lattices: face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of

2.0

and

2.5

Å respectively. The ratio of densities of lattices fcc to bcc for the metal M is _________ (Nearest integer)

Q15·ChemistryNumericalJEE Main 2023

A sample of a metal oxide has formula

M_{0.83}O_{1.00}

. The metal M can exist in two oxidation states +2 and +3. In the sample of

M_{0.83}O_{1.00}

, the percentage of metal ions existing in +2 oxidation state is _________ %. (nearest integer)

Q16·ChemistryNumericalJEE Main 2023

Iron oxide FeO crystallises in a cubic lattice with a unit cell edge length of 5.0 Å. If the density of FeO in the crystal is 4.0 g cm

^{-3}

, then the number of FeO units present per unit cell is _______ (nearest integer). (Given: molar mass of Fe and O is 56 and 16 g mol

^{-1}

respectively;

N_A=6.0\times10^{23}

mol

^{-1}

)

Q17·ChemistryNumericalJEE Main 2023

A metal

M

forms hexagonal close-packed structure. The total number of voids in

0.02

mol of it is _____

\times10^{21}

(Nearest integer). (Given

N_A=6.02\times10^{23}

)

Q18·ChemistrySingle correctJEE Main 2023

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 the cube. Y is at

\dfrac{1}{3}

rd of the total faces. The empirical formula of the compound is:

(A) $XY_{2.5}$
(B) $X_2Y_{1.5}$
(C) $X_2Y$
(D) $X_{1.5}Y_2$

Q19·ChemistryNumericalJEE Main 2023

When

\text{Fe}_{0.93}\text{O}

is heated in presence of oxygen, it converts to

\text{Fe}_2\text{O}_3

. The number of correct statement/s from the following is: A. The equivalent weight of

\text{Fe}_{0.93}\text{O}

\tfrac{\text{Molecular weight}}{0.79}

. B. The number of moles of

\text{Fe}^{2+}

and

\text{Fe}^{3+}

in 1 mole of

\text{Fe}_{0.93}\text{O}

is 0.79 and 0.14 respectively. C.

\text{Fe}_{0.93}\text{O}

is metal deficient with lattice comprising of cubic closed packed arrangement of

\text{O}^{2-}

ions. D. The % composition of

\text{Fe}^{2+}

and

\text{Fe}^{3+}

\text{Fe}_{0.93}\text{O}

is 85% and 15% respectively.

Q20·ChemistrySingle correctJEE Advanced 2022

Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closed to

(A)25
(B)35
(C)55
(D)75

Q21·ChemistryNumericalJEE Main 2022

Ionic radii of cation

A^{+}

and anion

B^{-}

are 102 and 181 pm respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for

B^{-}

A^{+}

is present in all octahedral voids. The edge length of the unit cell of the crystal AB is ______ pm. (Nearest Integer)

Q22·ChemistryNumericalJEE Main 2022

Metal M crystallizes into a FCC lattice with the edge length of

4.0\times10^{-8}

cm. The atomic mass of the metal is _____ g/mol. (Nearest integer). (Use :

\mathrm{N_A} = 6.02\times10^{23}\ \mathrm{mol^{-1}}

, density of metal, M = 9.03 g

\mathrm{cm^{-3}}

)

Q23·ChemistryNumericalJEE Main 2022

An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 g cm

^{-3}

. The number of atoms present in 180 g of the element is _______ × 10

^{23}

. (Nearest integer)

Q24·ChemistrySingle correctJEE Main 2022

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.

Q25·ChemistryNumericalJEE Main 2022

Metal deficiency defect is shown by

Fe_{0.93}O

. In the crystal, some

Fe^{2+}

cations are missing and loss of positive charge is compensated by the presence of

Fe^{3+}

ions. The percentage of

Fe^{2+}

ions in the

Fe_{0.93}O

crystals is __________ . (Nearest integer)

Q26·ChemistryNumericalJEE Main 2022

In a solid AB. A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is

A_xB_y

. The value of x is________. [nearest integer]

Q27·ChemistryNumericalJEE Main 2022

The distance between

Na^+

and

Cl^-

ions in solid NaCl of density 43.1 g

cm^{-3}

is ________ ×

10^{-10}

m. (Nearest Integer) (Given :

N_A

= 6.02 ×

10^{23}

mol^{-1}

)

Q28·ChemistryNumericalJEE Main 2022

Atoms of element X form hcp lattice and those of element Y occupy

\frac{2}{3}

of its tetrahedral voids. The percentage of element X in the lattice is__________ (Nearest integer)

Q29·ChemistrySingle correctJEE Advanced 2021

For the given close packed structure of a salt made of cation

\mathbf{X}

and anion

\mathbf{Y}

shown below (ions of only one face are shown for clarity) , the packing fraction is approximately (packing fraction =

\frac{\text{Packing efficiency}}{100}

)

(A)0.74
(B)0.63
(C)0.52
(D)0.48

Q30·ChemistryNumericalJEE Main 2021

The empirical formula for a compound with a cubic close packed arrangement of anions and with cations occupying all the octahedral sites in

\mathrm{A_xB}

. The value of x is __________ (Integer answer)

Q31·ChemistrySingle correctJEE Main 2021

Match items of List-I with those of List-II : List-I (Property) List-II (Example) (a) Diamagnetism (b) Ferrimagnetism (c) Paramagnetism (d) Antiferromagnetism (i) MnO (ii)

\mathrm{O_2}

(iii) NaCl (iv)

\mathrm{Fe_3O_4}

Choose the most appropriate answer from the options given below :

(A)(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
(B)(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)
(C)(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
(D)(a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

Q32·ChemistrySingle correctJEE Main 2021

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

Q33·ChemistrySingle correctJEE Main 2021

Select the correct statements. (A) Crystalline solids have long range order. (B) Crystalline solids are isotropic. (C) Amorphous solids 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)(B), (D) only
(B)(A), (B), (E) only
(C)(A), (C), (D) only
(D)(C), (D) only

Q34·ChemistrySingle correctJEE Main 2021

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

(A)Monoclinic
(B)Triclinic
(C)Orthorhombic
(D)Hexagonal

Q35·ChemistryNumericalJEE Main 2021

A copper complex crystallizing in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be 7.26 g cm

^{-3}

. The molar mass of copper complex is __________ g mol

^{-1}

. (Nearest integer) [Given :

N_A

= 6.022

\times 10^{23}

mol

^{-1}

]

Q36·ChemistrySingle correctJEE Main 2021

Given below are two statements. One is labelled as Assertion A and 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 false but R is true.
(B)Both A and R are true but R is NOT the correct explanation of A.
(C)A is true but R is false
(D)Both A and R are true and R is the correct explanation of A.

Q37·ChemistryNumericalJEE Main 2021

Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is __________.

Q38·ChemistrySingle correctJEE Main 2021

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)Ionic solid
(B)Molecular solid
(C)Metallic solid
(D)Covalent solid

Q39·ChemistrySingle correctJEE Main 2021

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)M $_{2}$ A $_{3}$
(B)M $_{4}$ A $_{3}$
(C)M $_{4}$ A
(D)MA $_{3}$

Q40·ChemistryNumericalJEE Main 2021

A certain element crystallises in a bcc lattice of unit cell edge length 27 Å. If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cell in Å will be ________. (Round off to the Nearest Integer). [Assume each lattice point has a single atom] [Assume

\sqrt{3}

= 1.73,

\sqrt{2}

= 1.41]

Q41·ChemistryNumericalJEE Main 2021

Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is _______ × 10

^{21}

. (Round off to the Nearest Integer).

Q42·ChemistryNumericalJEE Main 2021

The number of octahedral voids per lattice site in a lattice is ___________. (Rounded off to the nearest integer)

Q43·ChemistryNumericalJEE Main 2021

The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m

^{3}

is ______. [Molar mass of Cu : 63.54 g; Avogadro number = 6.022×10

^{23}

]

Q44·ChemistryNumericalJEE Main 2021

The coordination number of an atom in a body-centered cubic structure is ________________. [Assume that the lattice is made up of atoms]

Q45·ChemistryMultiple correctJEE Advanced 2020

The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

(A)The empirical formula of the compound is MX.
(B)The cation M and anion X have different coordination geometries.
(C)The ratio of M-X bond length to the cubic unit cell edge length is 0.866.
(D)The ratio of the ionic radii of cation M to anion X is 0.414.

Q46·ChemistrySingle correctJEE Main 2020

A crystal is made up of metal ions 'M

_1

' and 'M

_2

' and oxide ions. Oxide ions form a ccp lattice structure. The cation 'M

_1

' occupies 50% of octahedral voids and the cation 'M

_2

' occupies 12.5% of tetrahedral voids of oxide lattice. The oxidation numbers of 'M

_1

' and 'M

_2

' are respectively:

(A)+2, +4
(B)+1, +3
(C)+3, +1
(D)+4, +2

Q47·ChemistrySingle correctJEE Main 2020

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) $\dfrac{a}{2}$
(B) $\sqrt{2}a$
(C)a
(D) $\dfrac{a}{\sqrt{2}}$

Q48·ChemistryNumericalJEE Main 2020

An element with molar mass 2.7

\times

^{-2}

kg mol

^{-1}

forms a cubic unit cell with edge length 405 pm. If its density is 2.7

\times

^3

kg m

^{-3}

, the radius of the element is approximately __________

\times

^{-12}

m (to the nearest integer).

Q49·ChemistrySingle correctJEE Main 2020

'X' melts at low temperature and is a bad conductor of electricity in both liquid and solid state. X is:

(A)Silicon carbide
(B)Mercury
(C)Zinc sulphide
(D)Carbon tetrachloride

Q50·ChemistrySingle correctJEE Main 2020

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

(A)CsCl
(B)AgBr
(C)ZnS
(D)KBr

Q51·ChemistrySingle correctJEE Main 2019

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

(A)1 : 2 : 4
(B)4 : 2 : 3
(C)4 : 2 : 1
(D)8 : 1 : 6

Q52·ChemistrySingle correctJEE Main 2019

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) $\dfrac{a}{2}$
(B) $\sqrt{2}a$
(C) $\dfrac{3}{2}a$
(D)a

Q53·ChemistrySingle correctJEE Main 2019

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) $A_2B_2O$
(B) $AB_2O_4$
(C) $A_4B_2O$
(D) $A_2BO_4$

Q54·ChemistrySingle correctJEE Main 2019

Consider the bcc unit cells of the solid 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)90%
(B)75%
(C)65%
(D)45%

Q55·ChemistrySingle correctJEE Main 2019

A solid having density of

9 × 10^{3}

kg m

^{-3}

forms face centred cubic crystale of edge length

200\sqrt{2}

pm. What is the molar mass of the solid? [Avogadro constant ≅ 6 ×

10^{23}

and mol

^{-1}

, π ≅ 3]

(A)0.0432 kg mol $^{-1}$
(B)0.0216 kg mol $^{-1}$
(C)0.0305 kg mol $^{-1}$
(D)0.4320 kg mol $^{-1}$

Q56·ChemistrySingle correctJEE Main 2019

Which primitive unit cell has unequal edge length (a ≠ b ≠ c) and all axial angles different from 90°?

(A)Triclinic
(B)Hexagonal
(C)Monoclinic
(D)Tetragonal

Q57·ChemistrySingle correctJEE Main 2019

The one that is extensively used as a piezoelectric material is

(A)tridymite
(B)amorphous silica
(C)quartz
(D)mica

Q58·ChemistrySingle correctJEE Main 2019

At 100°C, copper(Cu) has FCC unit cell structure with cell edge length x Å. What is the approximate density of Cu(in g cm

^{-3}

) at this temperature? [Atomic mass of Cu = 63.55 u]

(A) $\dfrac{205}{x^{3}}$
(B) $\dfrac{105}{x^{3}}$
(C) $\dfrac{211}{x^{3}}$
(D) $\dfrac{422}{x^{3}}$

Q59·ChemistryNumericalJEE Advanced 2018

Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance. (i) Remove all the anions (X) except the central one (ii) Replace all the face centered cations (M) by anions (X) (iii) Remove all the corner cations (M) (iv) Replace the central anion (X) with cation (M) The value of

\left(\dfrac{\text{number of anions}}{\text{number of cations}}\right)

in Z is ___.

Q60·ChemistryIntegerJEE Advanced 2017

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g

cm^{-3}

, then the number of atoms present in 256 g of the crystal is

N \times 10^{24}

. The value of

N

Q61·ChemistryMultiple correctJEE Advanced 2016

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is(are)

(A)The number of the nearest neighbours of an atom present in the topmost layer is 12
(B)The efficiency of atom packing is 74%
(C)The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively
(D)The unit cell edge length is $2\sqrt{2}$ times the radius of the atom

Q62·ChemistryMultiple correctJEE Advanced 2015

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with

\mathbf{m}

fraction of octahedral holes occupied by aluminium ions and

\mathbf{n}

fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

(A) $\dfrac{1}{2},\ \dfrac{1}{8}$
(B) $1,\ \dfrac{1}{4}$
(C) $\dfrac{1}{2},\ \dfrac{1}{2}$
(D) $\dfrac{1}{4},\ \dfrac{1}{8}$

Q63·ChemistrySingle correctJEE Advanced 2013

The arrangement of X

^{-}

ions around A

^{+}

ion in solid AX is given in the figure (not drawn to scale). If the radius of X

^{-}

is 250 pm, the radius of A

^{+}

(A)104 pm
(B)125 pm
(C)183 pm
(D)57 pm

Solid State — frequently asked

How many questions from Solid State appear in JEE?

Solid State has appeared in 63 of the last 186 JEE Main and JEE Advanced papers — about 34% of them — contributing 63 questions in total across those papers.

Is Solid State an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 34% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Solid State questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

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Q1·ChemistryNumericalJEE Advanced 2025

The density (in g cm

^{-3}

) of the metal which forms a cubic close packed (ccp) lattice with an axial distance (edge length) equal to 400 pm is ______. Use: Atomic mass of metal = 105.6 amu and Avogadro's constant = 6

\times

^{23}

mol

^{-1}

Q2·ChemistrySingle correctJEE Advanced 2024

In a metal deficient oxide sample,

M_xY_2O_4

(

M

and

Y

are metals),

M

is present in both +2 and +3 oxidation states and

Y

is in +3 oxidation state. If the fraction of

M^{2+}

ions present in

M

\frac{1}{3}

, the value of

X

is______.

(A)0.25
(B)0.33
(C)0.67
(D)0.75

Q3·ChemistrySingle correctJEE Main 2024

Which of the following material is not a semiconductor?

(A)Germanium
(B)Graphite
(C)Silicon
(D)Copper oxide

Q4·ChemistryNumericalJEE Main 2024

The values of conductivity of some materials at 298.15 K in S m

^{-1}

are

2.1\times10^3

1.2\times10

, 3.91,

1.5\times10^{-2}

1\times10^{-7}

1.0\times10^3

. The number of conductors among the materials is ______.

Q5·ChemistryMultiple correctJEE Advanced 2023

Atoms of metals x, y, and z form face-centred cubic (fcc) unit cell of edge length

L_x

, body-centred cubic (bcc) unit cell of edge length

L_y

, and simple cubic unit cell of edge length

L_z

, respectively. If

r_z = \frac{\sqrt{3}}{2} r_y

;

r_y = \frac{8}{\sqrt{3}} r_x

;

M_z = \frac{3}{2} M_y

and

M_Z = 3M_x

. then the correct statement(s) is(are) [Given:

M_x

M_y

, and

M_z

are molar masses of metals x, y, and z, respectively.

r_x

r_y

, and

r_z

are atomic radii of metals x, y, and z, respectively.]

(A)Packing efficiency of unit cell of x > Packing efficiency of unit cell of y > Packing efficiency of unit cell of z
(B) $L_y > L_z$
(C) $L_x > L_y$
(D)Density of x > Density of y

Q6·ChemistrySingle correctJEE Main 2023

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

(A) $r_{Cs^+} + r_{Cl^-} = \dfrac{a}{\sqrt{2}}$
(B) $r_{Cs^+} + r_{Cl^-} = a$
(C) $r_{Cs^+} + r_{Cl^-} = \dfrac{\sqrt{3}}{2}a$
(D) $r_{Cs^+} + r_{Cl^-} = \dfrac{a}{2}$

Q7·ChemistryNumericalJEE Main 2023

Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4 Å. The radius of sodium atom is ____

\times 10^{-1}

Å (Nearest integer)

Q8·ChemistrySingle correctJEE Main 2023

Which one of the following pairs is an example of polar molecular solids?

(A) $SO_2(s),\ NH_3(s)$
(B) $SO_2(s),\ CO_2(s)$
(C) $HCl(s),\ AlN(s)$
(D) $MgO(s),\ SO_2(s)$

Q9·ChemistryNumericalJEE Main 2023

An atomic substance A of molar mass

12

mol^{-1}

has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is __________. (Nearest integer) Given the density of A is

3.0

mL^{-1}

and

N_A = 6.02 \times 10^{23}

mol^{-1}

Q10·ChemistrySingle correctJEE Main 2023

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

(A) $r=2\sqrt{2}a$ and $\sqrt{3}r=4a$
(B) $r=2\sqrt{2}a$ and $4r=\sqrt{3}a$
(C) $2\sqrt{2}r=a$ and $4r=\sqrt{3}a$
(D) $2\sqrt{2}r=a$ and $\sqrt{3}r=4a$

Q11·ChemistrySingle correctJEE Main 2023

A compound is formed by two elements

X

and

Y

. The element

Y

forms cubic close packed arrangement and those of element

X

occupy one third of the tetrahedral voids. What is the formula of the compound?

(A) $X_2Y_3$
(B) $X_3Y$
(C) $X_3Y_2$
(D) $XY_3$

Q12·ChemistryNumericalJEE Main 2023

Number of crystal systems from the following where body centred unit cell can be found, is ____. Cubic, orthorhombic, tetragonal, hexagonal, rhombohedral, monoclinic, triclinic.

Q13·ChemistrySingle correctJEE Main 2023

Which of the following represents the lattice structure of

\text{A}_{0.95}\text{O}

containing

\text{A}^{2+}

\text{A}^{3+}

and

\text{O}^{2-}

ions (structures A, B and C shown in the figure)?

(A)A only
(B)B and C only
(C)A and B only
(D)B only

Q14·ChemistryNumericalJEE Main 2023

A metal M crystallizes into two lattices: face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of

2.0

and

2.5

Å respectively. The ratio of densities of lattices fcc to bcc for the metal M is _________ (Nearest integer)

Q15·ChemistryNumericalJEE Main 2023

A sample of a metal oxide has formula

M_{0.83}O_{1.00}

. The metal M can exist in two oxidation states +2 and +3. In the sample of

M_{0.83}O_{1.00}

, the percentage of metal ions existing in +2 oxidation state is _________ %. (nearest integer)

Q16·ChemistryNumericalJEE Main 2023

Iron oxide FeO crystallises in a cubic lattice with a unit cell edge length of 5.0 Å. If the density of FeO in the crystal is 4.0 g cm

^{-3}

, then the number of FeO units present per unit cell is _______ (nearest integer). (Given: molar mass of Fe and O is 56 and 16 g mol

^{-1}

respectively;

N_A=6.0\times10^{23}

mol

^{-1}

)

Q17·ChemistryNumericalJEE Main 2023

A metal

M

forms hexagonal close-packed structure. The total number of voids in

0.02

mol of it is _____

\times10^{21}

(Nearest integer). (Given

N_A=6.02\times10^{23}

)

Q18·ChemistrySingle correctJEE Main 2023

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 the cube. Y is at

\dfrac{1}{3}

rd of the total faces. The empirical formula of the compound is:

(A) $XY_{2.5}$
(B) $X_2Y_{1.5}$
(C) $X_2Y$
(D) $X_{1.5}Y_2$

Q19·ChemistryNumericalJEE Main 2023

When

\text{Fe}_{0.93}\text{O}

is heated in presence of oxygen, it converts to

\text{Fe}_2\text{O}_3

. The number of correct statement/s from the following is: A. The equivalent weight of

\text{Fe}_{0.93}\text{O}

\tfrac{\text{Molecular weight}}{0.79}

. B. The number of moles of

\text{Fe}^{2+}

and

\text{Fe}^{3+}

in 1 mole of

\text{Fe}_{0.93}\text{O}

is 0.79 and 0.14 respectively. C.

\text{Fe}_{0.93}\text{O}

is metal deficient with lattice comprising of cubic closed packed arrangement of

\text{O}^{2-}

ions. D. The % composition of

\text{Fe}^{2+}

and

\text{Fe}^{3+}

\text{Fe}_{0.93}\text{O}

is 85% and 15% respectively.

Q20·ChemistrySingle correctJEE Advanced 2022

Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closed to

(A)25
(B)35
(C)55
(D)75

Q21·ChemistryNumericalJEE Main 2022

Ionic radii of cation

A^{+}

and anion

B^{-}

are 102 and 181 pm respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for

B^{-}

A^{+}

is present in all octahedral voids. The edge length of the unit cell of the crystal AB is ______ pm. (Nearest Integer)

Q22·ChemistryNumericalJEE Main 2022

Metal M crystallizes into a FCC lattice with the edge length of

4.0\times10^{-8}

cm. The atomic mass of the metal is _____ g/mol. (Nearest integer). (Use :

\mathrm{N_A} = 6.02\times10^{23}\ \mathrm{mol^{-1}}

, density of metal, M = 9.03 g

\mathrm{cm^{-3}}

)

Q23·ChemistryNumericalJEE Main 2022

An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 g cm

^{-3}

. The number of atoms present in 180 g of the element is _______ × 10

^{23}

. (Nearest integer)

Q24·ChemistrySingle correctJEE Main 2022

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.

Q25·ChemistryNumericalJEE Main 2022

Metal deficiency defect is shown by

Fe_{0.93}O

. In the crystal, some

Fe^{2+}

cations are missing and loss of positive charge is compensated by the presence of

Fe^{3+}

ions. The percentage of

Fe^{2+}

ions in the

Fe_{0.93}O

crystals is __________ . (Nearest integer)

Q26·ChemistryNumericalJEE Main 2022

In a solid AB. A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is

A_xB_y

. The value of x is________. [nearest integer]

Q27·ChemistryNumericalJEE Main 2022

The distance between

Na^+

and

Cl^-

ions in solid NaCl of density 43.1 g

cm^{-3}

is ________ ×

10^{-10}

m. (Nearest Integer) (Given :

N_A

= 6.02 ×

10^{23}

mol^{-1}

)

Q28·ChemistryNumericalJEE Main 2022

Atoms of element X form hcp lattice and those of element Y occupy

\frac{2}{3}

of its tetrahedral voids. The percentage of element X in the lattice is__________ (Nearest integer)

Q29·ChemistrySingle correctJEE Advanced 2021

For the given close packed structure of a salt made of cation

\mathbf{X}

and anion

\mathbf{Y}

shown below (ions of only one face are shown for clarity) , the packing fraction is approximately (packing fraction =

\frac{\text{Packing efficiency}}{100}

)

(A)0.74
(B)0.63
(C)0.52
(D)0.48

Q30·ChemistryNumericalJEE Main 2021

The empirical formula for a compound with a cubic close packed arrangement of anions and with cations occupying all the octahedral sites in

\mathrm{A_xB}

. The value of x is __________ (Integer answer)

Q31·ChemistrySingle correctJEE Main 2021

Match items of List-I with those of List-II : List-I (Property) List-II (Example) (a) Diamagnetism (b) Ferrimagnetism (c) Paramagnetism (d) Antiferromagnetism (i) MnO (ii)

\mathrm{O_2}

(iii) NaCl (iv)

\mathrm{Fe_3O_4}

Choose the most appropriate answer from the options given below :

(A)(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
(B)(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)
(C)(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
(D)(a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

Q32·ChemistrySingle correctJEE Main 2021

(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

Q33·ChemistrySingle correctJEE Main 2021

(A)(B), (D) only
(B)(A), (B), (E) only
(C)(A), (C), (D) only
(D)(C), (D) only

Q34·ChemistrySingle correctJEE Main 2021

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

(A)Monoclinic
(B)Triclinic
(C)Orthorhombic
(D)Hexagonal

Q35·ChemistryNumericalJEE Main 2021

A copper complex crystallizing in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be 7.26 g cm

^{-3}

. The molar mass of copper complex is __________ g mol

^{-1}

. (Nearest integer) [Given :

N_A

= 6.022

\times 10^{23}

mol

^{-1}

]

Q36·ChemistrySingle correctJEE Main 2021

(A)A is false but R is true.
(B)Both A and R are true but R is NOT the correct explanation of A.
(C)A is true but R is false
(D)Both A and R are true and R is the correct explanation of A.

Q37·ChemistryNumericalJEE Main 2021

Q38·ChemistrySingle correctJEE Main 2021

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)Ionic solid
(B)Molecular solid
(C)Metallic solid
(D)Covalent solid

Q39·ChemistrySingle correctJEE Main 2021

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)M $_{2}$ A $_{3}$
(B)M $_{4}$ A $_{3}$
(C)M $_{4}$ A
(D)MA $_{3}$

Q40·ChemistryNumericalJEE Main 2021

\sqrt{3}

= 1.73,

\sqrt{2}

= 1.41]

Q41·ChemistryNumericalJEE Main 2021

Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is _______ × 10

^{21}

. (Round off to the Nearest Integer).

Q42·ChemistryNumericalJEE Main 2021

The number of octahedral voids per lattice site in a lattice is ___________. (Rounded off to the nearest integer)

Q43·ChemistryNumericalJEE Main 2021

The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m

^{3}

is ______. [Molar mass of Cu : 63.54 g; Avogadro number = 6.022×10

^{23}

]

Q44·ChemistryNumericalJEE Main 2021

The coordination number of an atom in a body-centered cubic structure is ________________. [Assume that the lattice is made up of atoms]

Q45·ChemistryMultiple correctJEE Advanced 2020

The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

(A)The empirical formula of the compound is MX.
(B)The cation M and anion X have different coordination geometries.
(C)The ratio of M-X bond length to the cubic unit cell edge length is 0.866.
(D)The ratio of the ionic radii of cation M to anion X is 0.414.

Q46·ChemistrySingle correctJEE Main 2020

A crystal is made up of metal ions 'M

_1

' and 'M

_2

' and oxide ions. Oxide ions form a ccp lattice structure. The cation 'M

_1

' occupies 50% of octahedral voids and the cation 'M

_2

' occupies 12.5% of tetrahedral voids of oxide lattice. The oxidation numbers of 'M

_1

' and 'M

_2

' are respectively:

(A)+2, +4
(B)+1, +3
(C)+3, +1
(D)+4, +2

Q47·ChemistrySingle correctJEE Main 2020

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) $\dfrac{a}{2}$
(B) $\sqrt{2}a$
(C)a
(D) $\dfrac{a}{\sqrt{2}}$

Q48·ChemistryNumericalJEE Main 2020

An element with molar mass 2.7

\times

^{-2}

kg mol

^{-1}

forms a cubic unit cell with edge length 405 pm. If its density is 2.7

\times

^3

kg m

^{-3}

, the radius of the element is approximately __________

\times

^{-12}

m (to the nearest integer).

Q49·ChemistrySingle correctJEE Main 2020

'X' melts at low temperature and is a bad conductor of electricity in both liquid and solid state. X is:

(A)Silicon carbide
(B)Mercury
(C)Zinc sulphide
(D)Carbon tetrachloride

Q50·ChemistrySingle correctJEE Main 2020

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

(A)CsCl
(B)AgBr
(C)ZnS
(D)KBr

Q51·ChemistrySingle correctJEE Main 2019

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

(A)1 : 2 : 4
(B)4 : 2 : 3
(C)4 : 2 : 1
(D)8 : 1 : 6

Q52·ChemistrySingle correctJEE Main 2019

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) $\dfrac{a}{2}$
(B) $\sqrt{2}a$
(C) $\dfrac{3}{2}a$
(D)a

Q53·ChemistrySingle correctJEE Main 2019

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) $A_2B_2O$
(B) $AB_2O_4$
(C) $A_4B_2O$
(D) $A_2BO_4$

Q54·ChemistrySingle correctJEE Main 2019

(A)90%
(B)75%
(C)65%
(D)45%

Q55·ChemistrySingle correctJEE Main 2019

A solid having density of

9 × 10^{3}

kg m

^{-3}

forms face centred cubic crystale of edge length

200\sqrt{2}

pm. What is the molar mass of the solid? [Avogadro constant ≅ 6 ×

10^{23}

and mol

^{-1}

, π ≅ 3]

(A)0.0432 kg mol $^{-1}$
(B)0.0216 kg mol $^{-1}$
(C)0.0305 kg mol $^{-1}$
(D)0.4320 kg mol $^{-1}$

Q56·ChemistrySingle correctJEE Main 2019

Which primitive unit cell has unequal edge length (a ≠ b ≠ c) and all axial angles different from 90°?

(A)Triclinic
(B)Hexagonal
(C)Monoclinic
(D)Tetragonal

Q57·ChemistrySingle correctJEE Main 2019

The one that is extensively used as a piezoelectric material is

(A)tridymite
(B)amorphous silica
(C)quartz
(D)mica

Q58·ChemistrySingle correctJEE Main 2019

At 100°C, copper(Cu) has FCC unit cell structure with cell edge length x Å. What is the approximate density of Cu(in g cm

^{-3}

) at this temperature? [Atomic mass of Cu = 63.55 u]

(A) $\dfrac{205}{x^{3}}$
(B) $\dfrac{105}{x^{3}}$
(C) $\dfrac{211}{x^{3}}$
(D) $\dfrac{422}{x^{3}}$

Q59·ChemistryNumericalJEE Advanced 2018

\left(\dfrac{\text{number of anions}}{\text{number of cations}}\right)

in Z is ___.

Q60·ChemistryIntegerJEE Advanced 2017

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g

cm^{-3}

, then the number of atoms present in 256 g of the crystal is

N \times 10^{24}

. The value of

N

Q61·ChemistryMultiple correctJEE Advanced 2016

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is(are)

(A)The number of the nearest neighbours of an atom present in the topmost layer is 12
(B)The efficiency of atom packing is 74%
(C)The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively
(D)The unit cell edge length is $2\sqrt{2}$ times the radius of the atom

Q62·ChemistryMultiple correctJEE Advanced 2015

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with

\mathbf{m}

fraction of octahedral holes occupied by aluminium ions and

\mathbf{n}

fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

(A) $\dfrac{1}{2},\ \dfrac{1}{8}$
(B) $1,\ \dfrac{1}{4}$
(C) $\dfrac{1}{2},\ \dfrac{1}{2}$
(D) $\dfrac{1}{4},\ \dfrac{1}{8}$

Q63·ChemistrySingle correctJEE Advanced 2013

The arrangement of X

^{-}

ions around A

^{+}

ion in solid AX is given in the figure (not drawn to scale). If the radius of X

^{-}

is 250 pm, the radius of A

^{+}

(A)104 pm
(B)125 pm
(C)183 pm
(D)57 pm

Solid State — frequently asked

How many questions from Solid State appear in JEE?

Solid State has appeared in 63 of the last 186 JEE Main and JEE Advanced papers — about 34% of them — contributing 63 questions in total across those papers.

Is Solid State an important chapter for JEE?

Where do these Solid State questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.