2023
JEE Mains
MCQ
JEE Main 2023 (Online) 15th April Morning Shift
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.
$\mathrm{r}_{\mathrm{Cs}^{+}}+\mathrm{r}_{\mathrm{Cl}^{-}}=\frac{\mathrm{a}}{2}$
2023
JEE Mains
MCQ
JEE Main 2023 (Online) 10th April Evening Shift
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 $4 r=\sqrt{3} a$
2023
JEE Mains
MCQ
JEE Main 2023 (Online) 6th April Morning Shift
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.
$\mathrm{X_2Y}_{3}$
2023
JEE Mains
MCQ
JEE Main 2023 (Online) 1st February Morning Shift
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
2023
JEE Mains
MCQ
JEE Main 2023 (Online) 25th January Morning Shift
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.
$\mathrm{{X_{2.5}}Y}$
2022
JEE Mains
MCQ
JEE Main 2022 (Online) 30th June Morning Shift
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, NA = 6.0 $\times$ 1023 mol$-$1.
A.
5 NA
B.
6 NA
C.
15 NA
D.
25 NA
2022
JEE Mains
MCQ
JEE Main 2022 (Online) 28th June Morning Shift
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.
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th August Morning Shift
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 :
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
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 27th July Evening Shift
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) 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
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 27th July Morning Shift
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
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 20th July Morning Shift
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.
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.
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 18th March Evening Shift
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
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 18th March Morning Shift
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
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Evening Slot
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
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Evening Slot
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.
${\sqrt 2 a}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Morning Slot
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 )
(Avogadro constant (N A) = 6 $ \times $ 1023 mol–1 )
A.
8 NA
B.
40 NA
C.
4 NA
D.
2 NA
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Evening Slot
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
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
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
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
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.
$\sqrt 2 a$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
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
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
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%
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
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]
[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
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Morning Slot
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
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Evening Slot
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
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 11th January Morning Slot
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]
[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
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
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
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Morning Slot
Which premitive unit cell has unequal edge lengths (a $ \ne $ b $ \ne $ c) and all axial angles different from 90o?
A.
Hexagonal
B.
Tetragonal
C.
Triclinic
D.
Monoclinic
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Evening Slot
At 100oC, 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]
[Atomic Mass of Cu = 63.55 u]
A.
${{205} \over {{x^3}}}$
B.
${{105} \over {{x^3}}}$
C.
${{211} \over {{x^3}}}$
D.
${{422} \over {{x^3}}}$
2018
JEE Mains
MCQ
JEE Main 2018 (Offline)
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
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Evening Slot
All of the following share the same crystal structure except :
A.
LiCl
B.
NaCl
C.
RbCl
D.
CsCl
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Morning Slot
Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance ?
A.
B.
C.
D.
2017
JEE Mains
MCQ
JEE Main 2017 (Offline)
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
2015
JEE Mains
MCQ
JEE Main 2015 (Offline)
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
2014
JEE Mains
MCQ
JEE Main 2014 (Offline)
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.
${r_{C{s^ + }}} + {r_{C{l^ - }}} = 3a$
2013
JEE Mains
MCQ
JEE Main 2013 (Offline)
Which of the following exists as covalent crystals in the solid state?
A.
Silicon
B.
Sulphur
C.
Phosphorous
D.
Iodine
2012
JEE Mains
MCQ
AIEEE 2012
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
2011
JEE Mains
MCQ
AIEEE 2011
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
2010
JEE Mains
MCQ
AIEEE 2010
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%
2010
JEE Mains
MCQ
AIEEE 2010
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
2009
JEE Mains
MCQ
AIEEE 2009
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
2008
JEE Mains
MCQ
AIEEE 2008
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
2006
JEE Mains
MCQ
AIEEE 2006
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 $\pi r^3$
2005
JEE Mains
MCQ
AIEEE 2005
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
2004
JEE Mains
MCQ
AIEEE 2004
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
2003
JEE Mains
MCQ
AIEEE 2003
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
2002
JEE Mains
MCQ
AIEEE 2002
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
2023
JEE Mains
Numerical
JEE Main 2023 (Online) 13th April Evening Shift
Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of $4~\mathop A\limits^o $. The radius of sodium atom is __________ $\times ~10^{-1}$ $\mathop A\limits^o $ (Nearest integer)
Correct Answer: 17
Explanation:
In a body-centered cubic (BCC) lattice, the relationship between the edge length (a) and the atomic radius (r) is given by :
$\sqrt{3}a = 4r$
Given the unit cell edge length (a) of sodium metal as 4 Å :
$a = 4 ~\mathop A\limits^o$
We can now solve for the radius (r) of the sodium atom :
$4r = \sqrt{3}a$
$r = \frac{\sqrt{3}a}{4}$
$r = \frac{\sqrt{3} \times 4 ~\mathop A\limits^o}{4}$
$r = \sqrt{3} ~\mathop A\limits^o$
Now, we can approximate the numerical value :
$r \approx 1.732 ~\mathop A\limits^o$
To express the radius as a multiple of 10⁻¹ $\mathop A\limits^o$ :
$r = 1.732 \times 10^{1} \times 10^{-1} ~\mathop A\limits^o = 17.32 \times 10^{-1} ~\mathop A\limits^o$
So, the radius of the sodium atom is 17.32 × 10⁻¹ $\mathop A\limits^o$.
$\sqrt{3}a = 4r$
Given the unit cell edge length (a) of sodium metal as 4 Å :
$a = 4 ~\mathop A\limits^o$
We can now solve for the radius (r) of the sodium atom :
$4r = \sqrt{3}a$
$r = \frac{\sqrt{3}a}{4}$
$r = \frac{\sqrt{3} \times 4 ~\mathop A\limits^o}{4}$
$r = \sqrt{3} ~\mathop A\limits^o$
Now, we can approximate the numerical value :
$r \approx 1.732 ~\mathop A\limits^o$
To express the radius as a multiple of 10⁻¹ $\mathop A\limits^o$ :
$r = 1.732 \times 10^{1} \times 10^{-1} ~\mathop A\limits^o = 17.32 \times 10^{-1} ~\mathop A\limits^o$
So, the radius of the sodium atom is 17.32 × 10⁻¹ $\mathop A\limits^o$.
2023
JEE Mains
Numerical
JEE Main 2023 (Online) 11th April Morning Shift
An atomic substance A of molar mass $12 \mathrm{~g} \mathrm{~mol}^{-1}$ has a cubic crystal structure with edge length of $300 ~\mathrm{pm}$. The no. of atoms present in one unit cell of $\mathrm{A}$ is ____________. (Nearest integer)
Given the density of $\mathrm{A}$ is $3.0 \mathrm{~g} \mathrm{~mL}^{-1}$ and $\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-1}$
Correct Answer: 4
Explanation:
Given:
- Atomic substance A with molar mass $M = 12 \, \text{g mol}^{-1}$
- Cubic crystal structure with edge length $a = 300 \, \text{pm} = 300 \times 10^{-12} \, \text{m}$
- Density $\rho = 3.0 \, \text{g mL}^{-1}$
- Avogadro's number $N_A = 6.02 \times 10^{23} \, \text{mol}^{-1}$
First, calculate the volume of the unit cell $V = a^3 = (300 \times 10^{-12} \, \text{m})^3 = 27 \times 10^{-30} \, \text{m}^3$.
Next, calculate the mass of the unit cell using the given density. Density is mass over volume, so mass
$m = \rho \cdot V = 3.0 \, \text{g mL}^{-1} \cdot 27 \times 10^{-30} \, \text{m}^3 \cdot \frac{1 \, \text{mL}}{10^{-6} \, \text{m}^3} = 81 \times 10^{-24} \, \text{g}$.
Then, calculate the number of moles in one unit cell. The molar mass is mass over number of moles, so
$n = \frac{m}{M} = \frac{81 \times 10^{-24} \, \text{g}}{12 \, \text{g mol}^{-1}} = 6.75 \times 10^{-26} \, \text{mol}$.
Finally, calculate the number of atoms in one unit cell. The Avogadro constant is the number of atoms per mole,
so number of atoms $ = n \cdot N_A = 6.75 \times 10^{-26} \, \text{mol} \cdot 6.02 \times 10^{23} \, \text{mol}^{-1} = 4.06$.
Rounding to the nearest integer, we get 4 atoms. So, there are 4 atoms present in one unit cell of substance A.
2023
JEE Mains
Numerical
JEE Main 2023 (Online) 6th April Evening Shift
Number of crystal systems from the following where body centred unit cell can be found, is ____________.
Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic
Correct Answer: 3
Explanation:
Body-centered unit cells can be found in the following crystal systems among those listed:
- Cubic: Body-centered cubic (BCC) is one of the lattice structures that cubic systems can have.
- Tetragonal: A body-centered tetragonal system is also a possibility.
- Orthorhombic: The orthorhombic system can have a body-centered orthorhombic lattice.
Therefore, the number of crystal systems from the list where a body-centered unit cell can be found is 3.
2023
JEE Mains
Numerical
JEE Main 2023 (Online) 1st February Evening Shift
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\,\mathop A\limits^o $ respectively. The ratio of densities of lattices fcc to bcc for the metal M is ____________. (Nearest integer)
Correct Answer: 4
Explanation:
$\begin{aligned} & d_1 \text {, Density of fcc lattice of metal } M=\frac{4 \times M}{N_0\left(a_{\mathrm{fcc}}\right)^3} \\\\ & d_2 \text {, Density of bcc lattice of metal } M=\frac{2 \times M}{N_0\left(a_{\mathrm{bcc}}\right)^3} \\\\ & \frac{d_1}{d_2}=\frac{4}{2}\left(\frac{a_{\mathrm{bcc}}}{a_{\mathrm{fcc}}}\right)^3=2\left(\frac{2.5}{2}\right)^3=3.90 \simeq 4\end{aligned}$