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JEE 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 = $6 \times 1 0^{23} mol^{- 1}$

JEE Advanced 2015

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with $m$ fraction of octahedral holes occupied by aluminium ions and $n$ fraction of tetrahedral holes occupied by magnesium ions $m$ and $n$ respectively, are -

\frac{1}{2}, \frac{1}{8}

(B)

1, \frac{1}{4}

(C)

\frac{1}{2}, \frac{1}{2}

(D)

\frac{1}{4}, \frac{1}{8}

JEE Advanced 2018

LEVELJEE Main

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 $(\frac{number of anions}{number of cations})$ in Z is____.

JEE Advanced 2021

LEVELJEE Advanced

For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity) , the packing fraction is approximately (packing fraction = $\frac{Packing efficiency}{100}$ )

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).

* Multiple Correct Options

(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

JEE Advanced 2017

LEVELJEE Main

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 $N \times 1 0^{24}$ . The value of N is :

JEE Advanced 2022

LEVELJEE Advanced

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 closest to

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 $r_{z} = \frac{3}{2} r_{y}$ ; $r_{y} = \frac{8}{3} r_{x}$ ; $M_{z} = \frac{3}{2} M_{y}$ and $M_{z} = 3 M_{x}$ , 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.]

* Multiple Correct Options

(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

JEE Advanced 2016

LEVELJEE Main

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

* Multiple Correct Options

(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

22

times the radius of the atom

JEE Main 2020

LEVELJEE Advanced

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

JEE Main 2021

LEVELJEE Main

Match List-I with List-II. \begin{array}{ll} \text{List-I (Property)} & \text{List-II (Example)} \\ \text{A. Diamagnetism} & \text{1. MnO} \\ \text{B. Ferrimagnetism} & \text{2. } \text{O}_2 \\ \text{C. Paramagnetism} & \text{3. NaCl} \\ \text{D. Antiferromagnetism} & \text{4. } \text{Fe}_3\text{O}_4 \end{array} Choose the most appropriate answer from the options given below.

(A)

\to

2, B

\to

1, C

\to

3, D

\to

(B)

\to

1, B

\to

3, C

\to

4, D

\to

(C)

\to

3, B

\to

4, C

\to

2, D

\to

(D)

\to

4, B

\to

2, C

\to

1, D

\to

JEE Main 2011

LEVELJEE Main

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

(A)

A_{2} B

(B)

A B_{2}

(C)

A_{2} B_{2}

(D)

A_{2} B_{5}

LEVELJEE Main

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

(A)

2.57 \times 1 0^{21}

(B)

5.14 \times 1 0^{21}

(C)

1.28 \times 1 0^{21}

(D)

1.71 \times 1 0^{21}

JEE Main 2021

LEVELJEE Advanced

KBr is doped with $1 0^{- 5}$ mole per cent of $SrBr_{2}$ . The number of cationic vacancies in $1 g$ of KBr crystal is ......... $1 0^{14}$ (Round off to the nearest integer). [Atomic mass : $K = 39.1 u$ , $Br = 79.9 u$ , $N_{A} = 6.023 \times 1 0^{23}$ ]

JEE Main 2020

LEVELJEE Advanced

An element with molar mass $2.7 \times 1 0^{- 2} kg mol^{- 1}$ forms a cubic unit cell with edge length $405 pm$ . If its density is $2.7 \times 1 0^{3} kg m^{- 3}$ , the radius of the element is approximately ............ $\times 1 0^{- 12} m$ (to the nearest integer).

JEE Main 2021

LEVELJEE Main

The unit cell of copper corresponds to a face centered cube of edge length $3.596 \overset{˚}{A}$ 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 $= 6.022 \times 1 0^{23}$ ]

JEE Main 2020

LEVELJEE Main

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

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?

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.

Sodium metal crystallises in a body centred cubic lattice with a unit cell edge of $4.29 \overset{˚}{A}$ . The radius of sodium atom is approximately

(A)

1.86 \overset{˚}{A}

(B)

3.22 \overset{˚}{A}

(C)

5.72 \overset{˚}{A}

(D)

0.93 \overset{˚}{A}

JEE Main 2021

LEVELJEE Main

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 a copper complex is found to be $7.62 g cm^{- 3}$ . The molar mass of copper complex is ...... $g mol^{- 1}$ . (Nearest integer) [Given : $N_{A} = 6.022 \times 1 0^{23} mol^{- 1}$ ]

JEE Main 2020

LEVELJEE Main

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

Copper crystallises 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

JEE Main 2019

LEVELJEE Main

At $10 0^{\circ} C$ , copper (Cu) has FCC unit cell structure with cell edge length of $x \overset{˚}{A}$ . What is the approximate density of Cu (in $g cm^{- 3}$ ) at this temperature? [Atomic mass of Cu $= 63.55 u$ ]

(A)

\frac{211}{x ^{3}}

(B)

\frac{205}{x ^{3}}

(C)

\frac{105}{x ^{3}}

(D)

\frac{422}{x ^{3}}

LEVELBoard

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

(A)

\frac{20}{3} π r^{3}

(B)

\frac{24}{3} π r^{3}

(C)

\frac{12}{3} π r^{3}

(D)

\frac{16}{3} π r^{3}

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).

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 closest to

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

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } How many unit cells are present in a cube shaped ideal crystal of NaCl of mass 1.00 g? [Atomic mass : Na=23, Cl=35.5]

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

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?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Sodium metal crystallises in a body centred cubic lattice with a unit cell edge of 4.29 A˚. The radius of sodium atom is approximately

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

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Copper crystallises in fcc with a unit cell length of 361 pm. What is the radius of copper atom?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is atomic radius)

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

Sodium metal crystallises in a body centred cubic lattice with a unit cell edge of $4.29 \overset{˚}{A}$ . The radius of sodium atom is approximately

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

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