JEE Main PYQs on The Solid State: JEE Main Questions for Practice with Solutions

1.

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 :

• $\frac{a}{2}$
• a
• $\frac{3}{2} a $
• $\sqrt{2} a $

2.

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

3.

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

• Carbon tetrachloride
• Silicon carbide
• Mercury
• Zinc sulphide

4.

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:

• $+2, +4$
• $+3, +1$
• $+1, +3$
• $+4, +2$

5.

Which of the following material is not a semiconductor.

• Germanium
• Graphite
• Silicon
• Copper oxide

6.

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

• $\frac{105}{x^3}$
• $\frac{211}{x^3}$
• $\frac{205}{x^3}$
• $\frac{422}{x^3}$

7.

A solid having density of $9 \times 10^3 \; kg \; m^{-3}$ forms face centred cubic crystals of edge length $200 \sqrt{2}$ pm. What is the molar mass of the solid ? [Avogadro constant $\simeq 6 \times 10^{23} \, mol^{-1}, \pi \simeq 3]$

• ${0.0216 \; kg \; mol^{-1}}$
• ${0.0305 \; kg \; mol^{-1}}$
• ${0.4320\; kg \; mol^{-1}}$
• ${0.0432\; kg \; mol^{-1}}$

8.

A compound of formula $A_2B_3$ has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms :

• hcp lattice-A, $\frac{2}{3}$ Tetrachedral voids-B
• hcp lattice-B, $\frac{1}{3}$ Tetrachedral voids-A
• hcp lattice-B, $\frac{2}{3}$ Tetrachedral voids-A
• hcp lattice-A, $\frac{1}{3}$ Tetrachedral voids-B

9.

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 :

• ${ A_2BO_4}$
• ${ A_2B_2O}$
• ${ A_4B_2O}$
• ${ AB_2O_4}$

10.

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 $\frac{1}{3} rd$ of the total faces. The empirical formula of the compound is

• $X _2 Y _{1.5}$
• $X_{3} Y_2$ 

• $XY _{2, 5}$
• $X _{1.5} Y _2$

11.

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 $2$ ?

• 0.45
• 0.65
• 0.9
• 0.75

12.

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
• $\sqrt{2}$ a
• $\frac{ a }{\sqrt{2}}$
• $\frac{\text { a }}{2}$

13.

A diatomic molecule $X_{2}$ 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 $X _{2}$ is (Avogadro constant $\left.\left( N _{ A }\right)=6 \times 10^{23} \,mol ^{-1}\right)$

• $8\, N _{ A }$
• $40\, N _{ A }$
• $4 \,N _{ A }$
• $2 \,N _{ A }$

14.

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

• 0.134 a
• 0.027 a
• 0.067 a
• 0.047 a

15.

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 enter of cube $Y$ is at $\frac{1}{3} td$ of the total faces The empirical formula of the compound is

• $X _2 Y _{1.5}$
• $X _{2.5} Y$
• $XY _2, 5$
• $X _{1.5} Y _2$