Embibe Experts Solutions for Chapter: Solid State, Exercise 1: JEE Main - 6 September 2020 Shift 2

Ionic radii of cation ${\mathrm{A}}^{+}$ and anion ${\mathrm{B}}^{-}$ are $102$ and $181\mathrm{pm}$ respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for ${\mathrm{B}}^{-}.{\mathrm{A}}^{+}$ is present in all octahedral voids. The edge length of the unit cell of the crystal $\mathrm{AB}$ is___$\mathrm{pm}$.

When ${\mathrm{Fe}}_{0.93}\mathrm{O}$ is heated in presence of oxygen, it converts to ${\mathrm{Fe}}_2{\mathrm{O}}_3$. The number of correct statement/s from the following is ______ .

A. The equivalent weight of ${\mathrm{Fe}}_{0.93}\mathrm{O}$ is  $\frac{\mathrm{Molecular} \mathrm{weight}}{0.79}$

B. The number of moles of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ in $1$ mole of ${\mathrm{Fe}}_{0.93}\mathrm{O}$ is $0.79$ and $0.14$ respectively.

C. ${\mathrm{Fe}}_{0.93}\mathrm{O}$ is metal deficient with lattice comprising of cubic closed packed arrangement of ${\mathrm{O}}^{2-}$ ions.

D. The $\%$ composition of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ in ${\mathrm{Fe}}_{0.93}\mathrm{O}$ is $85\%$ and $15\%$ respectively.

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

A metal $\mathrm{M}$ forms hexagonal close-packed structure. The total number of voids in $0.02 \mathrm{mol}$ of it is _____ $\times {10}^{21}$ (Nearest integer)

(Given ${\mathrm{N}}_{\mathrm{A}}=6.02\times {10}^{23}$)

Iron oxide $\mathrm{FeO}$, crystallises in a cubic lattice with a unit cell edge length of $5.0Å$. If density of the $\mathrm{FeO}$ in the crystal is $4.0 \mathrm{g} {\mathrm{cm}}^{-3}$, then the number of $\mathrm{FeO}$ units present per unit cell is _____ (Nearest integer)

Given : Molar mass of $\mathrm{Fe}$ and $\mathrm{O}$ is $56$ and $16 \mathrm{g}$ ${\mathrm{mol}}^{-1}$ respectively.
${\mathrm{N}}_{\mathrm{A}}=6.0\times {10}^{23} {\mathrm{mol}}^{-1}$

A sample of a metal oxide has formula ${\mathrm{M}}_{0.83}{\mathrm{O}}_{1.00}$. The metal $\mathrm{M}$ can exist in two oxidation states $+2$ and $+3$. In the sample of ${\mathrm{M}}_{0.83}{\mathrm{O}}_{1.00}$, the percentage of metal ions existing in $+2$ oxidation state is $\%$. (nearest integer)

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

A.

B.

C.
 

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 $2.5\stackrel{°}{\mathrm{A}}$ respectively. The ratio of densities of lattices fcc to bec for the metal M is _______(Nearest integer)