Embibe Experts Solutions for Chapter: Solid State, Exercise 1: Exercise

Derive Bragg's equation.

In a face-centred cubic arrangement of $\mathrm{A}$ and $\mathrm{B}$ atoms, $\mathrm{A}$ atoms occupy the comers, and $\mathrm{B}$ atoms occupy the face centres of the unit cell. If one of the atoms is missing from the comer in each unit cell, what is the simplest formula of the compound?

$\mathrm{CsCl}$ crystallizes in cubic structure in which ${\mathrm{Cl}}^{-}$ ions are at the corners and ${\mathrm{Cs}}^{+ }$ions occupy centre of the unit cell. If radii of ${\mathrm{Cs}}^{+}$and ${\mathrm{Cl}}^{-}$ ions are $1.69 \stackrel{\circ }{\mathrm{A} }$and $1.81 \stackrel{\circ }{\mathrm{A}}$ respectively, calculate the edge length of the unit cell.

Copper crystallizes with face centered cubic unit cell. If the radius of the copper atom is $127.8 \mathrm{pm}$, calculate the density of the copper metal. (Atomic mass of $\mathrm{Cu} = 63.55 \mathrm{u}$and Avogadro’s number ${\mathrm{N}}_{\mathrm{A} }= 6.02 \mathrm{x} {10}^{23} {\mathrm{mol}}^{-1}$)

An element X crystallises in fcc structure, $208 \mathrm{g}$ of it has $4.28\times {10}^{24}$ atoms. Calculate the edge of unit cell if density of X is $7.2 \mathrm{g}/{\mathrm{cm}}^3$.

Niobium crystallizes in body-centred cubic structure. If the density is $8.55 \mathrm{g} \mathrm{c}{\mathrm{m}}^{-3},$ calculate atomic radius of niobium using its atomic mass $93\mathrm{U}$.

Explain briefly seven types of unit cell.

Unit cells can be classified into primitive and centered unit cells. Differentiate between primitive and centered unit cells.