Embibe Experts Solutions for Chapter: Solid State, Exercise 4: EXERCISE-4

The edge length of the unit cell of $\mathrm{KCl}(\mathrm{NaCl}$like structure ; $\mathrm{fcc})$ is $6.28\stackrel{\circ }{\mathrm{A}}.$ Assuming anion-cation contact along the cell edge, calculate the radius of the potassium ion. $\left({\mathrm{r}}_{\mathrm{Cl}}=1.8173\stackrel{\circ }{\mathrm{A}}\right).$.

If coordination number of primitive cubic arrangement is$\text{'}\mathrm{x}\text{'}, \mathrm{bcc}$ arrangement is$\text{'}\mathrm{y}\text{'}$ and $\mathrm{fcc}$ arrangement is $\text{'}\mathrm{z}\text{'}$ then give $\frac{x\times z}{y}.$

Thallium chloride, $\mathrm{TlCl} \left(240 \mathrm{g} {\mathrm{mol}}^{-1}\right)$ crystallises in either a simple cubic lattice or a face centred cubic lattice ${\mathrm{Cl}}^{-}$ions with ${\mathrm{Tl}}^{+}$ ions in the holes. If the density of the solid is $9.00 \mathrm{g}{ \mathrm{cm}}^{-3}$ and edge of the unit cell is $3.85\times {10}^{-8} \mathrm{cm},$ what is the unit geometry?

${\mathrm{BaTiO}}_3$ crystallizes in the prevoskite structure. The structure may be described as a cubic lattice with barium ions occupying the corner of the unit cell, oxide ions occupying the face-centers and titanium ion occupying the center of the unit cell.

$\left(\mathrm{a}\right)$ If titanium is described as occupying holes in $\mathrm{BaO}$ lattice, what type of holes does it occupy?

$\left(\mathrm{b}\right)$ What fraction of this type hole does it occupy?

Metallic gold crystallises in $\mathrm{fcc}$ lattice. The length of the cubic unit cell is $\mathrm{a}=4.07\stackrel{\circ }{\mathrm{A}}.$

$\left(\mathrm{a}\right)$ What is the closest distance between gold atoms.

$\left(\mathrm{b}\right)$ How many "nearest neighbours" does each gold atom have at the distance calculated in $\left(\mathrm{a}\right).$

$\left(\mathrm{c}\right)$ What is the density of gold?

$\left(\mathrm{d}\right)$ Prove that the packing fraction of gold is $0.74.$

Atomic Mass of Au=197, ${\mathrm{N}}_{\mathrm{A}}= 6.022 \mathrm{X} {10}^{23} {\mathrm{mol}}^{-1}$

The mineral hawleyite, one form of $\mathrm{CdS},$ crystallizes in one of the cubic lattices, with edge length $5.87\stackrel{\circ }{\mathrm{A}}.$ The density of hawleyite is $4.63 \mathrm{g}{ \mathrm{cm}}^{-3}.$Atomic mass of Cd= 112, S=32

$\left(\mathrm{i}\right)$ In which cubic lattice does hawleyite crystallize?

$\left(\mathrm{ii}\right)$ Find the Schottky defect in ${\mathrm{gcm}}^{-3}.$

A metal crystallises into two cubic phases, face-centred cubic$\left(\mathrm{fcc}\right)$ and body-centred cubic $\left(\mathrm{bcc}\right).$ Calculate the ratio of densities of BCC to FCC structure.

(Given: Atomic radius of metal is same in both crystal, $\sqrt{\frac{3}{2}}=1.2$ )

Multiply Answer by $10.$

An element $\mathrm{X}$ (atomic $\mathrm{wt}.$ $=125$ ) crystallises is simple cubic structure. If diameter of the largest atom which can be placed without disturbing unit cell is $366\mathrm{pm}.$ Find the density of pure element $\mathrm{X}$ in $\frac{\mathrm{gm}.}{{\mathrm{cm}}^3}$

$[$ Given : $\sqrt{3}=1.732,{ \mathrm{N}}_{\mathrm{A}}=6\times {10}^{23}]$