Saleha Pervez and Vandana Solutions for Chapter: The Solid State, Exercise 4: Chapter Practice

Which of the crystals will have more density, a crystal with bcc unit cells or a crystal with fcc unit cell?

The mineral haematite, ${\mathrm{Fe}}_2{\mathrm{O}}_3$ consists of a cubic close-packed array of oxide ions with ${\mathrm{Fe}}^{3+}$ ions occupying interstitial positions. Predict whether the iron ions are in the octahedral or tetrahedral holes. [Radius of ${\mathrm{Fe}}^{3+} = 0.65 \stackrel{\circ }{\mathrm{A}}$ and that of ${\mathrm{O}}^{2-} =1.45 \stackrel{\circ }{\mathrm{A}}$]
 

An element occurs in a bcc structure with a cell edge $300 \mathrm{pm}$. The density of the element is $5.2 \mathrm{g} {\mathrm{cm}}^{-3}$. How many atoms of the element does $200 \mathrm{g}$ of the element contain?

$\mathrm{AB}$ crystallises in a rock salt structure with $\mathrm{A} : \mathrm{B} = 1:1$. The shortest distance between $\mathrm{A}$ and $\mathrm{B}$ is ${\mathrm{y}}^{1/3} \mathrm{nm}$. The formula mass of $\mathrm{AB}$ is$6.023 \mathrm{Y}$, where $\mathrm{Y}$ is an arbitrary constant. Find the density in $\mathrm{kg} {\mathrm{m}}^{-3}.$

Calcium metal crystallises in a face centred cubic lattice with an edge length of $0.556 \mathrm{nm}$. What will happen to the density of the metal if it contains, (i) $0.5\%$ Frenkel defects and (ii) $0.2\%$ Schottky defects.

By X-ray diffraction methods, the unit length of $\mathrm{NaCl}$ is observed to be$0.5627 \mathrm{nm}$. The density of $\mathrm{NaCl}$ is found to be $2.164 \mathrm{g} {\mathrm{cm}}^{-3}$. What type of defect exists in the crystal? Calculate the percentage of ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{-}$ ions missing.

A crystal of lead $\left(\mathrm{II}\right)$ sulphide has a $\mathrm{NaCl}$ structure. In this crystal, the shortest distance between the ${\mathrm{Pb}}^{2+}$ ion and ${\mathrm{S}}^{2-}$ ion is $297 \mathrm{pm}$. What is the length of the edge of the unit cell in lead sulphide? Also, calculate the unit cell volume.

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 $7.2 \mathrm{g}/{\mathrm{cm}}^3$.