S C Kheterpal, S N Dhawan and, P N Kapil Solutions for Chapter: States of Matter: Solid State, Exercise 18: PROBLEMS FOR PRACTICE

Silver metal crystallises with a face-centred cubic lattice. The length of the unit cell is found to be $3\times {10}^{-8} \mathrm{cm}$. Calculate the atomic radius and density of silver. (Molar mass of $\mathrm{Ag}=108 \mathrm{g} {\mathrm{mol}}^{-1}, {\mathrm{N}}_{\mathrm{A}}=6.02\times {10}^{23 }{\mathrm{mol}}^{-1}$).

Niobium crystallises in body-centred cubic structure. If the atomic radius is $143.1 \mathrm{pm},$ calculate the density of niobium (Atomic mass $93 \mathrm{u}$).

Copper crystallises into a $\mathrm{fcc}$ lattice. Its edge length is $3.62\times {10}^{-8} \mathrm{cm}$. Calculate the density of copper (atomic mass of $\mathrm{Cu}=63.5 \mathrm{u}, {\mathrm{N}}_{\mathrm{A}}=6.022\times {10}^{23} {\mathrm{mol}}^{-1}$).

An element crystallizes in BCC structure. The edge length of its unit cell is $288 \mathrm{pm}$. If the density of the crystals is $7.2 \mathrm{g} {\mathrm{cm}}^{-3}$, How many atoms of this element are present in $100 \mathrm{g}$ ?

A compound $\mathrm{AB}$ crystallises in bcc lattice with the unit cell edge length of $380\mathrm{pm}$ . The distance between oppositely charged ions in the lattice is $329\mathrm{pm}$ . Calculate the radius of ${\mathrm{B}}^{-}$ if the radius of ${\mathrm{A}}^{+}$is $190\mathrm{pm}$.

Aluminium metal forms a cubic close-packed crystal structure. Its atomic radius is $125\times {10}^{-12}\mathrm{m}$. How many such unit cells are there in $1.00 {\mathrm{m}}^3$ of aluminium?

A uni-univalent ionic crystal $\mathrm{AX}$ is composed of the following radii (arbitrary units) :
$\begin{array}{cc}{\mathrm{A}}^{+}& {\mathrm{X}}^{-}\\ 1.0& 2.0\end{array}$
Assuming that ions are hard spheres, predict giving reasons whether the crystal will have sodium chloride or cesium chloride structure. Calculate the volume of the unit cell.

An element $\text{'}\mathrm{X}\text{'}$(At. mass$=40 {\mathrm{gmol}}^{-1}$) having $\mathrm{fcc}$ structure, has unit cell edge length of $400\mathrm{pm}$. Calculate the density of $\text{'}\mathrm{X}\text{'}$ and the number of unit cells in $4\mathrm{g}$ of $\text{'}\mathrm{X}\text{'}$ $({\mathrm{N}}_{\mathrm{A}}=6.022\times {10}^{23}{\mathrm{mol}}^{-1})$.