K L Chugh Solutions for Chapter: Solid State, Exercise 3: Follow Up Problems

The density of aluminium (atomic mass $=27$) is $2700 \mathrm{kg} {\mathrm{m}}^{-3}.$ If $\mathrm{Al}$ has $\mathrm{fcc}$ structure, calculate its atomic radius.
 

Chromium crystallizes in a body-centred cubic lattice, whose density is $7.20 \mathrm{g}/{\mathrm{cm}}^3.$ The length of the edge of unit cell is $288.4 \mathrm{pm}$. Calculate Avogadro's number. (Atomic mass of chromium$=52$).

An element of atomic mass $98.5 \mathrm{g} {\mathrm{mol}}^{-1}$ occurs in $\mathrm{f}.\mathrm{c}.\mathrm{c}.$ structure. If, its unit cell edge length is $500 \mathrm{pm}$ and its density is $5.22 \mathrm{g}{ \mathrm{cm}}^{-3}$, what is the value of Avogadro's constant?

$\mathrm{X}$-ray diffraction studies show that copper crystallizes in a $\mathrm{fcc}$ unit cell with cell edge of $3.608\times {10}^{-8} \mathrm{cm}.$ In a separate experiment, copper is determined to have a density of $8.92 \mathrm{g}/{\mathrm{cm}}^3$, calculate the atomic mass of copper.

An element occurs in the $\mathrm{bcc}$ structure. It has a cell edge of $250 \mathrm{pm}$. Calculate its atomic mass, if its density is $8.0 \mathrm{g}{ \mathrm{cm}}^{-3}$.
 

A metallic element has a body-centred cubic lattice. Each edge of the unit cell is $288 \mathrm{pm}$. The density of the metal is $7.20 \mathrm{g} {\mathrm{cm}}^{-3}.$ How many atoms of this metal are present in $100 \mathrm{g}$?

A body-centred cubic element of density, $10.3 \mathrm{g}{ \mathrm{cm}}^{-3}$ has a cell edge of $314 \mathrm{pm}$. Calculate the atomic mass of the element. $\left({\mathrm{N}}_{\mathrm{A}}=6.023\times {10}^{23}{ \mathrm{mol}}^{-1}\right)$.

The density of $\mathrm{KBr}$ is $2.75 \mathrm{g}{ \mathrm{cm}}^{-3}.$ The length of the edge of the unit cell is $654 \mathrm{pm}$. Show that $\mathrm{KBr}$ has a face centred cubic structure. $({\mathrm{N}}_{\mathrm{A}}=6.023\times {10}^{23}{ \mathrm{mol}}^{-1}$, atomic mass, $\mathrm{K}=39,\mathrm{Br}=80)$.