QUESTIONS AND PROBLEMS

Fundamental Concepts

$3\mathrm{.}1$ What is the difference between atomic struc

ture and crystal structure?

Unit Cells

Metallic Crystal Structures

$3\mathrm{.}2$ If the atomic radius of lead is $0\mathrm{.}175$ nm $,$ calcu

late the volume of its unit cell in cubic meters

$3\mathrm{.}3$ Show for the body$-$centered cubic crysta

structure that the unit cell edge length $a$ an

the atomic radius $R$ are related througl

$a=4\frac{R}{\sqrt[\phantom{2}]{3}}.$

$3\mathrm{.}4$ For the HCP crystal structure, show that th

ideal $\frac{c}{a}$ ratio is $1\mathrm{.}633.$

$3\mathrm{.}5$ Show that the atomic packing factor for BCC

is $0\mathrm{.}68.$

$3\mathrm{.}6$ Show that the atomic packing factor for HCl

is $0\mathrm{.}74.$

Density Computations

$3\mathrm{.}7$ Molybdenum has a BCC crystal structure, a

atomic radius of $0\mathrm{.}1363$ nm $,$ and an atomi

weight of $95\mathrm{.}94\frac{g}{m}ol.$ Compute and compar

its theoretical density with the experimenta

value found inside the front cover.

$3\mathrm{.}8$ Calculate the radius of a palladium atom

given that Pd has an FCC crystal structure,

density of $12\mathrm{.}0\frac{g}{c}{m}^3,$ and an atomic weight o

$106\mathrm{.}4\frac{g}{m}ol.$

$3\mathrm{.}9$ Calculate the radius of a tantalum atom

given that Ta has a BCC crystal structure,

density of $16\mathrm{.}6\frac{g}{c}{m}^3,$ and an atomic weight o

$180\mathrm{.}9\frac{g}{m}ol.$

$3\mathrm{.}10$ Some hypothetical metal has the simple cubi

crystal structure shown in Figure $3\mathrm{.}23.$ If it

atomic weight is $74\mathrm{.}5\frac{g}{m}ol$ and the atomi

radius is $0\mathrm{.}145$ nm $,$ compute its density.