And, for this problem, $R=0\mathrm{.}201nm,$ then

$V_C=\frac{(64)(0\mathrm{.}201(nm){)}^3}{3\sqrt[\phantom{2}]{3}}=0\mathrm{.}100n{m}^3$

Reserve Problem $02$: FCC unit cell volume

If the atomic radius of a metal that has the body$-$centered cubic crystal structure is $0\mathrm{.}201nm,$ calculate the volume of its unit cell.

Solution

Since this metal has an FCC crystal structure, the volume of its unit cell may be determined using Equation $3\mathrm{.}6$ as follows:

$V_C=16R^3\sqrt[\phantom{2}]{2}=(16)(0\mathrm{.}168nm{)}^3(\sqrt[\phantom{2}]{2})=0\mathrm{.}107n{m}^3$