Question

Aluminium crystallises in a cubic close-packed structure. Its metallic radius is $125pm$. (i) What is the length of the side of the unit cell? (ii) How many unit cells are there in $1.00c{m}^3$ of aluminium?

Answer 1

i) In CCP,

$4r=a\sqrt{2}$

$4\times 125=500=a\sqrt{2}$

$a=353.6$ pm $=3.536\mathring{A}$

ii) Let the number of atoms be $n$

$V=n\times V_m$

${10}^{-6}=n\times (3.536{)}^3\times {10}^{-30}$

$n=\frac{{10}^{24}}{(3.536{)}^3}=\frac{{10}^{24}}{44.21}=2.262\times {10}^{22}$ atoms