Question

Aluminium crystallises in a cubic close-packed structure. Its metallic radius is $125$ pm.

(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

It is given that aluminum crystallises in a cubic closed packed structure.

Its metallic radius is $125$ pm.

(i) For cubic close-packed structure

$a=2\sqrt{2}r=2\sqrt{2}\times 125=354$ pm

Here, $a$ is the edge length of the unit cell and $r$ is the atomic radius.

(ii) Volume of one unit cell

$=a^3=(354pm{)}^3=4.4\times {10}^{-23}c{m}^3$

$(1pm={10}^{-10}cm)$

Number of unit cells in $1.00c{m}^3=\frac{1.00c{m}^3}{4.4\times {10}^{-23}c{m}^3}=2.27\times {10}^{22}$