Question

It represents the interatomic distance in a unit cell. It is calculated by using following formula
$a=\sqrt[3]{3\frac{Z\times M}{\rho \times N_A}}$
For simple cubic, body-centred cubic and face-centred cubic structures value of Z is 1, 2 and 4 respectively.

Answer 1

density $=\frac{mass}{volume}$

vol. of unit cell $=a^3$

Total mass = mass of one unit cell $\times$ no of unit cell

i.e $d=\frac{ZM.}{a^3}=\frac{Z.M/N_A}{a^3}$

$\Rightarrow d=\frac{ZM.}{a^3{N}_A}\Rightarrow a^3=\frac{ZM}{d\times N_A}$

$a=\sqrt[3]{3\frac{ZM}{d\times N_A}}$

simple cubic has $1$ atom

body-centred has $2$ atom/unit cell

face centred has $4$ atom/unit cell.