An element crystal has a density of 8570 kg/m3 packing fraction is 0.68 . Determine mass of an atom if nearest neighbor distance is 2.86 Å

Density=8570 kg/m3

packing fraction=0.68

d=2.86Å

As packing fraction=0.68 it is a BCC crystal

$∵$ packing fraction$=\dfrac{\sqrt3\pi}{8}=0.68$

As it is BCC , number of atoms per unit cell is 2

As d=2.86Å for BCC

$d=\dfrac{\sqrt3a}{2}=2.86$

$a=2.86\times\dfrac{2}{\sqrt3}=3.302Å$

as,

$density=mass\times\dfrac{no.of atoms per unit cell}{a^3\times N}$

where N is Avogadro number …