Question

At ${1425}^{\circ }C,Fe$ crystallises in a body-centred cubic lattice whose edge length is $2.93\stackrel{\circ }{A}$. Assuming the atoms to be packed spheres, calculate:
(a) the radius of the spheres,
(b) the distance between centres of neighbouring spheres,
(c) the number of atoms of $Fe$ per unit lattice and
(d) the total volume occupied by an atom of $Fe$.

Answer 1

(a) $a\sqrt{3}=4r$ where, $a=$ edge length
$r=\frac{a\sqrt{3}}{4}=\frac{2.93\times \sqrt{3}}{4}=1.268\stackrel{\circ }{A}$
(b) Distance between the centres of neighbouring spheres
$=2r=2\times 1.268=2.537\stackrel{\circ }{A}$
(c) No. of atoms per unit cell $=8\times \frac{1}{8}+1=2$.
(d) Volume occupied by an atom of iron $=\frac{4}{3}\pi r^3$