Question

A certain element crystallises in a bcc lattice of unit cell edge length $27\stackrel{\circ }{A}$. If the same element under the same conditions crystallises in the fcc lattice. The edge length of the unit cell in $\stackrel{\circ }{A}$will be __________ (Round off to the nearest integer.)
[Assume each lattice point has a single atom]
[Assume $\sqrt{3}=1.73,\sqrt{2}=1.41]$

Answer 1

In BCC the relationship between edge length and radius of an atom is given by:

$4r=\sqrt{3}a$

$4r=\sqrt{3}\times 27$

$4r=1.73\times 27\stackrel{\circ }{A}=46.71\stackrel{\circ }{A}$

In FCC the relationship between edge length and radius of an atom is given by:

$4r=\sqrt{2}a\Rightarrow \frac{46.71}{1.41}=a\left(\text{edge length}\right)$

$\Rightarrow a=33\stackrel{\circ }{A}$