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]
$[\text{Assume}\sqrt{3}=1.73,\sqrt{2}=1.41]$

Answer 1

For bcc unit cell,
$\sqrt{3}a=4R\text{Where, a = edge length}R=\text{radius of sphere}a=\frac{4R}{\sqrt{3}}=27\stackrel{\circ }{A}\Rightarrow R=\frac{27\sqrt{3}}{4}\stackrel{\circ }{A}$
For fcc unit cell,
$\sqrt{2}a=4Ra=\frac{4}{\sqrt{2}}\left(\frac{27\sqrt{3}}{4}\right)\Rightarrow a=27\frac{\sqrt{3}}{\sqrt{2}}\stackrel{\circ }{A}\Rightarrow a=33.12\approx 33\stackrel{\circ }{A}$