Question

A certain element crystallises in a bcc lattice of unit cell edge length 27 \(\mathring{\mathrm{A}}\). If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cel in \(\mathring{\mathrm{A}}\) 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]

Hint:

The atomic radius is the same in both lattices: bcc has \(4r = \sqrt{3}\,a\) and fcc has \(4r = \sqrt{2}\,a\).

Answer 1

Correct Answer: 33

For bcc, atoms touch along the body diagonal: \(4r = \sqrt{3}\,a_{bcc}\), so \(r = \dfrac{1.73\times27}{4} = 11.68\ \mathring{\mathrm{A}}\).
For fcc, atoms touch along the face diagonal: \(4r = \sqrt{2}\,a_{fcc}\), so \(a_{fcc} = \dfrac{4r}{\sqrt{2}} = \dfrac{4\times11.68}{1.41} = 33.1\ \mathring{\mathrm{A}}\).
Rounded off: 33.
Answer: 33