Question:
A certain element crystallises in a bcc lattice of unit cell edge length 27 Å. If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cell in Å will be ________. (Round off to the Nearest Integer).
[Assume each lattice point has a single atom]
[Assume $\sqrt{3}=1.73, \sqrt{2}=1.41$ ]
Solution:
For $\mathrm{BCC} \sqrt{3} \mathrm{a}=4 \mathrm{r}$
so $\quad r=\frac{\sqrt{3}}{4} \times 27$
for $\mathrm{FCC} \quad \mathrm{a}=2 \sqrt{2} \mathrm{r}$
$=2 \times \sqrt{2} \times \frac{\sqrt{3}}{4} \times 27$
$=\frac{\sqrt{3}}{\sqrt{2}} \times 27$
$=33$
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