Question

A metal crystal has bcc lattice. Find the % fraction of edge length not covered by atom.

• A. $10.4\%$
• B. $13.4\%$
• C. $12.4\%$
• D. $11.4\%$

Answer 1

Answer: (B)

$\text{In bcc, }\text{r}=\frac{\sqrt{3}}{4}\text{a}$
Also, edge length of unit cell $=a$
radius of atom $=r$
$\therefore$ Edge length not covered by atom $=a-2r$
or $=\text{a}-\frac{\sqrt{3}}{2}\cdot \text{a}=\text{a}\left[\frac{2-\sqrt{3}}{2}\right]$
$\therefore$ Percentage fraction not covered
$=\frac{\text{a}\left[\frac{2-\sqrt{3}}{2}\right]}{\text{a}}\times 100=\text{0.134}\times 100=\text{13.4\%}$