Question

In $FCC$ unit cell, what fraction of edge is not covered by atoms?

• A. 0.134
• B. 0.293
• C. 0.26
• D. 0.32

Answer 1

Answer: (B)

$\frac{h}{a}=$ fraction of edge not covered by atoms

$2r+n=a$

$n=a-2r$

$\frac{a-2r}{a}=$ fraction of edge not covered

$2r=\frac{\sqrt{2a}}{2}$

$r=\frac{\sqrt{2a}}{4}=\frac{a}{2\sqrt{2}}$

$\frac{a-2\times \frac{a}{2\sqrt{2}}}{a}=$ fraction of edge not covered

$\frac{a\left(1-\frac{1}{\sqrt{2}}\right)}{a}=$ fraction of edge not covered

$\frac{\sqrt{2}-1}{\sqrt{2}}=\frac{1.414-1}{1.414}$

$=\frac{0.414}{1.414}=0.293=$ fraction of edge not covered