Question

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

• A. $0.134$
• B. $0.24$
• C. $0.293$
• D. None of these

Answer 1

Answer: (C)

$0.293$

In an edge length $2r$ distance is covered radius

So, remaining distance=$a-2r$ (uncovered)

Fraction of uncovered edge= $\frac{a-2r}{a}=1-\frac{2r}{a}$

also, $4r=a\sqrt{2}\Rightarrow \frac{r}{a}=\frac{1}{2\sqrt{2}}$

$⟶$ fraction of uncovered edge= $1-\frac{1}{\sqrt{2}}=0.29$