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

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

The Solid State

Solution:

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

$2 r+n=a$

$ n=a-2 r$

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

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

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

$\frac{a-2 \times \frac{a}{2 \sqrt{2}}}{a}=$ 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