If $a$ be the edge length of the unit cell and $r$ be the radius of an atom then for $f c c$ arrangement, the correct relation is:

4 a = \sqrt{3} r

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4 r = \sqrt{3} a

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4 r = \sqrt{2} a

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

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Solution

The correct option is C $4 r = \sqrt{2} a$
For face diagonal, the length of the face diagonal will be equal to
$a^{2} + a^{2} = 2 R + R + R$
$4 R = \sqrt{2} a$

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