Find the size of largest sphere that will fit in octahedral void in an ideal FCC crystal as a function of atomic radius r.

0.155 r

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0.225 r

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0.414 r

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0.732 r

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Solution

The correct option is D $0.414 r$
Let the radius of the octahedral void be $a$ and the spheres be $r$ .
In the adjoining figure it can be seen that,
$2 r \sqrt{2} = 2 r + 2 a$
$⟹ a = 0.414 r$ .

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