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Metallic gold...

Question

Metallic gold crystallises in the face centred cubic lattice. The length of cubic unit cell is $4.070 ˚ A$ . What is the closet distance between gold atoms?

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Solution

closest distance between two atoms is equal to R
$2 R = \frac{a \sqrt{2}}{2}$
$R = \frac{407 \sqrt{2}}{2}$
=144 pm

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