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Relation Between r and a

Silver crysta...

Question

Silver crystallizes with face centred cubic unit cell and each side of unit cell has length of 409 pm. What is the radius of an atom of silver?

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Solution

Let r be the radius and a is the edge length of the unit cell.

For FCC lattice,
$r = \frac{a}{2 \sqrt{2}}$
$r = \frac{409}{2 \times 1.4142}$
$r = 144.6 p m$

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