A metal crystallises with a face-centred cubic lattice.The edge of the unit cell is 408 pm. The diameter of the metal atom is

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144 pm

288 pm

408 pm

204 pm

answer is A.

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Detailed Solution

For fcc lattice $4 r = \sqrt{2} a$
$r = \frac{\sqrt{2} a}{4} = \frac{a}{2 \sqrt{2}} = \frac{408}{2 \sqrt{2}} = 144 pm$
Diameter, $d = 2 r = 2 \times 144 pm = 288 pm$

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