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Crystal Lattice and Unit Cell

Sodium metal ...

Question

Sodium metal crystallizes in body centred cubic unit cell. If the distance between nearest Na atoms is 368 pm, calculate the edge length of unit cell.

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Solution

nearest distance $= 2 r = 368$
$r = 184 m$
$\frac{\sqrt{3} 9}{4} = 184$
$9 = \frac{184 \times 4}{\sqrt{3}}$
$= 424.9$
$\approx 425 P m$

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