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Q.

In the body-centered cubic unit cell and face centered cubic unit cell, the radius of atom in ten of edge length (a) of the unit cell is respectively :

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a

$\frac{a}{2}, \frac{a}{2 \sqrt{2}}$

b

$\frac{\sqrt{3} a}{4}, \frac{a}{2 \sqrt{2}}$

c

$\frac{a}{2 \sqrt{2}}, \frac{\sqrt{3} a}{4}$

d

$\frac{\sqrt{3} a}{2}, \frac{a}{2 \sqrt{2}}$

answer is C.

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Detailed Solution

In BCC, radius of atom in ten of edge length (a) of the unit cell is $\frac{\sqrt{3} a}{4}$

In FCC, radius of atom in ten of edge length (a) of the unit cell is $\frac{a}{2 \sqrt{2}}$

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In the body-centered cubic unit cell and face centered cubic unit cell, the radius of atom in ten of edge length (a) of the unit cell is respectively :