If the edge length of a unit cell is 'a' in sc, bcc and fcc then find the radius of atom present in respective crystal system.

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For a simple cubic (sc) unit cell, atoms touch each other along the edge of the cube.

$2 r = a \Rightarrow r = \frac{a}{2}$

For a body-centered cubic (bcc) unit cell, atoms touch each other along the body diagonal.

$4 r = 3 a \Rightarrow r = \frac{3}{4} a$

For a face-centered cubic (fcc) unit cell, atoms touch each other along the face diagonal.

$4 r = 2 a \Rightarrow r = \frac{2}{4} a = \frac{a}{2 2}$

The radii for sc, bcc, and fcc are $\frac{a}{2}, \frac{3}{4} a, \frac{a}{2 2}$ respectively.

Answer: $\frac{a}{2}, \frac{3}{4} a, \frac{a}{2 2}$

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