Question

Find the total volume of a unit cell given the radius of the atom.

• A. \( 8r^3 \)
• B. \( \frac{64r^3}{3\sqrt{3}} \)
• C. \( \frac{32r^3}{\sqrt{2}} \)
• D. \( \frac{16r^3}{\sqrt{3}} \)

Hint:

The edge length \( a \) is related to the atomic radius \( r \) and depends on the type of cubic unit cell. Use \( a = 2r \) for simple cubic, \( a = \frac{4r}{\sqrt{3}} \) for BCC, and \( a = \frac{4r}{\sqrt{2}} \) for FCC.