In face centred cubic unit cell, what is the volume occupied?

Engineering

Chemistry

Voids or Interstitial Site and Radius Ratio

Question

$\frac{4}{3} {πr}^{3}$

$\frac{8}{3} {πr}^{3}$

$\frac{16}{3} {πr}^{3}$

$\frac{64 r^{3}}{3 \sqrt{3}}$

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In fcc unit cell, no. of atoms are

= [6 \times \frac{1}{2}] + [8 \times \frac{1}{8}] = 4

Volume of 1 spherical atom is

\frac{4}{3} {πr}^{3}

So, volume occupied by atoms in fcc unit cell will be

4 \times \frac{4}{3} {πr}^{3} = \frac{16}{3} {πr}^{3}

, where, r is radius of atom.

Hence, the correct option is C

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