Discussion Forum



1)

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


A) $\frac{4}{3} \pi r^{3}$

B) $\frac{8}{3} \pi r^{3}$

C) $\frac{16}{3} \pi r^{3}$

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

Answer:

Option C

Explanation:

 The volume occupied by the face centred cubic unit cell is $\frac{16}{3} \pi r^{3}$

 Packing fraction or volume occupied

 $Z_{eff}\times$   volume of c-atom = $\frac{Z_{eff}\times\frac{4}{3}\pi r^{3}}{a^{3}}$

 for fcc,   $Z_{eff}=4=\frac{4\times\frac{4}{3}\pi r^{3}}{a^{3}}$    (where , a=1)

172021773_c10.PNG

 = $\frac{16}{3} \pi r^{3}$