Total volume of atoms present in a face centred cubic unit cell of a metal is: (r is atomic radius)

Question

Total volume of atoms present in a face centred cubic unit cell of a metal is: (r is atomic radius) (A) (16/3) π r3 (B) (20/3) π r3 (C) (24/3) π r3 (D) (12/3) π r3

Tardigrade Admin · Accepted Answer

In fcc unic cell z=4 Hence, occupied volume by sphere =4 × (4/3) π r3 =(16/3) π r3

Q. Total volume of atoms present in a face centred cubic unit cell of a metal is : ( $r$ is atomic radius)

$\frac{16}{3} π r^{3}$

$\frac{20}{3} π r^{3}$

$\frac{24}{3} π r^{3}$

$\frac{12}{3} π r^{3}$

In fcc unic cell $z = 4$
Hence, occupied volume by sphere $= 4 \times \frac{4}{3} π r^{3}$
$= \frac{16}{3} π r^{3}$

Q. Total volume of atoms present in a face centred cubic unit cell of a metal is : (r is atomic radius)

316​πr3

320​πr3

324​πr3

312​πr3