Question

The total volume of atoms present in a face-centered cubic unit cell of a metal is: $(r$ is atomic radius)

• A. $\frac{16}{3}\pi r^3$
• B. $\frac{20}{3}\pi r^3$
• C. $\frac{24}{3}\pi r^3$
• D. $\frac{12}{3}\pi r^3$

Answer 1

Answer: (A)

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

$Z_{eff}$ in $FCC$ unit cell= $6\times \frac{1}{2}+\frac{1}{8}\times 8$

$=4$

Volume of one atom=$\frac{4}{3}\pi r^3$

Volume of atoms in $FCC$=$4\times \frac{4}{3}\pi r^3$

$=\frac{16}{3}\pi r^3$