Question

The total volume of atoms present in a $fcc$ unit cell of a metal with radius $r$ is:

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

Answer 1

The correct option is B $\frac{16}{3}\pi r^3$

For $FCC$ crystal,

Number of atoms $=4$

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

Total volume of atoms$=4\times \frac{4}{3}\pi r^3$

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

Hence, Option "B" is the correct answer.