What is the volume of the atoms having radius 'r' present in BCC unit cell?

\(\frac{8πr^3}{3}\)

The correct answer is option 3. \(\frac{8πr^3}{3}\)

In BCC unit cell, atoms are present at corners and at body centre.

Total number of atoms per unit cell = \(\frac{1}{8} \times 8 + 1 \times 1 + \frac{1}{2} \times 0 = 1 + 1 = 2\)

As atoms are considered to be spherical, 

Therefore, Volume of one atom \(= \frac{4}{3}\pi r^3\)

Volume of two atoms in each BCC unit cell is given by \(2 \times \frac{4}{3}\pi r^3 = \frac{8}{3}\pi r^3\)