The percentage of empty space in a body centred cell is:

The correct answer is Option (1) → 32

In a body-centred cubic unit cell there are 8 × 1/8 + 1 = 2 atoms, and the atoms touch along the body diagonal, so √3 a = 4r.

    Volume of 2 atoms = 2 × (4/3)πr³ = (8/3)πr³
    Volume of the cube = a³ = (4r/√3)³ = (64/3√3) r³
    Packing efficiency = [(8/3)πr³ / (64/3√3) r³] × 100 = 68%

Empty space = 100 − 68 = 32%.

Note: This question is from the pre-rationalised NCERT book (2022-23). The topic is not there in the latest NCERT book (2026-27), and it is also out of the CUET 2026 syllabus.

NCERT (Pre-rationalised edition, 2022-23):
Efficiency of Packing in Body-centred Cubic Structures – “… the atom at the centre will be in touch with the other two atoms diagonally arranged. … The length of the body diagonal c is equal to 4r, where r is the radius of the sphere (atom), as all the three spheres along the diagonal touch each other. Therefore, √3 a = 4r. … In this type of structure, total number of atoms is 2 and their volume is 2 × (4/3)πr³. … Packing efficiency = (Volume occupied by two spheres in the unit cell × 100) / (Total volume of the unit cell) = 68%”