What is the packing efficiency of simple cubic lattice?

The correct answer is Option (3) → 52.4%

In a simple cubic lattice the atoms sit only at the eight corners and touch each other along the edge, so the edge length is a = 2r.

    \( \displaystyle \text{Atoms per unit cell} = 8 \times \tfrac{1}{8} = 1 \)

    \( \displaystyle \text{Volume of the cell} = a^3 = (2r)^3 = 8r^3 \)

    \( \displaystyle \text{Packing efficiency} = \frac{\frac{4}{3}\pi r^3}{8r^3} \times 100 = \frac{\pi}{6} \times 100 = 52.4\% \)

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 Simple Cubic Lattice