Question

Calculate the number of atoms in a cubic based unit cell having one atom at each corner and two atoms on each diagonal.

Answer 1

The unit cell of a cubic system has 8 atoms at its corners, one at each corner of the cube.

Contribution of 8 atoms = `8 xx 1/8`

= 1 atom

In a cube, there are 4 space diagonals (body diagonals).

The problem says 2 atoms per diagonal.

So, total atoms on diagonals = 4 × 2 = 8 atoms

Total number of atoms per unit cell = (From corners) + (From diagonals)

= 1 + 8

= 9 atoms