How many number of atoms are there in a cube based unit cell having one atom on each comer and two atoms on each body diagonal of cube?

Question

How many number of atoms are there in a cube based unit cell having one atom on each comer and two atoms on each body diagonal of cube? (A) 8 (B) 6 (C) 4 (D) 9

Tardigrade Admin · Accepted Answer

There are four body diagonals. Atoms on the body diagonals are not shared by any other unit cell.
Contribution by atoms on corners

= 8 \times \frac{1}{8} = 1

and
Contribution by atoms on body diagonal

= 2 \times 4 = 8

Hence, total atoms in the cube based unit cell

= 8 + 1 = 9

Q. How many number of atoms are there in a cube based unit cell having one atom on each comer and two atoms on each body diagonal of cube?

8

6

4

9

There are four body diagonals. Atoms on the body diagonals are not shared by any other unit cell. Contribution by atoms on corners =8×81​=1 and Contribution by atoms on body diagonal =2×4=8 Hence, total atoms in the cube based unit cell =8+1=9

There are four body diagonals. Atoms on the body diagonals are not shared by any other unit cell.
Contribution by atoms on corners
$= 8 \times \frac{1}{8} = 1$ and
Contribution by atoms on body diagonal
$= 2 \times 4 = 8$
Hence, total atoms in the cube based unit cell $= 8 + 1 = 9$