How many number of atoms are there in a cube based unit cell having one atom on each corner 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 corner 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 comers

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

and Contribution by atoms on body diagonal

= 2 \times 4 = 8

∴

Total number of atoms

= 1 + 8 = 9

Q. How many number of atoms are there in a cube based unit cell having one atom on each corner 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 comers =8×81​=1 and Contribution by atoms on body diagonal =2×4=8 ∴ Total number of atoms =1+8=9

There are four body diagonals. Atoms on the body diagonals are not shared by any other unit cell.
Contribution by atoms on comers $= 8 \times \frac{1}{8} = 1$
and Contribution by atoms on body diagonal $= 2 \times 4 = 8$
$∴$ Total number of atoms $= 1 + 8 = 9$