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 the cube?

• A. $8$
• B. $6$
• C. $4$
• D. $9$

Answer 1

The correct option is D $9$

There are $8$ corners in a cube and hence $8$ atoms are placed at the corner of the cube. But these $8$ atoms are shared equally by $8$ separate units.Therefore,

Contribution of atoms placed at the corner $=8\times \frac{1}{8}=1$

There are $4$ body diagonals in a cube and the number of atoms at each body diagonal are $2$. Since these atoms are within the unit cell and hence are not shared by other units, therefore,

Contribution of atoms placed at the body diagonal $=2\times 4=8$

Hence, total atoms in the cube based unit cell $=8+1=9$