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

Answer 1

Answer: (D)

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 $=8+1=9$