Question

A cubic unit cell has one atom on each corner and one atom on each body diagonal. The number of atoms in the unit cell is ________.

• A. 3
• B. 5
• C. 4
• D. none of these

Answer 1

Answer: (B)

5

The given cubic unit cell has one atom on each corner and one atom on each body diagonal. The atom at corner is shared by $2$ unit cells and atom on the body diagonal is not shared. So, the contribution of atom on the corner to the unit cell is $\frac{1}{8}$ and contribution of atom on the body diagonal is $1$.

So, effective number of atom in unit cell $=\frac{1}{8}\times 8+4\times 1=1+4=5$