How many atoms are in the following cubic unit cell -(a) Simple cubic

1.	How many atoms are in the following cubic unit cell -(a) Simple cubic unit cell.(b) Body centered cubic unit cell.(c) Face centered cubic unit cell.
Answer» SIMPLE CUBIC UNIT CELL: 8 CONTRIBUTIONS from each vertex of the cube; Total number of atoms in a simple cubic unit cell is: $\sf{ = 8 \times ( \dfrac{1}{8} th \: contribution)}$ $\sf{ = 8 \times \dfrac{1}{8} }$ $\sf{ = 1 \: atom }$ BODY CENTRED UNIT CELL: Apart from 8 contributions from each vertex , there is an additional whole contributions from the body centre. Hence , total number of atoms: $\sf{ =( 8 \times \dfrac{1}{8}) + 1 }$ $\sf{ =1+ 1 }$ $\sf{ =2 \: atoms }$ FACE CENTRED UNIT CELL: There are 8 contributions from each vertex and 6 contributions from each face of the cube: $\sf{ =( 8 \times \dfrac{1}{8}) + (6 \times \dfrac{1}{2} )}$ $\sf{ =1+ 3}$ $\sf{ =4 \: atoms}$ Hope It Helps.