Question

A unit cell of the cubic system has eight atoms of an element A at the corners of the cell and two atoms of A inside the cell. There are twelve atoms of B on the faces of the cell and four atoms of B along the edges of the cell.

How many atoms of A are there in the unit cell?

How many atoms of B are there in the unit cell?

Answer 1

1)
8 atoms of A at corners and their contribution is 1/8
2 atoms of A inside the cell and their contribution is 1
SO,
Total number of A = 1/8 * 8 + 1 * 2
= 1 + 2
= 3
Answer: 3

2)
12 atoms of B at faces and their contribution is 1/2
4 atoms of B along edges and their contribution is 1/4
SO,
Total number of B = 1/2 * 12 + 1/4 * 4
= 6 + 1
= 7
Answer: 7