Question

Answer the following questions based on the above diagram:

The formula of the compound is :

• A. $AB{O}_2$
• B. $A_{2}B{O}_3$
• C. $A{B}_2{O}_4$
• D. $A_{2}B{O}_4$

Answer 1

The correct option is C $A{B}_2{O}_4$

(1) The number of A atoms present in the unit cell is 1.5.
One atom is completely present in the unit cell and the other atom is shared by 2 units cells and has contribution of one half to each unit cell.
(2) The number of B atoms present in the unit cell is 3.
One B atom is completely present in the unit cell.
8 B atoms are present along the edges each has contribution of 1/4 as it is shared by 4 unit cells. Thus 8 atoms contribute 8/4 = 2 to the unit cell. Total number of B atoms = 2+1 = 3.
(3) The number of O atoms present in the unit cell is 6.
8 C atoms are present along 8 corners and each contributes 1/8 to the unit cell as each is shared by 8 unit cells. Total contribution of 8 atoms will be 8 * 1/8 = 1.
4 C atoms are present along 4 edges and each contributes 1/4 to the unit cell as each is shared by 4 unit cells. Total contribution of 4 atoms will be 4 * 1/4 = 1.
1 C atom is completely present in the unit cell. Its contribution will be 1.
6 C atoms are present along 6 faces and each contributes 1/2 to the unit cell as each is shared by 2 unit cells. Total contribution of 6 atoms will be 6 * 1/2 = 2.
Total number of C atoms will be $1+1+1+3=6$
Hence, the ratio $A:B:O$ is $1.5:3:6$ or $1:2:4$
Hence, the formula of the compound is $A{B}_2{O}_4$