In a fcc arrangement of A and B atoms. A are present at the corners of

the unit cell and B are present at the face centres. If one atom of A is

missing from its position at the corners, what is the formula of the

compound?

A -> 1/8 * 7 = 7/8
B -> 1/2 * 6 = 3
Formula(Compound) = A_7/8 B₃ 
=A₇ B₂₄

 

Net contribution of corner atoms =  1 
                                                                  8
Number at atoms at corner = 7
Total atoms of A = 7 x 1  =  7 
                                         8      8

Contribution of Atoms at face center = 1 
                                                                        2
No of face center atoms = 6
Total atoms of B = 6 x  1  = 3
                                          2

Hence, formula of compund = A_7/8B₃
This is formula per unit cell.

General formula = A₇B₂₄