The Solid State - Result Question 28
####28. A compound is formed by elements $A$ and $B$. The crystalline cubic structure has the $A$ atoms at the corners of the cube and $B$ atoms at the body centre. The simplest formula of the compound is
(a) $A B$
(b) $A_6 B$
(c) $A B_6$
(d) $A_8 B_4$
[2000]
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Solution:
- (a) Given: Atoms are present at the corners of the cube $=A$ and atoms present at body centre $=B$. We know that a cubic unit cell has 8 corners. Therefore contribution of each atom at the corner $=\frac{1}{8}$. Since number of atoms per unit cell is 8 , therefore total contribution $=8 \times \frac{1}{8}=1$. We also know the one atom is in the body centre, therefore number of atoms per unit cell $=1$. Thus formula of the compound is $A B$.
