Solid State - Result Question 22
####22. A substance $A _x B _y$ crystallises in a face centred cubic (fcc) lattice in which atoms $A$ occupy each corner of the cube and atoms $B$ occupy the centres of each face of the cube. Identify the correct composition of the substance $A _x B _y$
$(2002,1 M)$
(a) $A B _3$
(b) $A _4 B _3$
(c) $A _3 B$
(d) composition cannot be specified
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Answer:
Correct Answer: 22. (a)
Solution:
- In cubic system, a corner contribute $\frac{1}{8}$ th part of atom to one unit cell and a face centre contribute $\frac{1}{2}$ part of atom to one unit cell. Therefore,
Number of $A$ per unit cell $=\frac{1}{8} \times 8=1$
Number of $B$ per unit cell $=\frac{1}{2} \times 6=3$
$$ \Rightarrow \quad \text { Formula }=A B _3 $$
