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An alloy made up of $A$ and $B$ metals crystallises in a cubic lattice, where $B$ atoms occupy the corners and $A$ atoms occupy the face centers. The formula of the alloy formed is
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The correct answer is:
$A_3 B$
In cubic lattice,
$B$ atoms occupy corners
$A$ atoms occupy face centres
Contribution of each atom $(B)$ present at corner $=1 / 8$
$$
\Rightarrow \quad 8 \times \frac{1}{8}=1
$$
Contribution of each atom $(A)$ present at centre of face
$$
\frac{1}{2} \times 6=3
$$
$B$ atoms occupy corners
$A$ atoms occupy face centres
Contribution of each atom $(B)$ present at corner $=1 / 8$
$$
\Rightarrow \quad 8 \times \frac{1}{8}=1
$$
Contribution of each atom $(A)$ present at centre of face
$$
\frac{1}{2} \times 6=3
$$
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