Discussion
In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is
Answer: A
The formula is \(\mathrm{A_2B_5}\).
In a face-centred cubic cell, corner atoms contribute \(1/8\) each and face-centre atoms \(1/2\) each:
\[n(\mathrm{A}) = 8\times\frac{1}{8} = 1,\qquad n(\mathrm{B}) = 6\times\frac{1}{2} = 3\]
Removing one face-centre B takes away \(1/2\) of an atom: \[n(\mathrm{B}) = 3 - \frac{1}{2} = \frac{5}{2}\]
\[\mathrm{A}:\mathrm{B} = 1:\frac{5}{2} = 2:5 \Rightarrow \mathrm{A_2B_5}\]
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