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# A compound formed by elements A and B has a cubic structure in which A atoms are at the corners of the cube and B atoms are at face centres .Derive the formula of the compound

$(a)\;A\qquad(b)\;B\qquad(c)\;AB_{3}\qquad(d)\;AB_{2}$

Answer : $\;AB_{3}$
As 'A' atom are present at the 8 corners of the cube therefore no of atoms of A in the unit cell = $\;\large\frac{1}{8} \times \normalsize 8=1\;$
As 'B' atoms present at the face corners of the cube therefore no of atoms of B in the unit cell = $\;\large\frac{1}{2} \times \normalsize 6=3\;$
Hence the formula of compound is $\;AB_{3}\;$