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A solid compound contains X,Y and Z atom...

A solid compound contains X,Y and Z atoms in a cubic lattice with X atoms occupying the corners,Y atoms in the body centred positions and Z atoms at the centres of faces of the unit cell. What is the empirical formula of the compound

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Since atom X is present at corner and one corner is shared by eight unit cells, Number of X atoms per unit cell `=(1)/(8)xx8 =1.`
Atom Y is present at body centered position and used by only one unit cell. So, number of Y atoms per unit cell = 1.
Atom Z is present at the centre of each face, so shared by two unit cells, thus numbers of Z atoms per unit cell `= (1)/(2) xx6 =3 .`
Hence, the formula of compound = `XYZ_(3)`
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