A crystalline solid is made of X , Y and Z elements. Atoms of element X form FCC packing; atoms of element Y occupy octahedral voids while atoms of element Z occupy tetrahedral voids. What will be the

Question

A crystalline solid is made of X , Y and Z elements. Atoms of element X form FCC packing; atoms of element Y occupy octahedral voids while atoms of element Z occupy tetrahedral voids. What will be the simplest formula of solid if atoms along one axis along the body diagonal are removed

TestHub · Accepted Answer

Number of atoms of X (at packing site, i.e., at corners and face-centres)

$= 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4$

Number of atoms of $Y = 4$

Number of atoms of $Z = 8$

Along one body diagonal there will be two X atoms, one Y atom and two Z atoms are found and are removed.

Number of atoms of X will be $= 4 - \frac{1}{8} \times 2 = \frac{15}{4}$

Number of atoms of Y will be $= 4 - 1 = 3$

Number of atoms of $Z$ will be $= 8 - 2 = 6$

$X : Y : X$

$\frac{15}{4} : 3 : 6$

$5 : 4 : 8$

∴ Simplest formula will be $X_{5} Y_{4} Z_{8}$

Chemistry - Solid State Question with Solution | TestHub

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