A crystal made up of particles X, Y, and Z. X forms fcc packing. Y occupies all octahedral voids of X and Z occupies all tetrahedral voids of X. It all particles along one body diagonal are removed, t

Question

A crystal made up of particles X, Y, and Z. X forms fcc packing. Y occupies all octahedral voids of X and Z occupies all tetrahedral voids of X. It all particles along one body diagonal are removed, then the formula of the crystal is

TestHub · Accepted Answer

For fcc, number of X atoms = 4/unit cell

Number of Tetrahedral Voids = Z = 8

Number of Octahedral Voids = Y = 4

Number of atoms removed along one body diagonal = 2X (corner) and 2Z (TVs) and 1 Y (OV at body centre)

$∴$ Number of X atoms left $= 4 - (2 \times \frac{1}{8}) = \frac{15}{4}$

Number of Y atom left = 4 - (1 × 1) = 3

Number of Z atom left = 8 - (2 × 1) = 6

The simplest formula $= X_{\frac{15}{4}} Y_{3} Z_{6} \Rightarrow X_{15} Y_{12} Z_{24}$
$\Rightarrow X_{5} Y_{4} Z_{8}$

Chemistry - Solid State Question with Solution | TestHub

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