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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

Options

  1. AXYZ 2
  2. BX 2 YZ 2
  3. CX 8 Y 4 Z 5
  4. DX 5 Y 4 Z 8

Correct answer

D. X 5 Y 4 Z 8

Step-by-step solution

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 × 1 8 = 1 5 4 Number of Y atom left = 4 - (1 × 1) = 3 Number of Z atom left = 8 - (2 × 1) = 6 The simplest formula = X 1 5 4 Y 3 Z 6 ⇒ X 1 5 Y 1 2 Z 2 4 ⇒ X 5 Y 4 Z 8

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