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A solid is formed and it has three types of atoms X, Y and Z. X forms a fcc lattice with Y atoms occupying all tetrahedral voids and Z atoms occupying half of octahedral voids. The formula of solid is

Options

  1. AX 4 Y Z 2
  2. BX 4 Y 2 Z
  3. CX Y 2 Z 4
  4. DX 2 Y 4 Z

Correct answer

D. X 2 Y 4 Z

Step-by-step solution

X is in f.c.c. lattice Number of atoms = a t o m a t c o r n e r × 1 8 + a t o m s a t f a c e s × 1 2 X = 8 × 1 8 + 6 × 1 2 = 4 Total tetrahedral voids = 8 As y are at T.V. So Y = 8 Number of Octahedra voids = 4 Z = 1 2 × 4 = 2 So X = 4 , Y = 8 , Z = 2 Hence the formula of solid is X 4 Y 8 Z 2 or X 2 Y 4 Z .

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