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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
Solid State

NTA Abhyas 2020 · Chemistry · Solid State

A solid is formed and it has three types of atoms X, Y and Z. X...

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. AX4YZ2{X}_{4}Y{Z}_{2}
  2. BX4Y2Z{X}_{4}{Y}_{2}Z
  3. CXY2Z4X{Y}_{2}{Z}_{4}
  4. DX2Y4Z{X}_{2}{Y}_{4}Z

Correct answer

D. X2Y4Z{X}_{2}{Y}_{4}Z

Step-by-step solution

X is in f.c.c. lattice
Number of atoms =atomatcorner×18+atomsatfaces×12= atomatcorner \times \dfrac{1}{8} + atomsatfaces \times \dfrac{1}{2}
X=8×18+6×12=4X = 8 \times \dfrac{1}{8} + 6 \times \dfrac{1}{2} = 4
Total tetrahedral voids =8= 8
As y are at T.V.
So Y=8Y = 8
Number of Octahedra voids =4= 4
Z=12×4=2Z = \dfrac{1}{2} \times 4 = 2
So X=4,Y=8,Z=2X = 4, Y = 8, Z = 2
Hence the formula of solid is X4Y8Z2{X}_{4}{Y}_{8}{Z}_{2} or X2Y4Z{X}_{2}{Y}_{4}Z.
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