Question

A crystal is made of particles A and B. A forms fcc packing and B occupies all the octahedral voids. If all the particles along the plane as shown in figure are removed, then the formula of the crystal will be.

\[\begin{array}{*{20}{l}}
  {A) - {\text{ }}AB} \\
  {B) - {\text{ }}{A_5}{B_7}} \\
  {C) - {\text{ }}{A_7}{B_5}}
\end{array}\]
D)- None of these.

Answer 1

Hint: A crystal or crystalline solid is a solid material whose constituents are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. a piece of a homogeneous solid substance having a natural geometrically regular form with symmetrically arranged plane faces.

Complete step by step solution:
In FCC total 4 octahedral voids were present.
So, it contains 4 A and 4 B atoms but all the particles along the plane as shown in the figure given in the question are removed.
This plane contains 23​ octahedral void atoms (1 at body center and 2 at edge center) and 23​ lattice atoms (2 face centers and 4 corners).\[\begin{array}{*{20}{l}}
  {A) - {\text{ }}AB} \\
  {B) - {\text{ }}{A_5}{B_7}} \\
  {C) - {\text{ }}{A_7}{B_5}}
\end{array}\]
So, the formula will be \[A3/2B3/2 = AB.\]
Hence, option A is the correct answer.

Note:
The void surrounded by six. sitting at the corners of a regular octahedron is called an octahedral void. The triangular voids in the second layer are just above the triangular voids in the first layer.A Lattice point is the position in the unit cell or in a crystal where the probability of finding an atom or an ion is the highest. In other words, the atoms or ions occupy the lattice points in a crystalline solid.