Question:

An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be

Updated On: Apr 26, 2024
  • $A_3B$
  • $AB_3$
  • $A_2B$
  • $AB$
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The Correct Option is B

Solution and Explanation

Number of A ions in the unit cell $ = \frac{1}{8} \times = 1 $ Number of B ions in the unit cell $ = \frac{1}{2} \times 6 = 3 $ Hence empirical formula of the compound $= AB_3$
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Concepts Used:

Unit Cells

The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell.

The characteristics of a unit cell are:

  • The dimensions are measured along the three edges, a, b and c. These edges can form different angles, they may be mutually perpendicular or may not.
  • The angles held by the edges are α (between b and c) β (between a and c) and γ (between a and b).

Therefore, a unit cell is characterised by six parameters such as a, b, c and α, β, γ.

Types of Unit Cell:

Numerous unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.

  1. Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
  2. Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
    1. Body-Centered Unit Cell: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.
    2. Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
    3. End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.