Question:

An alloy of copper, silver and gold is found to have copper atom constituting the ccp lattice. If silver atom occupy the edge centres and gold atom is present at body centred, the alloy has a formula

Updated On: Jun 20, 2024
  • $Cu_{4}Ag_{2}Au $
  • $Cu_{4}Ag_{4}Au $
  • $Cu4_{A}g_{3}Au $
  • $CuAgAu $
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The Correct Option is C

Solution and Explanation

In the unit cell number of Cu atoms (fcc/ccp)
$= 8 \times \frac{1}{6} + 6 \times \frac{1}{4} = 4 $
As Ag atoms occupying edge centred
$ =12 \times \frac{1}{4} = 3$
and Au atoms are presents at the body centred = 1
$ \therefore $ formula, $Cu_4 Ag_3Au$
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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.