Question:

Sodium crystallizes in bcc arrangement with the interfacial separation between the atoms at the edge $53\, pm$. The density of the solid is

Updated On: Jul 2, 2022
  • 1.23 g/cc
  • 485 g/cc
  • 4.85 g/cc
  • 123 g/cc
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The Correct Option is A

Solution and Explanation

Given, $a-2\, r=53\, pm$ For bcc structure, $4 r=\sqrt{3} a$ or $ 2 r=\frac{\sqrt{3}}{2} a$ $\Rightarrow a-\frac{\sqrt{3}}{2} a=53$ $\therefore a=395.6 \, pm$ Density $(d)=\frac{Z M}{N_{a} a}$ $d =\frac{2 \times 23}{6.023 \times 10^{23} \times(3.956)^{3} \times 10^{-24}} $ $=1.23 \,g / cc .$
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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.