2003 AIPMT The Solid StateImperfections in Solids: Schottky Defect Medium Question 43 of 45 in The Solid State

The pyknometric density of sodium chloride crystal is $2.165 \times 10^3$ kg m$^{-3}$ while its X-ray density is $2.178 \times 10^3$ kg m$^{-3}$. The fraction of unoccupied sites in sodium chloride crystal is :

A 5.96
B $5.96 \times 10^{-2}$
C $5.96 \times 10^{-1}$
D $5.96 \times 10^{-3}$

The answer is D.

Solution

The X-ray density is calculated from the unit cell dimensions assuming every lattice site is occupied. The pyknometric (measured) density is slightly lower because some sites are vacant (Schottky defects).
Fraction of unoccupied sites $= \dfrac{\text{X-ray density} - \text{pyknometric density}}{\text{X-ray density}}$
$= \dfrac{2.178 \times 10^3 - 2.165 \times 10^3}{2.178 \times 10^3} = \dfrac{0.013}{2.178}$
$= 5.96 \times 10^{-3}$
So the fraction of unoccupied sites is $5.96 \times 10^{-3}$.

Concept Fraction of vacant sites from densities

The Solid State in past papers

45 questions from this chapter have appeared across 23 exam years.