Question

# The pyknometric density of NaCl crystal is $2.165\times {{10}^{-3}}$ $kg{{m}^{-3}}$ while its X-ray density is $2.178\times {{10}^{-3}}$ $kg{{m}^{-3}}$. Therefore, the fraction of unoccupied sites in the NaCl crystal is:\begin{align} & a)5.96\times {{10}^{-4}} \\ & b)5.96\times {{10}^{-2}} \\ & c)5.96\times {{10}^{-1}} \\ & d)5.96\times {{10}^{-3}} \\ \end{align}

Hint: $Fraction\text{ of unoccupied sites = }\dfrac{\text{X-ray density(X) - Pyknometric Density(p)}}{X-ray\text{ density (X)}}$
Use this formula to try and calculate the required fraction. Be very careful of the units while you’re at it.

$Fraction\text{ of unoccupied sites = }\dfrac{\text{X-ray density(X) - Pyknometric Density(p)}}{X-ray\text{ density (X)}}$
$Fraction\text{ of unoccupied sites = }\dfrac{2.178\times {{10}^{-3}}\text{ - }2.165\times {{10}^{-3}}}{2.178\times {{10}^{-3}}}\approx 5.96\times {{10}^{-3}}$
Therefore, we can conclude that the fraction of empty spaces in a Sodium Chloride (NaCl) crystal is $5.96\times {{10}^{-3}}$.
Thus, we can conclude that the answer to this question is d) $5.96\times {{10}^{-3}}$