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using X-ray diffraction method , the unit length of NaCl crystal was observed to be 0.5627nm. The density of the crystal was found to be 2.164gcm^{-3} what type of defect exist in the crystal ? calculate the percentage Na^{+} and Cl^{-} missing from missing from the crystal lattice

NaCl has an ionic structure. So, the crystal can have only ionic defects.

We know that NaCl has fcc structure.

So , z = 4, M = 58.5 g mol

^{-1},a = 0.5627 nm=5.627 x 10

^{-8}

^{ }cm , N

_{A}= 6.022 x 10

^{23}

Now,

$Density=d=\frac{ZM}{{a}^{3}{N}_{A}}=\frac{4\times 58.5}{{\left(5.627\times {10}^{-8}\right)}^{3}\times 6.022\times {10}^{23}}=2.18gc{m}^{-3}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

But, observed density= 2.164 < d

Since the stoichiometry of the compound is maintained but the observed density is lesser than the calculated density, it has a Schottky type defect.

Now, change in density = 2.18-2.164 = 0.016 g cm

^{-3}

So ,

$Percentageofionsmis\mathrm{sin}g=Percentageofchangeinmass=\frac{0.016}{2.18}\times 100=0.734\%$

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