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Q)

Calcium crystallises in a face-centred cubic unit cell with a=0.556nm.Calculate the density if it contained 0.1% Frenkel defects.

$\begin{array}{1 1}1.5455g/cm^3\\2.5455g/cm^3\\3.5455g/cm^3\\4.5455g/cm^3\end{array} $

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A)
Frenkel defects do not change the value of the theoretical density because the atom is only occupying an interstitial position instead of lattice position.
Thus density can be determined using
$\rho=\large\frac{Mz}{N_0a^3}$
$a=0.556nm=0.556\times 10^{-9}m$
$\Rightarrow 0.556\times 10^{-7}cm$
$\rho$(with Frenkel defects)=$\large\frac{40\times 4}{6.023\times 10^{23}\times (0.556\times 10^{-7})^3}$
$\Rightarrow 1.5455g/cm^3$
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