Question

If an element (at. wt. $=50$ ) crystallizes in $fcc$ lattice, with a $=0.50\, nm$. What is the density of unit cell if it contains $0.25 \%$ schottky defects (use $N_{A}=6 \times 10^{23}$ ). Give your answer as multiple of $10^{-24}$.

Answer 1

$\rho_{\text {theoretical }}= \frac{N \times \text { mol. wt }}{ a ^{3} \times N_{ a }}$
$=\frac{4 \times 50}{\left(0.50 \times 10^{-7}\right)^{3} cm ^{3} \times 6 \times 10^{23}}$
$=\frac{200}{0.75 \times 10^{-21+23}}=2.66\, g / cm ^{3}$
$\%$ missing $=\frac{\rho_{\text {theo }}-\rho_{\exp }}{\rho_{\exp }} \times 100$
$0.25 =\frac{2.66-\rho_{\exp }}{2.66} \times 100$
$0.00665 =2.66-\rho_{\exp }$
$\rho_{\exp } =2.66665\, g / cm ^{3}$