Question

The mineral hawleyite, one form of CdS, crystallizes in one of the cubic lattices with edge length of $5.87$ $\mathring{A}$. The density of hawleyite is $4.63$ g cm${}^{-3}$.

Find the Schottky defect in g cm${}^{-3}$.

• A. $0.33$
• B. $0.29$
• C. $0.60$
• D. $0.12$

Answer 1

The correct option is D $0.12$

The molar mass of CdS is 144.5 g/mol

The expression for the density of the unit cell is $d=\frac{M\times Z}{N_A\times a^3}$

$4.63=\frac{144.5\times Z}{6.023\times {10}^{23}\times (5.87\times {10}^{-8}{)}^3}$

The number of molecules in the unit cell, $Z=3.9\approx 4$

The theoretical density of CdS using $Z=4$

$d=\frac{M\times Z}{N_A\times a^3}$

$d=\frac{144.5\times 4}{6.023\times {10}^{23}\times (5.87\times {10}^{-8}{)}^3}$

$=4.75g/c{m}^3$

The Schottky defect $=4.75-4.63=0.12g/c{m}^3$