Question

Calcium crystallizes in a face centred cubic unit cell with a $=0.556$ nm. Calculate the density if it contains:

(i) $0.1\%$ Frenkel defect
(ii) $0.1\%$ Schottky defect

• A. $1.546,1.546$
• B. $1.546,1.544$
• C. $15.46,15.46$
• D. $21.76,41.66$

Answer 1

Answer: (B)

$1.546,1.544$

$1.$ In frenkel defect there is no change in original density

$\rho =\frac{Z\times M_A}{N_A\times a^3}$

$⟹\rho =\frac{4\times 40}{6.023\times {10}^{23}\times 171.8\times {10}^{-24}}$

$⟹\rho =1.546$ $g/c{m}^3$

$2.$ In schottky defect $Z_{eff}$ changes so density changes

$Z_{new}=4-\frac{4\times 0.1}{100}=3.996$

$\rho =\frac{Z\times M_A}{N_A\times a^3}$

$⟹\rho =\frac{3.996\times 40}{6.023\times {10}^{23}\times 171.8\times {10}^{-24}}$

$⟹\rho =1.544$$g/c{m}^3$