Question

Iron occurs as bcc as well as fcc unit cell. If the effective radius of an atom of iron is $124$ pm, the density (in g cm${}^{-3}$) of iron in both these structures are, respectively :

• A. $7.887,8.59$
• B. $8.59,7.887$
• C. $14.287,16.248$
• D. $16.248,14.287$

Answer 1

The correct option is A $7.887,8.59$

For bcc unit cell, the edge length, $a=\frac{4r}{\sqrt{3}}=\frac{4\times 124}{\sqrt{3}}=286.4$ pm
The number of formula units per unit cell $Z=2$
Density $=\frac{\text{Z}\times \text{Molar mass}}{\text{Avogadro's number}\times a^3}$
Density $=\frac{2\times 55.85}{6.023\times {10}^{23}\times (286.4\times {10}^{-10}{)}^3}=7.887gc{m}^{-3}$
For fcc unit cell, the edge length, $a=\frac{4r}{\sqrt{2}}=\frac{4\times 124}{\sqrt{2}}=350.8$ pm
The number of formula units per unit cell $Z=4$
Density $=\frac{\text{Z}\times \text{Molar mass}}{\text{Avogadro's number}\times a^3}$
Density $=\frac{4\times 55.85}{6.023\times {10}^{23}\times (350.8\times {10}^{-10}{)}^3}=8.59gc{m}^{-3}$