Question

When heated above ${916}^{\circ }C$, iron changes its bcc crystalline form to fcc without the change in the radius of atom. The ratio of density of the crystal before and after heating is:
Given:
$[At.wt.ofFe=56gmo{l}^{-1}]$

• A. 1.57
• B. 0.91
• C. 0.25
• D. 1.73

Answer 1

The correct option is B 0.91

Density of the unit cell,
$\rho =\frac{Z\times M}{N_A(a^3\times {10}^{-30})}gc{m}^{-3}$
where,
$Z=\text{No. of atoms in a unit cell}M=\text{Molar mass}{N}_A=\text{Avagadro number}$

For bcc,
$\text{Edge length of a bcc, a}=\frac{4r}{\sqrt{3}}$
$\therefore$
${\rho }_1=\frac{2\times 56}{{\left(\frac{4r}{\sqrt{3}}\right)}^3}$

For fcc,
$\text{Edge length of a fcc, a}=\frac{4r}{\sqrt{2}}$
$\therefore$
${\rho }_2=\frac{4\times 56}{(2\sqrt{2}r{)}^3}$
$\therefore$
$\text{Required ratio,}=\frac{{\rho }_1}{{\rho }_2}=\frac{1}{2}\times \frac{(2\sqrt{2}{)}^3}{(\frac{4}{\sqrt{3}}{)}^3}=0.918$