Discussion Forum

Iron crystallizes in several modifications. At about 911°C, the bcc ' α ' form undergoes a transition to fcc 'γ ' form. If the distance between the two nearest neighbours is the same in the two forms at the transition temperature, the ratio of the density of iron in fcc form (ρ₂) to that of iron of bcc form (ρ₁ ) at the transition temperature

Answer:

Explanation:

 In α - form distance between nearest neighbour atom is $\frac{\sqrt{3}a_{1}}{2}$

In γ form distance between nearest neighbour atom is $\frac{a_{2}}{\sqrt{2}}$

.'. $\frac{\sqrt{3}a_{1}}{2}$ = $\frac{a_{2}}{\sqrt{2}}$  (given)

or $\frac{a_{2}}{a_{1}}= \sqrt{\frac{3}{2}}$

$\frac{\rho_{1}}{\rho_{2}}= \frac{z_{1}}{z_{2}}\left(\frac{a_{2}}{a_{}}\right)^{3}$

= $\frac{1}{2}\left(\sqrt{\frac{3}{2}}\right)^{3}$ = 0.918