Question

Iron crystallizes in several modifications. At about $911^{\circ }C$, the bcc ${}^{\prime }{\alpha }^{\prime }$ form undergoes a trasition to fcc ${}^{\prime }{\gamma }^{\prime }$ 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 fee form $\left({\rho }_2\right)$ to that of iron of bcc form $\left({\rho }_1\right)$ at the transition temperature

• A. $\frac{{\rho }_1}{{\rho }_2}=0.918$
• B. $\frac{{\rho }_1}{{\rho }_2}=0.718$
• C. $\frac{{\rho }_1}{{\rho }_2}=0.518$
• D. $\frac{{\rho }_1}{{\rho }_2}=0.318$

Answer 1

Answer: (A)

In $\alpha$ - form distance between nearest
neighbours atom is $\frac{\sqrt{3}{a}_1}{2}.$
In $\gamma$ form distance between nearest neighbours atom is $\frac{a_2}{\sqrt{2}}.$
$\therefore \frac{\sqrt{3}{a}_1}{2}=\frac{a_2}{\sqrt{2}}$ (given)
or $\frac{a_2}{a_1}=\sqrt{\frac{3}{2}}$
$\frac{{\rho }_1}{\rho }=\frac{Z_1}{Z_2}{\left(\frac{a_2}{a_1}\right)}^3=\frac{1}{2}{\left(\sqrt{\frac{3}{2}}\right)}^3=0.918$