Q. Iron exhibits bcc structure at room temperature. Above 900°C, it transforms to fcc structure. The ratio of density of iron at room temperature to that at 900°C (assuming molar mass and atomic radii of iron remains constant with temperature) is
A) $\frac{3\sqrt{3}}{4\sqrt{2}}$
B) $\frac{4\sqrt{3}}{3\sqrt{2}}$
C) $\frac{\sqrt{3}}{\sqrt{2}}$
D) $\frac{1}{2}$
Explanation
[Solution] $\rho \propto Z/a^3$. bcc: Z = 2, $a = 4r/\sqrt{3}$; fcc: Z = 4, $a = 2\sqrt{2}r$. Ratio $= \frac{2 \cdot 3\sqrt{3}/64}{4/(16\sqrt{2})} = \frac{3\sqrt{3}}{4\sqrt{2}}$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.