Question

Iron crystallizes in several modifications. At about 911°C, the bcc ‘a’ form undergoes a transition to the ‘\(\gamma\)’ form. If the distance between the two nearest neighbors is the same in the two forms at the transition temperature, the ratio of the density of iron in \( \text{ferrite} (\rho_1) \) to that of iron in \( \text{austenite} (\rho_2) \) at the transition temperature is

• 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. \( \frac{\rho_1}{\rho_2} = 0.318 \)

Hint:

The density of a substance is inversely related to the volume of the unit cell.

Answer 1

The Correct Option is A

Step 1: Use the relationship between density and atomic packing.
The density of a substance is inversely proportional to the volume of the unit cell. Since the number of atoms and the size of the unit cell remain constant, we calculate the ratio of the densities at the transition temperature.
Step 2: Conclusion.
Thus, the ratio of densities is \( 0.918 \).
Final Answer: \[ \boxed{\frac{\rho_1}{\rho_2} = 0.918} \]