-form of iron exists in BCC form and -form of iron exists in FCC structure. Assuming that the distan — Solid State Chemistry Question

💡 Solution & Explanation

Let nearest neighbour distance be $2r$. For BCC ($\alpha$), $a_\alpha = \frac{4r}{\sqrt{3}}$. For FCC ($\gamma$), $a_\gamma = \frac{4r}{\sqrt{2}}$. Ratio of densities $\frac{\rho_\gamma}{\rho_\alpha} = \left(\frac{Z_\gamma}{Z_\alpha}\right) \times \left(\frac{a_\alpha}{a_\gamma}\right)^3 = \left(\frac{4}{2}\right) \times \left(\frac{4r / \sqrt{3}}{4r / \sqrt{2}}\right)^3 = 2 \times \left(\frac{\sqrt{2}}{\sqrt{3}}\right)^3 = \frac{4\sqrt{2}}{3\sqrt{3}}$. Therefore, correct answer is A.