Iron transforms from fcc ( $a = 364 pm$ ) to bcc ( $a = 285 pm$ ) on cooling, the unit cell edges being measured at the same temperature for the two forms. Find the ratio $ρ_{bcc} / ρ_{fcc}$ (two decimals).

Numerical answer type, tolerance 0.01.

Answer: 1.04

Same element, so

M

cancels and

ρ \propto Z / a^{3}

\frac{ρ _{b cc}}{ρ _{f cc}} = \frac{2/28 5 ^{3}}{4/36 4 ^{3}} = \frac{1}{2} (\frac{364}{285})^{3} = \frac{1}{2} \times 2.0834 = 1.04