[\dfrac{3\sqrt{3}}{4\sqrt...] Iron exhibits bcc structure at room temperature. Above 900°C, it transforms to fcc structure. The ra

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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

$\dfrac{3\sqrt{3}}{4\sqrt{2}}$

$\dfrac{4\sqrt{3}}{3\sqrt{2}}$

$\dfrac{\sqrt{3}}{\sqrt{2}}$

$\dfrac{1}{2}$

Explanation:

For BCC lattice : Z = 2, $a=\dfrac{4r}{\sqrt 3}$
For FCC lattice : Z = 4, $a=2\sqrt{2}r$
∴$\dfrac{d_{25^°c}}{d_{900^°c}}=\dfrac{\left(\dfrac{ZM}{N_Aa^3}\right)_{BCC}}{\left(\dfrac{ZM}{N_Aa^3}\right)_{FCC}}$
$\dfrac{2}{4}\left(\dfrac{2\sqrt{2}r}{\dfrac{4r}{\sqrt{3}}}\right)^3$
$\left(\dfrac{3\sqrt{3}}{4\sqrt{2}}\right)$

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