When sodium is heated above 1000 K,its cryst | vedclass

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(B) The packing fraction $(PF)$ of a crystal structure is defined as the fraction of the total volume occupied by the atoms.For $bcc$,$Z_1 = 2$ and $4

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$0.91$

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(B) The packing fraction $(PF)$ of a crystal structure is defined as the fraction of the total volume occupied by the atoms.For $bcc$,$Z_1 = 2$ and $4r = \sqrt{3}a_1$,so $PF_{bcc} = \frac{2 	imes \frac{4}{3} \pi r^3}{a_1^3} = \frac{2 	imes \frac{4}{3} \pi r^3}{(4r/\sqrt{3})^3} = \frac{\sqrt{3}\pi}{8} \approx 0.68$.For $fcc$,$Z_2 = 4$ and $4r = \sqrt{2}a_2$,so $PF_{fcc} = \frac{4 	imes \frac{4}{3} \pi r^3}{a_2^3} = \frac{4 	imes \frac{4}{3} \pi r^3}{(4r/\sqrt{2})^3} = \frac{\pi}{3\sqrt{2}} \approx 0.74$.The ratio of the fraction of volume occupied is $\frac{PF_{bcc}}{PF_{fcc}} = \frac{\sqrt{3}\pi / 8}{\pi / (3\sqrt{2})} = \frac{3\sqrt{6}}{8} = \frac{3 	imes 2.449}{8} = \frac{7.347}{8} \approx 0.918 \approx 0.91$.

When sodium is heated above $1000 \ K$,its crystal structure changes from $bcc$ to $fcc$. Assuming the metallic radius of the atom remains unchanged,the ratio of the fraction of volume occupied by atoms in $bcc$ and $fcc$ structures will be .......

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