The edge lengths of a simple cubic (sc) and a | vedclass

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(B) For a simple cubic $(sc)$ unit cell: Number of atoms $(Z_1)$ = $1$,and edge length $a = 2r_1$,so $r_1 = a/2$.Volume occupied by atoms = $Z_1 	ime

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$\sqrt{2}:2$

Vedclass · Answer

(B) For a simple cubic $(sc)$ unit cell: Number of atoms $(Z_1)$ = $1$,and edge length $a = 2r_1$,so $r_1 = a/2$.Volume occupied by atoms = $Z_1 	imes \frac{4}{3} \pi r_1^3 = 1 	imes \frac{4}{3} \pi (a/2)^3 = \frac{4}{3} \pi \frac{a^3}{8} = \frac{\pi a^3}{6}$.For a face-centered cubic $(fcc)$ unit cell: Number of atoms $(Z_2)$ = $4$,and edge length $a = 2\sqrt{2}r_2$,so $r_2 = a/(2\sqrt{2})$.Volume occupied by atoms = $Z_2 	imes \frac{4}{3} \pi r_2^3 = 4 	imes \frac{4}{3} \pi (a/(2\sqrt{2}))^3 = \frac{16}{3} \pi \frac{a^3}{16\sqrt{2}} = \frac{\pi a^3}{3\sqrt{2}}$.Ratio of volume occupied = $\frac{	ext{Volume}_{sc}}{	ext{Volume}_{fcc}} = \frac{\pi a^3 / 6}{\pi a^3 / (3\sqrt{2})} = \frac{3\sqrt{2}}{6} = \frac{\sqrt{2}}{2}$.

The edge lengths of a simple cubic $(sc)$ and a face-centered cubic $(fcc)$ unit cell are equal. The ratio of the volume occupied by atoms in these two structures is .....

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