The ratio of densities if the same element un | vedclass

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(A) The density of a unit cell is given by the formula: $ho = \frac{Z 	imes M}{N_A 	imes a^3}$.For both $FCC$ (Face-Centered Cubic) and $HCP$ (Hex

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$1$

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(A) The density of a unit cell is given by the formula: $ho = \frac{Z 	imes M}{N_A 	imes a^3}$.For both $FCC$ (Face-Centered Cubic) and $HCP$ (Hexagonal Close Packing),the coordination number is $12$ and the packing efficiency is the same,which is $74\%$.Since the element is the same,the molar mass $(M)$ and Avogadro's number $(N_A)$ are constant.For $FCC$,the number of atoms per unit cell $(Z)$ is $4$ and the edge length $(a)$ is $2\sqrt{2}r$.For $HCP$,the number of atoms per unit cell $(Z)$ is $6$,the height $(h)$ is $4\sqrt{2/3}r$,and the base area is $6\sqrt{3}r^2$.In both structures,the atoms occupy the same volume fraction of the space. Because the packing efficiency is identical for both $FCC$ and $HCP$ $(74\%)$,the density of the crystal lattice formed by the same element in both arrangements will be identical.Therefore,the ratio of densities is $1:1$ or $1$.

The ratio of densities if the same element undergoes $FCC$ and $HCP$ close packing is:

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