The ratio of densities if the same element un | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(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:

Similar Questions

Hexagonal close packed arrangement of ions is described as

Calculate the void volume of a simple cubic unit cell if the volume of the unit cell is $5.5 \times 10^{-22} \ cm^3$.

How will you distinguish between the following pairs of terms:
$(i)$ Hexagonal close-packing $(hcp)$ and cubic close-packing $(ccp)$?

Calculate the volume occupied by a particle in $bcc$ unit cell if the volume of unit cell is $8.2 \times 10^{-23} \ cm^3$.

In a $ccp$ structure of $X$ atoms,$Y$ atoms occupy half of the octahedral voids. If one $X$ atom and one $Y$ atom in each unit cell are replaced by a $Z$ atom,the molecular formula of the solid will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module