What is the percentage of space occupied in a | vedclass

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

Question

(C) In a $bcc$ (body-centered cubic) unit cell,the number of atoms per unit cell $(n)$ is $2$.The packing efficiency $(P.E.)$ is calculated using the

Vedclass · Accepted Answer

$68$

Vedclass · Answer

(C) In a $bcc$ (body-centered cubic) unit cell,the number of atoms per unit cell $(n)$ is $2$.The packing efficiency $(P.E.)$ is calculated using the formula:$P.E. = \frac{n 	imes \frac{4}{3}\pi r^3}{a^3}$For $bcc$,the relation between edge length $(a)$ and radius $(r)$ is $r = \frac{\sqrt{3}a}{4}$,which implies $a = \frac{4r}{\sqrt{3}}$.Substituting the values:$P.E. = \frac{2 	imes \frac{4}{3}\pi r^3}{(\frac{4r}{\sqrt{3}})^3} = \frac{\frac{8}{3}\pi r^3}{\frac{64r^3}{3\sqrt{3}}} = \frac{8\pi}{3} 	imes \frac{3\sqrt{3}}{64} = \frac{\sqrt{3}\pi}{8}$$P.E. \approx 0.68$ or $68\%$.

What is the percentage of space occupied in a $bcc$ arrangement (in $\%$)?

Similar Questions

Calculate the volume occupied by all particles in an $fcc$ unit cell if the volume of the unit cell is $1.6 \times 10^{-23} \ cm^3$.

$A$ two-dimensional solid pattern formed by two different atoms $X$ and $Y$ is shown below. The black and white squares represent atoms $X$ and $Y,$ respectively. The simplest formula for the compound based on the unit cell from the pattern is

How will you distinguish between the following pairs of terms:
$(iii)$ Tetrahedral void and octahedral void?

How much part of an atom occupies each corner of a $bcc$ unit cell?

In a compound formed by atoms $A$ and $B$, atoms $A$ form a cubic close-packed $(CCP)$ structure, while atoms $B$ are located at the center of each edge. If the edge length of the cubic unit cell is $115 \ pm$, the distance of atom $A$ from the center of the cube is .......... $pm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module