What is the percentage efficiency of packing | vedclass

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

Question

(D) Packing efficiency is defined as the fraction of the total volume of the unit cell occupied by the atoms.For a $BCC$ (Body-Centered Cubic) structu

Vedclass · Accepted Answer

$68$

Vedclass · Answer

(D) Packing efficiency is defined as the fraction of the total volume of the unit cell occupied by the atoms.For a $BCC$ (Body-Centered Cubic) structure:$1$. The number of atoms per unit cell $(z)$ is $2$.$2$. The relationship between the edge length $(a)$ and the atomic radius $(r)$ is $r = \frac{\sqrt{3}a}{4}$,or $a = \frac{4r}{\sqrt{3}}$.$3$. The volume of the unit cell $(V)$ is $a^3 = (\frac{4r}{\sqrt{3}})^3 = \frac{64r^3}{3\sqrt{3}}$.$4$. The volume occupied by $2$ atoms is $2 	imes \frac{4}{3} \pi r^3 = \frac{8}{3} \pi r^3$.$5$. Packing efficiency = $\frac{	ext{Volume of atoms}}{	ext{Volume of unit cell}} 	imes 100 = \frac{\frac{8}{3} \pi r^3}{\frac{64r^3}{3\sqrt{3}}} 	imes 100 = \frac{\sqrt{3} \pi}{8} 	imes 100 \approx 0.68 	imes 100 = 68 \%$.

What is the percentage efficiency of packing in $BCC$ structure (in $\%$)?

Similar Questions

An ionic compound is formed between a metal $M$ and a non-metal $Y$. If $M$ occupies half the octahedral voids in the cubic close-packed arrangement formed by $Y$,the chemical formula of the ionic compound is

$A$ crystalline solid is made of $X$,$Y$ and $Z$ elements. Atoms of $X$ form $FCC$ packing; atoms of $Y$ occupy octahedral voids while atoms of $Z$ occupy tetrahedral voids. What will be the simplest formula of the solid if atoms along one body diagonal are removed?

The correct option for the number of tetrahedral and octahedral voids in a hexagonal primitive unit cell is:

If $Z$ is the number of atoms in the unit cell that represents the closest packing sequence $ABCABC .....,$ the number of tetrahedral voids in the unit cell is

If the number of atoms in a unit cell is $2$,then the number of tetrahedral and octahedral voids will be ....... and ....... respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module