A metal crystallizes in both fcc and bcc latt | vedclass

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

Question

(C) The density $d$ of a unit cell is given by $d = \frac{Z 	imes M}{N_A 	imes a^3}$, where $Z$ is the number of atoms per unit cell, $M$ is the mol

Vedclass · Accepted Answer

$1.01$

Vedclass · Answer

(C) The density $d$ of a unit cell is given by $d = \frac{Z 	imes M}{N_A 	imes a^3}$, where $Z$ is the number of atoms per unit cell, $M$ is the molar mass, $N_A$ is Avogadro's number, and $a$ is the edge length. For $bcc$, $Z_1 = 2$ and $a_1 = 300 \ pm$. For $fcc$, $Z_2 = 4$ and $a_2 = 380 \ pm$. The ratio of densities is $\frac{d_{bcc}}{d_{fcc}} = \frac{Z_1}{Z_2} 	imes \left(\frac{a_2}{a_1}ight)^3$. Substituting the values: $\frac{d_{bcc}}{d_{fcc}} = \frac{2}{4} 	imes \left(\frac{380}{300}ight)^3 = 0.5 	imes (1.266)^3$. $\frac{d_{bcc}}{d_{fcc}} = 0.5 	imes 2.03 = 1.015 \approx 1.01$.

$A$ metal crystallizes in both $fcc$ and $bcc$ lattice structures with unit cell edge lengths of $380 \ pm$ and $300 \ pm$ respectively. The ratio of their densities $(bcc/fcc)$ is:

Similar Questions

An element has an $fcc$ structure. If its edge length is $200 \, pm$, calculate the density of this element having a mass of $200 \, g$. $[200 \, g$ of the element contains $24 \times 10^{23}$ atoms.$]$

$A$ metal has a $fcc$ lattice. The edge length of the unit cell is $404 \, pm$. The density of the metal is $2.72 \, g \, cm^{-3}$. The molar mass of the metal is :- ............ $g \, mol^{-1}$ ( $N_A$ Avogadro constant $= 6.02 \times 10^{23} \, mol^{-1}$ )

What is the number of unit cells present in $3.9 \ g$ of potassium if it crystallizes in $BCC$ structure?

The crystal of $CsBr$ has an edge length of $437 \ pm$. If the density of the crystal is $4.24 \ g \ cm^{-3}$, determine the type of crystal structure of $CsBr$ (Atomic mass of $Cs = 133, Br = 80$).

An element (atomic mass $100 \ g/mol$) having $bcc$ structure has unit cell edge $400 \ pm$. Then density of the element is (in $g/cm^3$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module