An element occurs in the body-centred cubic ( | vedclass

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

Question

(A) $1$. For a $BCC$ unit cell, the number of atoms per unit cell $(Z)$ is $2$. $2$. The edge length $(a)$ is $288 \ pm = 288 	imes 10^{-10} \ cm$. $

Vedclass · Accepted Answer

$24.2 	imes 10^{23}$

Vedclass · Answer

(A) $1$. For a $BCC$ unit cell, the number of atoms per unit cell $(Z)$ is $2$. $2$. The edge length $(a)$ is $288 \ pm = 288 	imes 10^{-10} \ cm$. $3$. The volume of the unit cell $(V)$ is $a^3 = (288 	imes 10^{-10} \ cm)^3 \approx 2.39 	imes 10^{-23} \ cm^3$. $4$. The density $(ho)$ is given by $ho = \frac{Z 	imes M}{N_A 	imes a^3}$. $5$. Rearranging to find the molar mass $(M)$: $M = \frac{ho 	imes N_A 	imes a^3}{Z} = \frac{7.2 	imes 6.022 	imes 10^{23} 	imes 2.39 	imes 10^{-23}}{2} \approx 51.8 \ g \ mol^{-1}$. $6$. The number of moles in $208 \ g$ is $n = \frac{	ext{mass}}{M} = \frac{208}{51.8} \approx 4.015 \ mol$. $7$. The number of atoms is $n 	imes N_A = 4.015 	imes 6.022 	imes 10^{23} \approx 24.18 	imes 10^{23} \approx 24.2 	imes 10^{23}$.

An element occurs in the body-centred cubic $(BCC)$ structure with an edge length of $288 \ pm$. The density of the element is $7.2 \ g \ cm^{-3}$. The number of atoms present in $208 \ g$ of the element is nearly:

Similar Questions

For a simple cubic system,find the ratio of the interplanar distances between the $(100)$,$(110)$,and $(111)$ planes.

The distance between two parallel $(111)$ planes in a crystal with an edge length of $300 \, pm$ is ................ $pm$.

Calculate the density of a metal having molar mass $197 \ g \ mol^{-1}$ if it forms $fcc$ structure. $\left[a^3 \times N_{A}=40 \ cm^3 \ mol^{-1}\right]$ (in $g \ cm^{-3}$)

Calculate the volume of the unit cell for an element having a molar mass of $92 \ g \ mol^{-1}$ that forms a $bcc$ structure,given $\left[\varrho \times N_{A} = 5.0 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$.

An element $A$ has a face-centred cubic $(fcc)$ structure with an edge length equal to $361 \ pm$. The radius of atom $A$ is ............... $pm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module