An element has a bcc structure with a cell ed | vedclass

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

Question

$(A)$ For a $bcc$ unit cell, the number of atoms per unit cell $(n)$ is $2$. The edge length $(a)$ is $288 \ pm = 288 	imes 10^{-10} \ cm = 2.88 	im

Vedclass · Accepted Answer

$51.78 \ g \ mol^{-1}$

Vedclass · Answer

$(A)$ For a $bcc$ unit cell, the number of atoms per unit cell $(n)$ is $2$. The edge length $(a)$ is $288 \ pm = 288 	imes 10^{-10} \ cm = 2.88 	imes 10^{-8} \ cm$. The density formula is $ho = \frac{n 	imes M}{a^{3} 	imes N_{A}}$. Rearranging for molar mass $(M)$: $M = \frac{ho 	imes a^{3} 	imes N_{A}}{n}$. Substituting the values: $M = \frac{7.2 	imes (2.88 	imes 10^{-8})^{3} 	imes 6.022 	imes 10^{23}}{2}$. $M = \frac{7.2 	imes 23.8878 	imes 10^{-24} 	imes 6.022 	imes 10^{23}}{2} \approx \frac{103.56}{2} \approx 51.78 \ g \ mol^{-1}$. Thus, the correct option is $A$.

An element has a $bcc$ structure with a cell edge of $288 \ pm$. The density of the element is $7.2 \ g \ cm^{-3}$. What is the atomic mass of the element?

Similar Questions

An element with atomic mass $100$ has a $bcc$ structure and edge length $400 \, pm$. The density of the element is .............. $g \, cm^{-3}$.

$KF$ has a structure similar to $NaCl$. If the density of the crystal is $2.48 \, g/cm^3$, the distance between $K^+$ and $F^-$ ions will be ............. $pm$. (Atomic masses: $K = 39 \, amu, F = 19 \, amu$)

An element crystallizes in an $fcc$ unit cell structure with an edge length of $200 \, pm$. If $200 \, g$ of the element contains $24 \times 10^{23}$ atoms, what is its density in $g/cm^3$?

An element has a body-centred cubic $(bcc)$ structure with a cell edge of $288 \, pm$. The density of the element is $7.2 \, g/cm^{3}$. How many atoms are present in $208 \, g$ of the element?

How many unit cells are present in $100 \ g$ of an element with $fcc$ crystal structure having density $10 \ g/cm^{3}$ and edge length $100 \ pm$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module