The number of atoms in 2.4 g of body-centred | vedclass

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

Question

(C) For a $BCC$ crystal,the number of atoms per unit cell,$Z = 2$.The density formula is $d = \frac{Z 	imes M}{a^3 	imes N_A}$.Given: $d = 10 \ g \

Vedclass · Accepted Answer

$6 	imes 10^{22}$

Vedclass · Answer

(C) For a $BCC$ crystal,the number of atoms per unit cell,$Z = 2$.The density formula is $d = \frac{Z 	imes M}{a^3 	imes N_A}$.Given: $d = 10 \ g \ cm^{-3}$,$a = 200 \ pm = 200 	imes 10^{-10} \ cm = 2 	imes 10^{-8} \ cm$,$N_A = 6 	imes 10^{23} \ mol^{-1}$,$Z = 2$.Calculating molar mass $(M)$:$M = \frac{d 	imes a^3 	imes N_A}{Z} = \frac{10 	imes (2 	imes 10^{-8})^3 	imes 6 	imes 10^{23}}{2} = \frac{10 	imes 8 	imes 10^{-24} 	imes 6 	imes 10^{23}}{2} = 24 \ g \ mol^{-1}$.Number of moles in $2.4 \ g$ = $\frac{2.4 \ g}{24 \ g \ mol^{-1}} = 0.1 \ mol$.Number of atoms = $	ext{moles} 	imes N_A = 0.1 	imes 6 	imes 10^{23} = 6 	imes 10^{22} \ atoms$.

The number of atoms in $2.4 \ g$ of body-centred cubic $(BCC)$ crystal with edge length $200 \ pm$ is (density = $10 \ g \ cm^{-3}$,$N_A = 6 \times 10^{23} \ atoms \ mol^{-1}$)

Similar Questions

The edge length of $fcc$ type unit cell of copper having atomic radius $127.6 \ pm$ is equal to (in $pm$)

An element crystallises in $fcc$ type of unit cell. The volume of one unit cell is $24.99 \times 10^{-24} \ cm^{3}$ and density of the element is $7.2 \ g \ cm^{-3}$. Calculate the number of unit cells in $36 \ g$ of a pure sample of the element.

$NaCl$ has $4$ formula units per unit cell. If the edge length of the unit cell is $0.564 \, nm$,then the density of the crystal is ............ $\text{g/cm}^3$. $(NaCl = 58.5 \, \text{g/mol})$

$A$ metal crystallizes in a $bcc$ unit cell having unit cell volume $2.5 \times 10^{-23} \text{ cm}^3$. Find the number of unit cells in $18 \text{ g}$ of the metal if the density of the metal is $7.2 \text{ g cm}^{-3}$.

The cubic unit cell of aluminium (Molar mass $27.0 \ g \ mol^{-1}$) has an edge length of $405 \ pm$. Its density is $2.70 \ g \ cm^{-3}$. The type of unit cell is

Vedclass Test Series

Exam Paper Generator

Online Exam Module