(A) For a $bcc$ unit cell, the number of atoms per unit cell $Z = 2$. The density formula is given by $d = \frac{Z \times M}{a^3 \times N_A}$. Here, $

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$6.022 \times 10^{23} \,mol^{-1}$

(A) For a $bcc$ unit cell, the number of atoms per unit cell $Z = 2$. The density formula is given by $d = \frac{Z \times M}{a^3 \times N_A}$. Here, $d = 7.874 \,g/cm^3$, $Z = 2$, $M = 55.845 \,g/mol$, and $a = 286.65 \,pm = 286.65 \times 10^{-10} \,cm$. Rearranging for $N_A$: $N_A = \frac{Z \times M}{d \times a^3}$. $N_A = \frac{2 \times 55.845}{7.874 \times (286.65 \times 10^{-10})^3}$. $N_A = \frac{111.69}{7.874 \times 23.556 \times 10^{-24}}$. $N_A \approx 6.022 \times 10^{23} \,mol^{-1}$.

Class 12 Chemistry Solid State Mathematical analysis of cubic system and Bragg’s equation

Easy

$Fe$ crystallizes in a $bcc$ lattice. If the edge length is $286.65 \,pm$ and the density is $7.874 \,g/cm^3$, calculate the Avogadro number. $(Fe = 55.845 \,u)$

A
$6.022 \times 10^{23} \,mol^{-1}$
B
$6.045 \times 10^{23} \,mol^{-1}$
C
$5.980 \times 10^{23} \,mol^{-1}$
D
$6.120 \times 10^{23} \,mol^{-1}$

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Mathematical analysis of cubic system and Bragg’s equation

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The distance between $Na^{+}$ and $Cl^{-}$ ions in solid $NaCl$ of density $2.165 \ g \ cm^{-3}$ is $........ \times 10^{-10} \ m$. (Nearest Integer)
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$Fe$ crystallizes in a $bcc$ lattice. If the edge length is $286.65 \,pm$ and the density is $7.874 \,g/cm^3$, calculate the Avogadro number. $(Fe = 55.845 \,u)$

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Find the molar mass of an element that crystallizes forming a unit cell structure having an edge length of $4 \times 10^{-8} \ cm$ and containing $4$ particles. (Density $\rho = 19.7 \ g \ cm^{-3}$)

$A$ substance has a density of $2 \ g \ cm^{-3}$. It crystallizes in the $fcc$ crystal with an edge length of $600 \ pm$. The molar mass of the substance (in $g \ mol^{-1}$) is $(N_{A} = 6 \times 10^{23} \ mol^{-1})$

Copper crystallises in $fcc$ structure with a unit cell length of $361 \ pm$. What is the radius of copper atom? ............ $pm$

Calculate the number of atoms in $0.3 \ g$ of a metal if it forms a $bcc$ structure,given that $[\rho \times a^3 = 3 \times 10^{-22} \ g]$.

The distance between $Na^{+}$ and $Cl^{-}$ ions in solid $NaCl$ of density $2.165 \ g \ cm^{-3}$ is $........ \times 10^{-10} \ m$. (Nearest Integer)(Given : $N_{A} = 6.02 \times 10^{23} \ mol^{-1}$,Molar mass of $NaCl = 58.5 \ g \ mol^{-1}$)

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$A$ substance has a density of $2 \ g \ cm^{-3}$. It crystallizes in the $fcc$ crystal with an edge length of $600 \ pm$. The molar mass of the substance (in $g \ mol^{-1}$) is
$(N_{A} = 6 \times 10^{23} \ mol^{-1})$

The distance between $Na^{+}$ and $Cl^{-}$ ions in solid $NaCl$ of density $2.165 \ g \ cm^{-3}$ is $........ \times 10^{-10} \ m$. (Nearest Integer)
(Given : $N_{A} = 6.02 \times 10^{23} \ mol^{-1}$,Molar mass of $NaCl = 58.5 \ g \ mol^{-1}$)