(D) The density $d$ of a unit cell is given by the formula: $d = \frac{Z \times M}{N_{A} \times a^3}$,where $Z$ is the number of atoms per unit cell,$

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(D) The density $d$ of a unit cell is given by the formula: $d = \frac{Z \times M}{N_{A} \times a^3}$,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 $fcc$,$Z = 4$ and $a = 2.0 \ \mathring{A}$.For $bcc$,$Z = 2$ and $a = 2.5 \ \mathring{A}$.The ratio of densities is: $\frac{d_{fcc}}{d_{bcc}} = \frac{4 \times M / (N_{A} \times 2.0^3)}{2 \times M / (N_{A} \times 2.5^3)}$.$\frac{d_{fcc}}{d_{bcc}} = \frac{4}{8} \times \frac{15.625}{1} = 0.5 \times 15.625 = 7.8125$.The nearest integer is $8$.

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

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$A$ metal $M$ crystallizes into two lattices: face-centered cubic $(fcc)$ and body-centered cubic $(bcc)$ with unit cell edge lengths of $2.0 \ \mathring{A}$ and $2.5 \ \mathring{A}$ respectively. The ratio of densities of the $fcc$ lattice to the $bcc$ lattice for the metal $M$ is $...........$ (Nearest integer).

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A
$2$
B
$4$
C
$6$
D
$8$

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Mathematical analysis of cubic system and Bragg’s equation

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Iron crystallizes in different structures. At $911 \, ^oC$,it undergoes a transition from $bcc$ to $fcc$ structure. If the distance between the nearest neighbors is the same in both structures at the transition temperature,the ratio of the densities of $bcc$ and $fcc$ structures will be ..........

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In a $CsCl$ crystal,the interionic distance between $Cs^+$ and $Cl^-$ ions is:

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Iron exhibits $bcc$ structure at room temperature. Above $500^{\circ} C$,it transforms to $fcc$ structure. Find the ratio of the density of iron at room temperature to that at $500^{\circ} C$. (Assume the atomic radii and the molar mass of iron remain constant even with variation in temperature)

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In an ionic compound with a $bcc$ structure, the distance between the two nearest ions is $173 \, pm$. What is the edge length of the unit cell in $pm$?

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An atomic substance $A$ of molar mass $12 \ g \ mol^{-1}$ has a cubic crystal structure with an edge length of $300 \ pm$. The number of atoms present in one unit cell of $A$ is $.....$ (Nearest integer). Given the density of $A$ is $3.0 \ g \ cm^{-3}$ and $N_{A} = 6.02 \times 10^{23} \ mol^{-1}$.

MediumJEE MAIN 2023

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Iron crystallizes in different structures. At $911 \, ^oC$,it undergoes a transition from $bcc$ to $fcc$ structure. If the distance between the nearest neighbors is the same in both structures at the transition temperature,the ratio of the densities of $bcc$ and $fcc$ structures will be ..........

In a $CsCl$ crystal,the interionic distance between $Cs^+$ and $Cl^-$ ions is:

Iron exhibits $bcc$ structure at room temperature. Above $500^{\circ} C$,it transforms to $fcc$ structure. Find the ratio of the density of iron at room temperature to that at $500^{\circ} C$. (Assume the atomic radii and the molar mass of iron remain constant even with variation in temperature)

In an ionic compound with a $bcc$ structure, the distance between the two nearest ions is $173 \, pm$. What is the edge length of the unit cell in $pm$?

An atomic substance $A$ of molar mass $12 \ g \ mol^{-1}$ has a cubic crystal structure with an edge length of $300 \ pm$. The number of atoms present in one unit cell of $A$ is $.....$ (Nearest integer). Given the density of $A$ is $3.0 \ g \ cm^{-3}$ and $N_{A} = 6.02 \times 10^{23} \ mol^{-1}$.

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