(A) For an $FCC$ unit cell,the number of atoms per unit cell $(n)$ is $4$. Density formula: $\rho = \frac{n \times M}{a^3 \times N_A}$ Rearranging for

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(A) For an $FCC$ unit cell,the number of atoms per unit cell $(n)$ is $4$. Density formula: $\rho = \frac{n \times M}{a^3 \times N_A}$ Rearranging for edge length $(a)$: $a^3 = \frac{n \times M}{\rho \times N_A} = \frac{4 \times 60 \ g \ mol^{-1}}{6.23 \ g \ cm^{-3} \times 6.02 \times 10^{23} \ mol^{-1}}$ $a^3 = \frac{240}{37.5046 \times 10^{23}} \ cm^3$ $a^3 \approx 6.4 \times 10^{-23} \ cm^3 = 64 \times 10^{-24} \ cm^3$ Taking the cube root: $a = \sqrt[3]{64 \times 10^{-24}} \ cm = 4.0 \times 10^{-8} \ cm$.

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

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An element (atomic mass $= 60$) has a face-centered cubic $(FCC)$ structure with a density of $6.23 \ g \ cm^{-3}$. The edge length of the unit cell is.... $(N_A = 6.02 \times 10^{23} \ mol^{-1})$

A
$4.0 \times 10^{-8} \ cm$
B
$4.9 \times 10^{-8} \ cm$
C
$5.3 \times 10^{-8} \ cm$
D
$4.4 \times 10^{-8} \ cm$

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Mathematical analysis of cubic system and Bragg’s equation

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An element (atomic mass $= 60$) has a face-centered cubic $(FCC)$ structure with a density of $6.23 \ g \ cm^{-3}$. The edge length of the unit cell is.... $(N_A = 6.02 \times 10^{23} \ mol^{-1})$

Similar Questions

Gold crystallizes in an $fcc$ unit cell with an edge length of $408 \text{ pm}$. What is the radius of the gold atom (in $\text{ pm}$)?

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

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 ..........

The radius of $K^{+}$ is $133 \ pm$ and that of $Cl^{-}$ is $181 \ pm$. The volume of the unit cell of $KCl$ expressed in $10^{-22} \ cm^{3}$ is

Calculate the density of a metal having a unit cell volume of $64 \times 10^{-24} \ cm^3$ and a molar mass of $192 \ g \ mol^{-1}$,containing $4$ particles per unit cell. (in $g \ cm^{-3}$)

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