(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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The density of $KBr$ is $2.75 \, g \, cm^{-3}$ and the unit cell edge length is $654 \, pm$. Given the atomic masses $K = 39$ and $Br = 80$, what is the crystal structure of $KBr$?

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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

Nickel crystallises in a $fcc$ type of unit cell,with edge length $0.3524 \ nm$. Calculate the radius of nickel atom. (in $nm$)

An element crystallises in a $bcc$ type of unit cell. The density and edge length of the unit cell are $4 \ g \ cm^{-3}$ and $500 \ pm$ respectively. What is the atomic mass of the element?

Copper crystallises in a $ccp$ arrangement and the accepted value of the metal ion radius was found to be $1.28 \ \mathring{A}$. Calculate the density of copper in grams per cubic centimetre. (Atomic weight of copper is $63.5 \ g/mol$,$N_A = 6.022 \times 10^{23} \ mol^{-1}$) (in $g/cm^3$)

An element crystallises in $bcc$ type having atomic radius $1.33 \times 10^{-8} \ cm$,the edge length of the unit cell will be:

The density of $KBr$ is $2.75 \, g \, cm^{-3}$ and the unit cell edge length is $654 \, pm$. Given the atomic masses $K = 39$ and $Br = 80$, what is the crystal structure of $KBr$?

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