(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

The edge length of a unit cell of a metal having a molar mass of $75 \ g/mol$ is $5 \ \mathring{A}$. It crystallizes in a cubic lattice. If the density is $2 \ g/cm^3$, find the radius of the metal atom in $pm$. (Given: $N_A = 6 \times 10^{23}$)

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$CsBr$ has $bcc$ structure with edge length $4.3 \ \mathring{A}$. The shortest interionic distance in between $Cs^{+}$ and $Br^{-}$ (in $\mathring{A}$) is :

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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.... $(N_A = 6.02 \times 10^{23} \ mol^{-1})$

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The edge length of a unit cell of a metal having a molar mass of $75 \ g/mol$ is $5 \ \mathring{A}$. It crystallizes in a cubic lattice. If the density is $2 \ g/cm^3$, find the radius of the metal atom in $pm$. (Given: $N_A = 6 \times 10^{23}$)

An ionic compound $X^{+}Y^{-}$ has a $bcc$ structure. The distance between two nearest ions is $1.73 \, \mathring{A}$. What would be the edge length of the unit cell in $pm$?

Calculate the molar mass of an element having density $7.8 \ g \ cm^{-3}$ that forms a $bcc$ unit cell. $\left[a^3 \cdot N_{A} = 16.2 \ cm^3 \ mol^{-1}\right]$

$A$ given metal crystallises out with a cubic structure having edge length of $361 \, pm$. If there are four metal atoms in one unit cell,what is the radius of one atom? .............. $pm$

$CsBr$ has $bcc$ structure with edge length $4.3 \ \mathring{A}$. The shortest interionic distance in between $Cs^{+}$ and $Br^{-}$ (in $\mathring{A}$) is :

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