(A) For a $bcc$ structure, the number of atoms per unit cell, $Z = 2$. Given: $a = 287 \, pm = 287 \times 10^{-10} \, cm = 2.87 \times 10^{-8} \, cm$.

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(A) For a $bcc$ structure, the number of atoms per unit cell, $Z = 2$. Given: $a = 287 \, pm = 287 \times 10^{-10} \, cm = 2.87 \times 10^{-8} \, cm$. Atomic mass of $Cr$, $M = 51.99 \, \text{g/mol} \approx 52 \, \text{g/mol}$. Avogadro's number, $N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}$. Density $d = \frac{Z \times M}{N_A \times a^3}$. $d = \frac{2 \times 52}{(6.022 \times 10^{23}) \times (2.87 \times 10^{-8})^3}$. $d = \frac{104}{14.236} \approx 7.305 \, \text{g/cm}^3$.

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

Medium

For a $Cr$ crystal crystallizing in a $bcc$ structure, the edge length of the unit cell is $287 \, pm$. What is the density of the crystal in $\text{g/cm}^3$? $(Cr = 51.99 \, \text{g/mol})$

A
$7.3$
B
$14.6$
C
$3.65$
D
$7.3 \times 10^7$

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Mathematical analysis of cubic system and Bragg’s equation

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If the edge length of the unit cell of an element crystallizing in a $bcc$ structure is $400 \, pm$, then the density of the crystal will be ............ $\text{g/cm}^3$. (Atomic weight $= 100 \, \text{g/mol}$)

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For a $Cr$ crystal crystallizing in a $bcc$ structure, the edge length of the unit cell is $287 \, pm$. What is the density of the crystal in $\text{g/cm}^3$? $(Cr = 51.99 \, \text{g/mol})$

Similar Questions

Calculate the edge length of a simple cubic unit cell if the radius of an atom is $167.3 \ pm$. (in $pm$)

If an element having atomic number $96$ crystallises in a cubic lattice with a density of $10.3 \ g \ cm^{-3}$ and an edge length of $314 \ pm$, then the structure of the solid is:

An element has a $bcc$ structure with a cell edge of $288 \ pm$. The density of the element is $7.2 \ g \ cm^{-3}$. What is the atomic mass of the element?

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