(D) The formula for density is $d = \frac{Z \times M}{a^3 \times N_{A}}$.For a $bcc$ structure, the number of atoms per unit cell $Z = 2$.The edge len

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(D) The formula for density is $d = \frac{Z \times M}{a^3 \times N_{A}}$.For a $bcc$ structure, the number of atoms per unit cell $Z = 2$.The edge length $a = 288 \ pm = 2.88 \times 10^{-8} \ cm$.The Avogadro constant $N_{A} = 6.022 \times 10^{23} \ mol^{-1}$.Substituting the values: $7.8 = \frac{2 \times M}{(2.88 \times 10^{-8} \ cm)^3 \times 6.022 \times 10^{23} \ mol^{-1}}$.$M = \frac{7.8 \times (2.88 \times 10^{-8})^3 \times 6.022 \times 10^{23}}{2}$.$M \approx 56.1 \ g \ mol^{-1}$.

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

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Calculate the molar mass of a metal having a density of $7.8 \ g \ cm^{-3}$ that crystallizes in a $bcc$ structure with an edge length of $288 \ pm$.

MHT CET 2022 All MHT CET

A
$120.0 \ g \ mol^{-1}$
B
$86.2 \ g \ mol^{-1}$
C
$108.1 \ g \ mol^{-1}$
D
$56.1 \ g \ mol^{-1}$

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Mathematical analysis of cubic system and Bragg’s equation

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$A$ substance has a density of $2 \ g \ cm^{-3}$. It crystallizes in the $fcc$ crystal with an edge length of $600 \ pm$. The molar mass of the substance (in $g \ mol^{-1}$) is
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$A$ metal has a cubic lattice of side length $2.88 \, \mathring{A}$. The density of the metal is $7.2 \, g/cm^3$. How many unit cells are present in $7.2 \, mg$ of the metal?

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An element having an atomic radius of $0.14 \ nm$ crystallizes in an $fcc$ unit cell. What is the length of a side of the cell in $nm$?

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Derive the expression for the density $(d)$ of a unit cell: $d = \frac{zM}{a^3 N_A}$.

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Calculate the molar mass of a metal having a density of $7.8 \ g \ cm^{-3}$ that crystallizes in a $bcc$ structure with an edge length of $288 \ pm$.

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$A$ substance has a density of $2 \ g \ cm^{-3}$. It crystallizes in the $fcc$ crystal with an edge length of $600 \ pm$. The molar mass of the substance (in $g \ mol^{-1}$) is $(N_{A} = 6 \times 10^{23} \ mol^{-1})$

Calculate the number of unit cells present in $1 \text{ g}$ of a metal if the product of the density of the metal and the volume of the unit cell is $2.5 \times 10^{-22} \text{ g}$.

$A$ metal has a cubic lattice of side length $2.88 \, \mathring{A}$. The density of the metal is $7.2 \, g/cm^3$. How many unit cells are present in $7.2 \, mg$ of the metal?

An element having an atomic radius of $0.14 \ nm$ crystallizes in an $fcc$ unit cell. What is the length of a side of the cell in $nm$?

Derive the expression for the density $(d)$ of a unit cell: $d = \frac{zM}{a^3 N_A}$.

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$A$ substance has a density of $2 \ g \ cm^{-3}$. It crystallizes in the $fcc$ crystal with an edge length of $600 \ pm$. The molar mass of the substance (in $g \ mol^{-1}$) is
$(N_{A} = 6 \times 10^{23} \ mol^{-1})$