(C) The effective number of atoms in an $fcc$ unit cell is $Z = 4$. The formula for density is $d = \frac{Z \times M}{N_{A} \times a^3}$. Given: $d =

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(C) The effective number of atoms in an $fcc$ unit cell is $Z = 4$. The formula for density is $d = \frac{Z \times M}{N_{A} \times a^3}$. Given: $d = 11.21 \ g \ cm^{-3}$,$a = 4 \ \mathring{A} = 4 \times 10^{-8} \ cm$,$N_{A} = 6.023 \times 10^{23} \ mol^{-1}$. Rearranging for molar mass $(M)$: $M = \frac{d \times N_{A} \times a^3}{Z}$. $M = \frac{11.21 \times 6.023 \times 10^{23} \times (4 \times 10^{-8})^3}{4}$. $M = \frac{11.21 \times 6.023 \times 10^{23} \times 64 \times 10^{-24}}{4}$. $M = 11.21 \times 6.023 \times 16 \times 0.1 = 108.0 \ g \ mol^{-1}$.

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

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The crystal structure of an element has an $fcc$ lattice. If the edge length of the crystal is $4 \ \mathring{A}$,what is the atomic weight (in $g \ mol^{-1}$) of the element,if the density of the crystal is $11.21 \ g \ cm^{-3}$ $(N_{A} = 6.023 \times 10^{23} \ mol^{-1})$?

AP EAMCET 2022 All AP EAMCET

A
$63.5$
B
$85.5$
C
$108.0$
D
$197.0$

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Mathematical analysis of cubic system and Bragg’s equation

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The crystal structure of an element has an $fcc$ lattice. If the edge length of the crystal is $4 \ \mathring{A}$,what is the atomic weight (in $g \ mol^{-1}$) of the element,if the density of the crystal is $11.21 \ g \ cm^{-3}$ $(N_{A} = 6.023 \times 10^{23} \ mol^{-1})$?

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Calculate the density of a metal with molar mass $56 \ g \ mol^{-1}$ that crystallises in a $bcc$ structure with an edge length of $288 \ pm$. (in $g \ cm^{-3}$)

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