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The Solid State — Chemistry STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceChemistryThe Solid State5 Marks
Question
An element has fcc structure with a cell edge 200pm. Calculate the density of element, if $200\ g$ of the element contains $24 \times 1023$ atoms.
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Answer

$a = 200pm \times 10^{-10}cm = 2 \times 10^{-8}cm, z = 4 (for fcc)$,
Mass of unit cell $=\frac{200\times4}{24\times10^{23}}$
$=33.33\times10^{-23}\text{g}$
$\text{Density}=\frac{\text{Masso funitcell}}{\text{Volumeo funticell}}$
$=\frac{33.33\times10^{23}\text{g}}{(2\times10^{8}\text{cm})^3}=41.6\text{g/cm}^{-3}$

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