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Q)

A metallic element has a cubic lattice .Each edge of the unit cell is $2A^{\large\circ}$.The density of the metal is $2.5gcm^{-3}$.The unit cells in 200g of the metal are ?

$\begin{array}{1 1}1\times 10^{25}\\2\times 10^{15}\\3\times 10^{25}\\4\times 10^{25}\end{array} $

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A)
Edge length of the unit cell =$2A^{\large\circ}=2\times 10^{-8}cm$
Volume of the unit cell =$(2\times 10^{-8})^3cm^3$
$\Rightarrow 8\times 10^{-24}cm^3$
Mass of the unit cell =Volume $\times$ density
$\Rightarrow 8\times 10^{-24}\times 2.5g$
No. of unit cells in 200g of the metal =$\large\frac{\text{Mass of meta}}{\text{Mass of unit cell}}$
$\Rightarrow \large\frac{200}{8\times 10^{-24}\times 2.5}$
$\Rightarrow 1\times 10^{25}$
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