Calculate the number of unit cells in 3 g of | vedclass

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Question

(A) For a simple cubic unit cell, the number of atoms per unit cell, $Z = 1$.The volume of one unit cell, $V = a^3 = (336 	imes 10^{-10} \ cm)^3 = 3.

Vedclass · Accepted Answer

$8.41 	imes 10^{21}$

Vedclass · Answer

(A) For a simple cubic unit cell, the number of atoms per unit cell, $Z = 1$.The volume of one unit cell, $V = a^3 = (336 	imes 10^{-10} \ cm)^3 = 3.793 	imes 10^{-23} \ cm^3$.The mass of one unit cell is given by $m_{uc} = 	ext{Density} 	imes 	ext{Volume} = 9.4 \ g \ cm^{-3} 	imes 3.793 	imes 10^{-23} \ cm^3 = 3.565 	imes 10^{-22} \ g$.The number of unit cells in $3 \ g$ of metal is calculated as $\frac{	ext{Total mass}}{	ext{Mass of one unit cell}} = \frac{3 \ g}{3.565 	imes 10^{-22} \ g} \approx 8.41 	imes 10^{21}$.

Calculate the number of unit cells in $3 \ g$ of a metal that crystallises in a simple cubic unit cell with an edge length of $336 \ pm$. (Density of metal $= 9.4 \ g \ cm^{-3}$)

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