Calculate the number of atoms in 100 , g of a | vedclass

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(B) For an $fcc$ structure, the number of atoms per unit cell, $Z = 4$. Given: Mass $W = 100 \, g$, Density $d = 10 \, g/cm^3$, Edge length $a = 200 \

Vedclass · Accepted Answer

$0.5 	imes 10^{25}$

Vedclass · Answer

(B) For an $fcc$ structure, the number of atoms per unit cell, $Z = 4$. Given: Mass $W = 100 \, g$, Density $d = 10 \, g/cm^3$, Edge length $a = 200 \, pm = 200 	imes 10^{-10} \, cm = 2 	imes 10^{-8} \, cm$. The number of unit cells in $100 \, g$ is given by $N_{unit cells} = \frac{W}{d 	imes a^3}$. $N_{unit cells} = \frac{100}{10 	imes (2 	imes 10^{-8})^3} = \frac{10}{8 	imes 10^{-24}} = 1.25 	imes 10^{24}$. Total number of atoms $= Z 	imes N_{unit cells} = 4 	imes 1.25 	imes 10^{24} = 5 	imes 10^{24} = 0.5 	imes 10^{25}$.

Calculate the number of atoms in $100 \, g$ of a crystal that crystallizes in an $fcc$ structure, given that its density is $10 \, g/cm^3$ and the edge length is $200 \, pm$.

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