Calculate the number of atoms present in 1 g | vedclass

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(D) For an $fcc$ unit cell,the number of atoms per unit cell $(Z)$ is $4$.
The mass of one unit cell is given by the product of density $(\varrho)$ a

Vedclass · Accepted Answer

$5.882 	imes 10^{21}$

Vedclass · Answer

(D) For an $fcc$ unit cell,the number of atoms per unit cell $(Z)$ is $4$.
The mass of one unit cell is given by the product of density $(\varrho)$ and volume $(a^3)$,which is $\varrho 	imes a^3 = \frac{Z 	imes M}{N_A}$.
Given $\varrho 	imes a^3 = 6.8 	imes 10^{-22} \ g$,this represents the mass of one unit cell.
The number of unit cells in $1 \ g$ of the element is $\frac{1 \ g}{6.8 	imes 10^{-22} \ g/	ext{unit cell}} \approx 1.4706 	imes 10^{21} \ 	ext{unit cells}$.
Since each $fcc$ unit cell contains $4$ atoms,the total number of atoms in $1 \ g$ is $4 	imes 1.4706 	imes 10^{21} = 5.8824 	imes 10^{21}$ atoms.
Thus,the correct option is $D$.

Calculate the number of atoms present in $1 \ g$ of an element if it forms an $fcc$ unit cell structure. [ $\varrho \times a^3 = 6.8 \times 10^{-22} \ g$ ]

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