Copper crystallizes in an fcc lattice with an | vedclass

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(A) For an $fcc$ unit cell,the number of atoms per unit cell $(n)$ is $4$. Edge length $(a)$ = $3.61 	imes 10^{-8} \, cm$. Atomic mass of $Cu$ $(M_w)

Vedclass · Accepted Answer

$8.96$

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(A) For an $fcc$ unit cell,the number of atoms per unit cell $(n)$ is $4$. Edge length $(a)$ = $3.61 	imes 10^{-8} \, cm$. Atomic mass of $Cu$ $(M_w)$ = $63.5 \, g \, mol^{-1}$. Avogadro's number $(N_A)$ = $6.023 	imes 10^{23} \, mol^{-1}$. Density $(d)$ = $\frac{n 	imes M_w}{a^3 	imes N_A}$. $d = \frac{4 	imes 63.5}{(3.61 	imes 10^{-8})^3 	imes 6.023 	imes 10^{23}}$. $d = \frac{254}{47.0458 	imes 10^{-24} 	imes 6.023 	imes 10^{23}}$. $d = \frac{254}{28.339} \approx 8.96 \, g \, cm^{-3}$.

Copper crystallizes in an $fcc$ lattice with an edge length of $3.61 \times 10^{-8} \, cm$. If the measured density is $8.92 \, g \, cm^{-3}$,calculate the theoretical density of the crystal in $g \, cm^{-3}$. (Atomic mass of $Cu = 63.5 \, g \, mol^{-1}$)

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