If the density of a gold (Au) crystal crystal | vedclass

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(B) For a $ccp$ structure,the number of atoms per unit cell $Z = 4$. Density $d = \frac{Z 	imes M}{N_A 	imes a^3}$,where $M = 197 \, g/mol$ and $N_A

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$1.439 	imes 10^{-8} \, cm$

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(B) For a $ccp$ structure,the number of atoms per unit cell $Z = 4$. Density $d = \frac{Z 	imes M}{N_A 	imes a^3}$,where $M = 197 \, g/mol$ and $N_A = 6.022 	imes 10^{23} \, mol^{-1}$. $a^3 = \frac{Z 	imes M}{d 	imes N_A} = \frac{4 	imes 197}{19.3 	imes 6.022 	imes 10^{23}} = \frac{788}{116.22 	imes 10^{23}} \approx 6.78 	imes 10^{-23} \, cm^3 = 67.8 	imes 10^{-24} \, cm^3$. $a = \sqrt[3]{67.8 	imes 10^{-24}} \approx 4.078 	imes 10^{-8} \, cm$. For $ccp$ structure,$4r = \sqrt{2}a$,so $r = \frac{\sqrt{2} 	imes a}{4} = \frac{1.414 	imes 4.078 	imes 10^{-8}}{4} \approx 1.44 	imes 10^{-8} \, cm$.

If the density of a gold $(Au)$ crystal crystallizing in a $ccp$ structure is $19.3 \, g/cm^3$,what will be the radius of the atom? (Given: $Au = 197 \, amu$)

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