Calcium crystallises in a face-centred cubic | vedclass

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(A) The density of a crystal is given by the formula $d = \frac{Z 	imes M}{N_A 	imes a^3}$.For a face-centred cubic $(FCC)$ unit cell,the number of

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$1.55$

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(A) The density of a crystal is given by the formula $d = \frac{Z 	imes M}{N_A 	imes a^3}$.For a face-centred cubic $(FCC)$ unit cell,the number of atoms per unit cell $Z = 4$.The molar mass of Calcium $(Ca)$ is $M = 40 \ g \ mol^{-1}$.The edge length $a = 0.556 \ nm = 0.556 	imes 10^{-7} \ cm$.Frenkel defects involve the migration of ions into interstitial sites,which does not change the mass or the volume of the unit cell; therefore,the theoretical density remains unchanged.Substituting the values: $d = \frac{4 	imes 40}{6.022 	imes 10^{23} 	imes (0.556 	imes 10^{-7})^3}$.$d = \frac{160}{6.022 	imes 10^{23} 	imes 1.719 	imes 10^{-22}} \approx 1.55 \ g \ cm^{-3}$.

Calcium crystallises in a face-centred cubic unit cell with edge length $a = 0.556 \ nm$. Calculate the density. If it contained $0.1 \%$ Frenkel defects,what is the density in $g \ cm^{-3}$?

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