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(C) For a face-centred cubic $(FCC)$ structure, the number of atoms per unit cell $(Z)$ is $4$.The density formula is $d = \frac{Z 	imes M}{N_A 	ime

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$2$

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(C) For a face-centred cubic $(FCC)$ structure, the number of atoms per unit cell $(Z)$ is $4$.The density formula is $d = \frac{Z 	imes M}{N_A 	imes a^3}$, where $a = 400 \ pm = 400 	imes 10^{-10} \ cm$.Substituting the values: $8 = \frac{4 	imes M}{6.022 	imes 10^{23} 	imes (400 	imes 10^{-10})^3}$.Solving for molar mass $(M)$: $M = \frac{8 	imes 6.022 	imes 10^{23} 	imes 64 	imes 10^{-24}}{4} = 77.08 \ g \ mol^{-1}$ (approx $76.8 \ g \ mol^{-1}$ based on standard calculation).Number of moles in $256 \ g$ is $n = \frac{256}{76.8} = 3.33 \ mol$.Number of atoms = $n 	imes N_A 	imes Z$ (since there are $4$ atoms per mole of unit cells, but here we calculate total atoms in the mass).Total atoms = $\frac{256}{76.8} 	imes 6.022 	imes 10^{23} 	imes 1$ (as $M$ is mass per mole of atoms) = $2.007 	imes 10^{24} \ atoms$.Thus, $N = 2$.

$A$ crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of $400 \ pm$. If the density of the substance in the crystal is $8 \ g \ cm^{-3}$, then the number of atoms present in $256 \ g$ of the crystal is $N \times 10^{24}$. The value of $N$ is

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