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Density of a unit cell is represented as
\( \rho=\frac{\text { Effective no. of atom }(\mathrm{s}) \times \text { Atomic mass } / \text { formula mass }}{\text { Volume of a unit cell }}=\frac{Z \cdot M}{N_{A} \cdot a^{3}} \)
where, mass of unit cell = mass of effective no. of atom(s) or ion(s).
\( M= \) At. mass/formula mass
\( \begin{aligned} N_{A} &=\text { Avogadro's no. } \Rightarrow 6.023 \times 10^{23} \\ a &=\text { edge length of unit cell } \end{aligned} \)
An element crystallizes in a structure having fcc unit cell of an edge \( 200 \mathrm{pm} \). Calculate the density, if \( 100 \mathrm{~g} \) of this element contains \( 12 \times 10^{23} \) atoms:
(a) \( 41.66 \mathrm{~g} / \mathrm{cm}^{3} \)
(b) \( 4.166 \mathrm{~g} / \mathrm{cm}^{3} \)
(c) \( 10.25 \mathrm{~g} / \mathrm{cm}^{3} \)
(d) \( 1.025 \mathrm{~g} / \mathrm{cm}^{3} \)
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