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Gold crystallizes with FCC lattice for which the side length of the unit cell is Å. If the density oSolid State Chemistry Question

Question

Gold crystallizes with FCC lattice for which the side length of the unit cell is $5.0$ Å. If the density of gold is $10.5 \text{ g/cm}^3$, the value of Avogadro number is (Au = 198)

Answer: B

💡 Solution & Explanation

Density $d = \frac{Z \times M}{N_A \times a^3} \implies 10.5 = \frac{4 \times 198}{N_A \times (5.0 \times 10^{-8})^3} \implies N_A = \frac{792}{10.5 \times 125 \times 10^{-24}} = \frac{792}{1312.5 \times 10^{-24}} = 6.034 \times 10^{23}$. Therefore, correct answer is B.

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