Aluminium crystallizes in cubic system with unit cell edge length equal to Å. If its density is , th — Solid State Chemistry Question

💡 Solution & Explanation

Let's find $Z$. Density = $\frac{Z \times M}{N_A \times a^3} \implies \frac{45}{16} = \frac{Z \times 27}{6 \times 10^{23} \times 64 \times 10^{-24}} \implies \frac{45}{16} = \frac{27Z}{38.4} \implies Z = \frac{45 \times 38.4}{16 \times 27} = 4$. The lattice is FCC. For FCC, $4r = \sqrt{2}a \implies r = \frac{\sqrt{2} \times 4.0}{4} = \sqrt{2} = 1.414$ Å. Therefore, correct answer is A.