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Lead metal has a density of 11.34 g/cm³ and crystallises in a face-centred cubic (FCC) lattice. (Molar mass of Pb = 207.2 g/mol, NA = 6.022 * 10²³) Which of the following alternatives are correct?

1. The volume of one unit cell is 1.214 * 10⁻²² cm³
2. The volume of one unit cell is 1.214 * 10⁻¹⁹ cm³
3. The atomic radius of lead is 175 pm
4. The atomic radius of lead is 155.1 pm

Correct answer: The volume of one unit cell is 1.214 * 10⁻²² cm³

Solution

Volume of unit cell V = 4 * 207.2 / (6.022*10²³ * 11.34) = 828.8 / (6.829*10²⁴) = 1.214*10⁻²² cm³. Edge length a = (1.214*10⁻²²)^(1/3) = 4.950*10⁻⁸ cm = 495 pm. Atomic radius r = a*sqrt(2)/4 = 495*1.414/4 ≈ 175 pm.

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