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Lead has a density of 11.34 g/cm³ and crystallizes in a face-centred cubic lattice. Given atomic weight of Pb = 207 g/mol, which of the following statements 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

For FCC: Z = 4. V_cell = Z*M/(NA*d) = 4*207/(6.022e23*11.34) = 828/6.829e24 = 1.213e-22 cm³ (option A is correct). Edge length a = (V)^(1/3) = (1.213e-22)^(1/3) ≈ 4.95e-8 cm = 495 pm. Atomic radius r = a/(2*sqrt(2)) = 495/(2*1.414) ≈ 175 pm (option C is also correct). This is a multiple-correct question with answers A and C.

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