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A monoatomic solid element crystallises in a cubic system. Its atomic radius is 1.0 Angstrom and the ratio of packing fraction to density is 0.1 cm³/g. If N_A = 6 * 10²³, what is the atomic mass of the element?

1. 8*pi
2. 16*pi
3. 80*pi
4. 4*pi

Correct answer: 8*pi

Solution

For a general cubic structure, packing fraction (PF) = z * (4/3)*pi*r³ / a³, and density rho = z*M / (N_A * a³). So PF/rho = [(4/3)*pi*r³ * N_A] / M. Substituting r = 1e-8 cm and N_A = 6e23: PF/rho = (4/3)*pi*(1e-8)³*6e23 / M = (4/3)*pi*6e-1 / M = 8*pi*10⁻¹ / M. Setting this equal to 0.1: M = 8*pi*10⁻¹ / 0.1 = 8*pi. Wait this gives 8*pi. Let me recheck units.

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