[Olympiad] A metal crystallizes in a body-centered cubic (BCC) lattice. If the unit cell edge length is 300 pm and the density is 10.0 g/cm³, what is the approximate atomic mass of the metal?
- 40 g/mol
- 81 g/mol
- 120 g/mol
- 162 g/mol
📝 Detailed explanation
Density = (Z × M) / (Nₐ × a³). For BCC, Z=2.M = (Density × Nₐ × a³) / Z = (10 × 6.022 × 10²³ × (3 × 10⁻⁸)³) / 2
M = (10 × 6.022 × 10²³ × 2.7 × 10⁻²³) / 2 = (10 × 16.26) / 2 = 81.3 g/mol.