[Olympiad] Silver crystallizes in a face-centered cubic (FCC) lattice with a unit cell edge length of 408 pm. Calculate the density of Silver (in g/cm³). (Atomic mass of Ag = 107.9 g/mol)
- 5.25 g/cm³
- 10.5 g/cm³
- 12.4 g/cm³
- 21.0 g/cm³
📝 Batafsil tushuntirish
FCC unit cell contains 4 atoms.Density = (Z * M) / (Na * a³).
a = 408 pm = 4.08 × 10⁻⁸ cm.
Density = (4 * 107.9) / (6.022 × 10²³ * (4.08 × 10⁻⁸)³)
Density = 431.6 / (6.022 × 10²³ * 6.79 × 10⁻²³) = 431.6 / 40.89 ≈ 10.55 g/cm³.