Calculate unit cell volume using density, atomic mass, and atoms per cell from diagram, then find cubic lattice spacing

Steps:

• Compute volume per atom: V = (3.5 × 10^{-26} kg) / (9.2 × 10^3 kg m^{-3}) = 3.8 × 10^{-30} m³/atom
• Diagram shows 10 atoms per cubic unit cell, so unit cell volume = 10 × 3.8 × 10^{-30} m³ = 3.8 × 10^{-29} m³
• Lattice parameter (shortest distance between adjacent atoms) d = (3.8 × 10^{-29})^{1/3}
• d ≈ 3.4 × 10^{-10} m

Why C is correct:

• Matches the lattice spacing formula d = (Z m / ρ)^{1/3} for Z = 10 atoms per cubic cell as indicated by the diagram

Why the others are wrong:

• A: Assumes ~1 atom per cell, yielding ~2× larger spacing
• B: Results from exponent error (e.g., 10^{-28} instead of 10^{-29} for volume)
• D: Assumes ~2 atoms per cell (e.g., BCC), yielding smaller spacing

Final answer: C