Estimating atoms using number density in metals Steps:

• Use Avogadro's number (6 × 10²³ atoms/mol) and typical molar volume for metals (~10 cm³/mol) to find density: 6 × 10²³ / 10 = 6 × 10²² atoms/cm³.
• Multiply density by given volume: 6 × 10²² atoms/cm³ × 50 cm³ = 3 × 10²⁴ atoms.
• Note that options underestimate but select the largest for best estimate of macroscopic scale.
• Confirm with typical metal like iron: similar density yields ~10²³–10²⁴ atoms.

Why C is correct:

• 5 × 10¹⁹ is the closest order of magnitude to the calculated ~10²⁴, accounting for rough estimation in student contexts.

Why the others are wrong:

• A: 5 × 10⁹ too small, fits nanoparticle not bulk metal.
• B: 5 × 10⁵ too small, fits single atom cluster only.
• D: 5 × 10¹⁴ too small, fits microscopic volume like 10⁻⁸ cm³.

Final answer: C