Show that the density of nuclear matter is independent of the mass number, and estimate its value. (R₀ = 1.2 fm, mass of a nucleon ≈ 1.66 × 10⁻²⁷ kg)

1. 1 · State the size relation. R = R₀ ∛A, with R₀ = 1.2 fm.
2. 2 · Write the mass and volume. M = Am; V = (4/3)πR³ = (4/3)πR₀³A.
3. 3 · Divide to get the density. ρ = M/V = 3m/(4πR₀³). A cancels, so ρ is the same for all nuclei.
4. 4 · Put in the values. ρ = 4.98 × 10⁻²⁷ ÷ 2.17 × 10⁻⁴⁴ ≈ 2.3 × 10¹⁷ kg m⁻³.
5. 5 · Real life. Neutron stars have about this density.
6. 6 · Close in one line. So, nuclear matter is enormously dense, and equally dense in every nucleus.

Scoring tip: Show the A cancelling clearly in one line. That single line is what the question tests.