The ratio of the density of oxygen nucleus (₈¹⁶O) and helium nucleus (₂⁴He) is

Solution

Physics sir · 4 steps

Nuclear volume grows in step with mass number, so A cancels and every nucleus has the same density.

1. Size of a nucleus. The radius of a nucleus is R = R₀ A^(1/3), with R₀ ≈ 1.2 fm. So its volume 4/3π R³ = 4/3π R₀³ A is proportional to A.
2. Mass of a nucleus. The mass is about A m, where m is the mass of one nucleon. Divide mass by volume.

   ρ = (A m)/(4/3π R₀³ A) = 3m/(4π R₀³)

3. No A left. The mass number cancels completely, so ρ is the same for every nucleus, about 2.3 × 10¹⁷ kg m⁻³. The atomic number Z never enters either.
4. So. ρ_O : ρ_(He) = 1 : 1, which is option (b).

The idea to keep. Since R ∝ A^(1/3), nuclear volume and mass both scale with A. Nuclear density is therefore the same for all nuclei, light or heavy.

Answer from the NTA final answer key. Solution by PrepWiser.