For two nuclei having mass numbers A₁ and A₂, assume R = R₀A¹ᐟ³. The ratio of their average nuclear densities ρ₁:ρ₂ is approximately:
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Question

For two nuclei having mass numbers A₁ and A₂, assume R = R₀A¹ᐟ³. The ratio of their average nuclear densities ρ₁:ρ₂ is approximately:

G1 Physics · Accepted Answer

Average nuclear density is ρ = M/V. For a nucleus of mass number A, M ≈ Amₙ, where mₙ denotes the average nucleon mass. Also, R = R₀A¹ᐟ³. Therefore, V = (4/3)πR³ = (4/3)πR₀³A. Hence, ρ = Amₙ / [(4/3)πR₀³A] = 3mₙ/(4πR₀³). The factor A cancels, so average nuclear density is approximately independent of mass number. Therefore, ρ₁:ρ₂ = 1:1. Correct option: C.