Mass numbers of two nuclei are in the ratio of 4: 3. Their nuclear densities will be in the ratio of

Solution

Physics sir · 3 steps

Write density as mass over volume and watch A cancel. Every nucleus is equally dense.

1. Size of a nucleus. The radius of a nucleus grows as R = R₀ A^(1/3), where R₀ ≈ 1.2 fm. So its volume is 4/3π R³ = 4/3π R₀³ A, which is directly proportional to A.
2. Mass of a nucleus. Each nucleon has nearly the same mass m, so the nuclear mass is about mA. Mass is also directly proportional to A.

   ρ = mA/(4/3π R₀³ A) = 3m/(4π R₀³)

3. So. The density has no A left in it, so it is the same for every nucleus. The mass ratio 4 : 3 does not matter, and the densities are in the ratio 1 : 1, option (c).

The idea to keep. Nuclear volume and nuclear mass both scale as A, so nuclear density is a constant, about 2.3 × 10¹⁷ kg m⁻³, for all nuclei.

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