Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The nuclear density of nuclides ₅¹⁰ B, ₃⁶ Li, ₂₆⁵⁶ Fe, ₁₀²⁰ Ne and ₈₃²⁰⁹ Bi can be arranged as ρ_(Bi)^N>ρ_(Fe)^N>ρ_(Ne)^N>ρ_B^N>ρ_(Li)^N
Reason R: The radius R of nucleus is related to its mass number A as R=R₀ A^(1 / 3), where R₀ is a constant.
In the light of the above statements, choose the correct answer from the options given below

Solution

Physics sir · 4 steps

Put R = R₀A^(1/3) into mass over volume and watch A cancel: every nucleus has the same density.

1. Mass and volume. A nucleus with mass number A has mass about Am, where m is the mass of one nucleon. Its volume is 4/3π R³, and with R = R₀A^(1/3) we get R³ = R₀³A.

   ρ = Am/(4/3π R₀³ A) = 3m/(4π R₀³)

2. A cancels. The density has no A left in it. So ⁶₃Li, ¹⁰₅B, ²⁰₁₀Ne, ⁵⁶₂₆Fe and ²⁰⁹₈₃Bi all have the same nuclear density, about 2.3 × 10¹⁷ kg m⁻³.
3. Check each statement. Assertion A ranks the densities in order of mass number, which is false: they are all equal. Reason R, R = R₀A^(1/3), is the standard empirical result and is true.
4. So. A is false and R is true, which is option (c).

The idea to keep. Nuclear volume grows in step with A, just as mass does, so nuclear density is the same for every nucleus. A heavier nucleus is bigger, not denser.

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