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 ₅¹⁰B, ₃⁶Li, ₂₆⁵⁶Fe, ₁₀²⁰Ne and ₈₃²⁰⁹Bi can be arranged as ρBiN > ρFeN > ρNeN > ρBN > ρLiN Reason R: The radius R of nucleus is related to its mass number A as R = R₀ A1/3, where R₀ is a constant. In the light of the above statements, choose the correct answer from the options given below (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true but R is NOT the correct explanation of A (c) A is false but R is true (d) A is true but R is false

Answer: (c). R is true: R = R₀ A1/3. From R, ρ = (3m)/(4π R₀³) is the same for all nuclei. So the ordering in A is wrong: A is false. So the answer is (c) A is false but R is true.

Given below are two statements: one is labelled as Assertion A and… | JEE Main 2023 (30 Jan, Shift 2)

Q14JEE Main 2023 · 30 JAN · SHIFT 2Easy

Nucleus: Composition, Size & Nuclear Force

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A: The nuclear density of nuclides ${}_{5}^{10}\text{B}, {}_{3}^{6}\text{Li}, {}_{26}^{56}\text{Fe}, {}_{10}^{20}\text{Ne}$ and ${}_{83}^{209}\text{Bi}$ can be arranged as $\rho_{\text{Bi}}^{\text{N}} > \rho_{\text{Fe}}^{\text{N}} > \rho_{\text{Ne}}^{\text{N}} > \rho_{\text{B}}^{\text{N}} > \rho_{\text{Li}}^{\text{N}}$

Reason R: The radius $R$ of nucleus is related to its mass number $A$ as $R = R_0 A^{1/3}$ , where $R_0$ is a constant.

In the light of the above statements, choose the correct answer from the options given below

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Answer: (c)

R is true: $R = R_0 A^{1/3}$ .
From R, $\rho = \frac{3m}{4\pi R_0^3}$ is the same for all nuclei.
So the ordering in A is wrong: A is false.
So the answer is (c) A is false but R is true.

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Nucleus: Composition, Size & Nuclear Force question from JEE Main 2023 (30 Jan, Shift 2)

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