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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 B510,L36i,F2656e,N1020eandB83209i 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=R0A^(1)/(3), where R0 is a constant. In the light of the above statement, choose the correct answer from the options given below :

Both A and R are true and R is the correct explanation of A

Both A and R are true but R is NOT the correct explanation of A

Atoms & Nuclei

JEE Main level, single correct, medium

169 of 239

Question 169 of 239

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 $B510,L36i,F2656e,N1020e\text{and}B83209i$ can be arranged as ${\rho }_{Bi}^{N}\gt {\rho }_{Fe}^{N}\gt {\rho }_{Ne}^{N}\gt {\rho }_{B}^{N}\gt {\rho }_{Li}^{N}$
Reason R : The radius $R$ of nucleus is related to its mass number $A$ as $R={R}_{0}{A}^{\dfrac{1}{3}}$ , where ${R}_{0}$ is a constant.
In the light of the above statement, choose the correct answer from the options given below :

Show answer and solution

Answer: (B) A is false but R is true

Nuclear density is given by,

\rho =\dfrac{m}{\dfrac{4}{3}\pi {\left({R}_{0}\right)}^{3}}

, where

m

is mass of proton. Clearly it is independent of

A

and same for all nucleus.
Radius of the nucleus is given by,

R={R}_{0}{A}^{\dfrac{1}{3}}

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