Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The density of the copper ( 2964 Cu) nucleus is greater than that of the carbon ( 612 C) nucleus. Reason (R): The nucleus of mass number A has a radius proportional to A1 / 3. In the light of the above statements, choose the most appropriate answer from the options given below:

(A) (\mathrm{A}) is correct but (\mathrm{R}) is not correct

(C) Both (\mathrm{A}) and (\mathrm{R}) are correct and (\mathrm{R}) is the correct explanation of (A)

(D) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

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JEE Mains · Physics · STD 12 - Nuclei

JEE Mains 2025
Easy
MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The density of the copper \(\left({ }_{29}^{64} \mathrm{Cu}\right)\) nucleus is greater than that of the carbon \(\left({ }_6^{12} \mathrm{C}\right)\) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to \(\mathrm{A}^{1 / 3}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(B) \((\mathrm{A})\) is not correct but \((\mathrm{R})\) is correct

Step-by-step Solution

Detailed explanation

\(\rho=\frac{\mathrm{M}}{\mathrm{~V}}=\frac{\mathrm{m}_{\mathrm{n}} \times \mathrm{A}}{\frac{4}{3} \pi \mathrm{R}^3}=\frac{\mathrm{m}_{\mathrm{n}} \times \mathrm{A}}{\frac{4}{3} \pi \mathrm{AR}_0^3}\)
So \(\rho\) is almost is constant
\(\begin{aligned}
& \mathrm{R}=\mathrm{R}_0 \mathrm{~A}^{1 / 3} \\
& \mathrm{R} \propto \mathrm{~A}^{1 / 3}
\end{aligned}\)

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