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JEE Main 20257 AprilEvening Shift

Exam: JEE Main
Year: 2025
Date: 7 April
Shift: Evening Shift
Subject: Physics
Chapter: Nuclear Physics

JEE Main 2025 · 7 April · Evening Shift · Physics · Nuclear Physics

Given below are two statements: one is labelled as Assertion (A)...

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 :

Options

A $(\mathrm{A})$ is correct but $(\mathrm{R})$ is not correct
B $(\mathrm{A})$ is not correct but $(\mathrm{R})$ is correct
CBoth $(\mathrm{A})$ and $(\mathrm{R})$ are correct and $(\mathrm{R})$ is the correct explanation of (A)
DBoth (A) and (R) are correct but (R) is not the correct explanation of (A)

Correct answer

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

Step-by-step solution

\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}<br/>& \mathrm{R}=\mathrm{R}_0 \mathrm{~A}^{1 / 3} \\ & \mathrm{R} \propto \mathrm{~A}^{1 / 3}<br/>\end{aligned}

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