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 (^ 64_29 Cu) nucleus is greater than that of the carbon (^ 12_6 C) nucleus. Reason (R): The nucleus of mass number A has a radius proportional to A^1/3 . In the light of the above statements, choose the most appropriate answer from the options given below:

(A) is not correct but (R) is correct

(A) is correct but (R) is not correct

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

Both (A) and (R) are correct and (R) is the correct explanation of (A)

Atoms and Nuclei PYQ — JEE Main 2025 · 7 Apr · Shift 2 · Q63 with Solution

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Correct answer: C

Use the nuclear radius relation

For a nucleus of mass number $A$ , $R = R_0 A^{1/3}$ where $R_0$ is a constant.

So, the Reason (R) is correct.
Find how nuclear volume depends on $A$

Since volume of a nucleus is proportional to $R^3$ , $V \propto R^3 \propto \left(A^{1/3}\right)^3 = A$

Thus, $V \propto A$
Find how nuclear mass depends on $A$

Nuclear mass is approximately proportional to the number of nucleons: $M \propto A$
Compute nuclear density dependence

Density is $\rho = \frac{M}{V}$

Since both $M \propto A$ and $V \propto A$ , $\rho \propto \frac{A}{A} = \text{constant}$

Therefore, nuclear density is approximately the same for all nuclei, including $^{64}_{29}\text{Cu}$ and $^{12}_{6}\text{C}$ .
Check Assertion (A)

Assertion says: density of copper nucleus is greater than that of carbon nucleus.

This is false, because nuclear density is approximately constant.
Check Reason (R)

Reason says: radius of nucleus is proportional to $A^{1/3}$ .

This is true.
Choose the correct option
- Assertion (A): Not correct
- Reason (R): Correct
Hence, the correct option is: $\boxed{\text{C}}$